Rules and Examples of
VIEWPOINT
APPROPRIATE FOR
Artists and Designers, etc.

In English and Latin;

Featuring a simple and quick method to
DRAW in PERSPECTIVE
All DESIGNS related to ARCHITECTURE,
IN A NEW WAY,
Completely free from the clutter of hidden lines:

by that GREAT MASTER of it,
ANDREA POZZO, Soc. Jes.

Engraved in 105 large folio plates and decorated with 200 initial letters for the explanatory texts: Printed from copper plates on the finest paper
By John Sturt.

Translated into English from the original printed in Rome in 1693 in Latin and Italian.
By Mr. John James of Greenwich.

LONDON:
PRINTED by Benj. Motte, 1707.
Sold by John Sturt in Golden Lion Court in
Aldersgate Street.

Perspective
Artists
and
Architects,

ANDREÆ PUTEI,
AND SOCIETY OF JESUS.

In which the most efficient way of designing is taught
Optically encompasses everything related to Architecture.

LONDON:
Printed after the Roman model, 1693.
From the engraving by John Sturt, and decorated under his care:
Printed by Benj. Motte, 1717.

May it please you, Your Majesty!

The condescension of the late Emperor of Germany to support this job in the original couldn't have led me to the presumption of placing the translation at Your Royal Feet; unless the art of viewpoint, which it addresses, was so closely related to the noble arts of artwork and architecture. Your Majesty has been kind enough to honor the first of these, both by expressing satisfaction with the performances and by extending Your Royal generosity to that great master of it, Signor Verrio.

And even though matters of greater importance have delayed Your Majesty’s orders to rebuild Whitehall from its ruins, Architecture has still received support during Your Majesty incredibly successful reign: Look at the recent progress made on the impressive structures of S. PAUL's, Greenwich-Hospital, and Blenheim Palace.

These seem to indicate that a time is coming when, with the blessing of peace and the positive influence of Your Majesty’s government, WHITEHALL will become a structure worthy of its great Restoration Specialist, and its name will be celebrated among Castles, just as Your Royal virtues are renowned among Royals: When Your Majesty’s subjects will strive just as much for their country's honor in the Arts of Design and Civil Architecture as they have already done in the Military Strategy and Personal Courage.

Before this Happy Season, I think this Making Perspective Art Practical may be fitting; it is one of the most useful, though until now, the most obscure and confusing, of all the linear arts. I therefore, with all respect, kindly ask for Your Majesty’s forgiveness for this address and Your gracious support for this example of English engraving; if Your Majesty graciously extends Your Royal Support, it will truly inspire the future efforts of,

Your Majesty, if it pleases you!

Your Most Committed Follower,

J. Sturt.

However, the Art of PERSPECTIVE must be recognized as highly important and absolutely necessary in the practice of Painting, Architecture, and Sculpture; especially in the first of these, where nothing commendable can be achieved without its help. Yet, the challenges and complexities faced in the initial attempts, along with the confusion and chaos of lines in its practice, have meant that the best instructions, so far translated into English, have attracted very few to pursue this study in a way that would make their work truly valuable.

It's something strange that, among so many educated people who have tackled this topic—Priests, Architects, and Painters—very few, if any, have provided proper guidance to avoid the disorder and confusion of lines that often accompany applying their rules. In most cases, the entire area for the work is limited by the lines of the plan and horizon; when the scale is small and the viewer's height isn't very elevated, it makes the project quite confusing. And when those lines overlap (which often happens), the approach becomes completely unworkable.

This author's extensive experience in the practice of Perspective has provided him with great rules to streamline the work and address the mentioned challenges. He has generously shared these insights, particularly in the Tenth and Eleventh Figures. While the first three or four plates may seem similar to methods previously used by others, anyone who carefully observes and applies the rules and examples in the following figures will recognize the significant advantage this approach offers in creating a clear, distinct Perspective-Plan and upright design. This allows for a finished piece to be derived without any unnecessary complexity. The explanations of the rules provided here are concise and informative, and the architectural designs showcased to illustrate them are impressive and grand.

The way of designing, where the perspective is drawn on multiple layers of frames stacked behind each other, and the scenes of theaters where the grooves are angled away from the center line, is also explained here: And using our Author’s method, Horizontal Perspective, or that of ceilings, becomes easier than the Vertical, or that against a straight wall. Overall, it seems that everything needed to make a work like this complete is included; except for designs that are either circular or filled with many columns: For these, the Author has promised in the Sixty-fifth Figure that he has provided a more suitable rule in a SECOND Volume; which may also potentially be made English in time, if this section receives support.

What? the Author initially planned to include in that Second Volume, he later added to the Ninety-third and subsequent Figures of this Book: In the last of which, special attention should be paid to his Conclusion; That if Painters want to avoid serious mistakes, they need to follow the Rules of Perspective just as carefully when depicting Figures of Men and Animals as they do when painting Columns, Cornices, or other Elements of Architecture.

So no one should be discouraged in their initial attempts because of the brevity or silence of our author; (who, writing in a country where the principles of this art are more widely known than here, didn’t need to elaborate on certain points as much as might be considered necessary for beginners) we will try to explain as clearly as we can a couple of points that are most likely to be misunderstood or pose a challenge at the beginning; and then we’ll add some advice for those who will attempt to put these rules into practice.

The Author, in his explanations of the first Plate, has provided some insight into what he wants his readers to grasp about Designing in Perspective; and since having a clear understanding of this concept is very useful for making the work easier, we thought it appropriate to describe a bit more specifically what the Art of Perspective means: however, we will currently focus only on what is received on a flat and even surface, whether vertical or horizontal; this being much more commonly used, and when properly understood, makes the challenges of circular or irregular surfaces easier to tackle.

PERSPECTIVE is the art of representing, on a flat surface, like a wall, ceiling, canvas, paper, or something similar, the appearances of objects as seen from a specific viewpoint. Although in longer works, two, three, or more viewpoints are sometimes used, it’s more accurate to say those are several combined views rather than one piece of perspective. For more on this, see the author's opinion at the end of this treatise.

In Perspective, the Eye of the Beholder is regarded as a point from which rays are thought to radiate to every angle of the object. The wall or canvas to be painted (which we will refer to as the Section) is imagined to be positioned at right angles to the axis of those rays and, by cutting through them, to capture the appearance of the object in greater or lesser proportion, depending on how far the Section is from the Point of Sight. Our Author’s rule is that the distance from the eye should equal the greatest dimension of the object, whether in length or height: for example, to view a building that is a hundred feet long and fifty feet high, the distance should be a hundred feet; to view a tower that is sixty feet wide and a hundred and fifty feet tall, the distance should be a hundred and fifty feet. This distance should not be strictly understood as the space between the eye and the object, but rather the space between that and the Section, which our Author calls the Line of the Plan or Ground-line; for it is often necessary for the Section to be placed some distance in front of the object due to projections of cornices and other parts of the work that extend outward, as illustrated in the Eighth Figure.

The Place of the Eye, in relation to its Height above the Ground, should be positioned in a way that feels most natural and appealing to the Object. In Architecture, the Bases and lower Parts of a Building shouldn’t be placed above the Eye level, and their Cornices and Entablatures have a negative effect when below it. General Perspectives actually require the View to be taken from a Bird’s Eye perspective; on other occasions, the Place of the Eye can change. However, the best and most common Rule is to keep it at a height of no more than five or six Feet above the Ground. The Height of the Eye above the Ground, through which a Line is drawn, called the horizontal Line, is set according to the same Scale of Proportion that the Design has to the actual Work; and the Point of Sight is placed in such a way that it makes the Object most pleasant. From the Point of Sight, either on one side or both sides of the horizontal Line, you must set, using the same Scale, the Distance from the Section. With these Points of Sight and Distance, along with the Measurements of the Parts brought on the Lines of the Plan and Elevation of the Section, by the same Scale; all the Examples in this Volume are rendered into Perspective, as is clear upon examining the Figures.

What we would suggest, in terms of advice, is,

I. Make sure you carefully understand what the Author means by Breadth, Length, and Height in his Explanation of the Fifth Plate before you start working with any Figure; otherwise, you'll definitely get it wrong, especially with the Third Figure.

II. That the Rules of the Tenth and Eleventh Figures be especially observed to avoid confusion in the plans and uprights.

III. That regarding the layout of the perspective plans and uprights, in relation to the finished pieces in the twelfth and many subsequent figures, you will notice how quickly those pieces can be drawn using just your drawing square, without needing compasses; viz. the vertical lines from the perspective plan and the horizontal lines from the perspective upright, or section.

IV. To get used to working on projects that have a lot of lines, create separate perspective plans and elevations for each part to avoid any confusion. This way, you can have one plan and elevation for the building's basement. Once that’s done, remove them and add the ones for the main part of the house. When that’s complete, do the same for the attic, etc. Always make sure to place the plan below and the elevation on one side of your drawing so that your drawing square can easily manage both. This will greatly speed up your work.

V. That the Author’s advice to follow the figures in order should be strictly adhered to in practice; this will greatly help make the whole process easier and more enjoyable.

This is the summary of what we thought was most important to inform you about; and we only ask one more thing: If any mistakes slipped through the printing that we hope are few or none, please correct and forgive them.

To accomplish harmony and symmetry in the visual representation of buildings, one must draw from architecture. Therefore, it's essential to practice your skills in this drawing and understanding for a while until you learn to form the outline of each elevation and derive the section of its full height, as can be seen throughout the work, especially in figures sixty-eight and seventy. Indeed, from the outline and the section derives the appropriate depth of individual elements in the visual representations.

I'll share a plan of great importance; you need to understand the second figure well before you move on to the third, and I’d like the same to be said for the others; we’ve arranged them in a way that what comes first is necessary to grasp what follows. If there are any explanations that you don’t understand at first, be sure to take a close look at the diagram multiple times; and conversely, if anything is missing in the diagrams, you can fill in those gaps with the explanations. I hope, with your kindness, you'll easily forgive any mistakes you notice.

The perspective of structures discussed here cannot have any grace or proportion without the assistance of architecture. Therefore, it’s essential that you spend some time practicing drawing and studying that art until you can easily outline the plan of any upright and then project the section or profile, as demonstrated throughout this work, particularly in Figures Sixty-eight and Seventy. The appropriate depth of each part of the perspective is determined by its plan and profile.

I want to add one more important thing: make sure you fully understand the Second Figure before moving on to the Third and so on. The concepts are arranged in such a way that knowing the previous Figure is always necessary for understanding the next one. If you come across something that seems difficult in the description at first, taking a close look at the Figure may help you out. Conversely, if you don’t find everything you’re looking for in the Figure, feel free to check the explanation. I hope you’ll kindly overlook and forgive any errors you find in this work.

Ars Perspectiva, the eye, although the sharpest of our external senses, deceives us with wonderful pleasure; it is also essential for those who, when painting, need to properly assign the position and deformation of individual figures, and to intensify or lessen colors & shadows as needed. However, they gradually reach this understanding without realizing it, those who, not satisfied with just the study of geometry, have become accustomed to precisely deforming every Order of Architecture. Nevertheless, among the many who have approached work of this kind with great enthusiasm, we count only a few who have not lost heart from the very beginning due to the lack of teachers and books that clearly and systematically teach optical projections, from the principles of this art to its complete perfection. However, since I have come to realize, through many years of extensive practice, that I have acquired considerable skill in this discipline, I believe I will satisfy the desires of the students and consult their progress if I publish the most straightforward methods for completing the optical delineations of the individual Orders of Architecture, using a common rule from which we have removed all the pitfalls of hidden lines. Then, if time & strength granted by Divine Goodness allows me to write another Work, I will complete any projections following the rule I currently use, which is much easier & more universal than the common & widely known rule, although this is the foundation of another. Therefore, Reader, take up your task with diligence and a steady mind; and resolve to lead all the lines of your operations to the true point of sight, for the glory of God Almighty. Thus, with the most honorable wishes, as I hope for you and promise, you will be successful.

The Art of PERSPECTIVE wonderfully tricks the Eye, the most delicate of all our senses; and it’s essential for anyone who wants to give proper space and proportion to their figures in Painting, as well as the right strength to the lights and shadows in the artwork. This could be subtly achieved if people, not satisfied with just studying Drawing, would train themselves to accurately depict the various Orders of Architecture. However, among many who have passionately taken on this task, very few have succeeded without feeling disheartened due to a lack of teachers and books that clearly and systematically explain the Rules of Perspective Projections, from the basic principles of the Art to its full mastery. Therefore, believing that through long and consistent practice in such works, I have developed a method to make this easier, I thought it might benefit and satisfy those interested to publish a straightforward approach to designing the various Orders of Architecture in Perspective, using a simple and easy rule, free from complicated lines. If God grants me Life and Health to create another Book, I will demonstrate the method for creating Perspective works using the rule I currently utilize, which is simpler and more general than the traditional method, although this serves as its foundation. So, dear Reader, my advice is to joyfully begin your work with a determination to draw all its lines towards that true point, the Glory of GOD; and I dare to predict and promise you success in such an honorable endeavor.

At the request of the engraver, we have reviewed this volume of Viewpoint; and believe it is a work that deserves support, and is very suitable for instruction in that art.

Explication of the Lines of the Plane & Horizon, as well as Points of View & Distance.

To understand the principles of perspective more easily, I’ll present to you a depiction of a temple, in which, among other things, something related to perspective should be illustrated. The geometric outline of this temple is A, the geometric height in length is B, and the width is C. At A is the position of a person observing the line DE, to which the wall to be painted is adjacent. At B, the same person from that same distance looks at the line FG, which reflects the height of the wall. In figure C, we assume the person stands directly opposite the wall: the same proportions measured are transferred from the actual wall into figure C, which represents it on a smaller scale.

The first line Hi is called the ground line or plane, from which it begins and on which the building rests. The second line NON, which is parallel to the first, is called the horizontal line, where point O (the eye point) and point N (the point of distance) are placed. There are two points of distance set from us, so you can use whichever one you prefer; for optical representations, one point of distance is sufficient: no optical drawing can be made without first designating two parallels, one for the plane or ground and the other for the horizontal, marking in the horizontal line the eye point or optic point, and the point of distance. Furthermore, the same thing should be represented in three Schemes, so that you see the place from which the figure C should be viewed as point N on line NO, which we should conceive as normally fixed at O; and the distance between O & N should be the same as the distance between A & DE, and between B & GF.

In images that take up a lot of space, the focal point is usually placed at the center of a horizontal line. When the height of the image is greater than its width, the distance NO will not be equal to the height. If the width of the image is greater than the height, the distance NO will not be equal to the width; this way, one can grasp the entire space of the image in a single glance. Furthermore, although the same distance may be applied differently in the footprint A and in the elevations B & C, the visual sections of the footprint A and elevation B completely align with the visual sections of figure C.

If we want the audience to see the wall depicted at A & B as being distanced from the lines DE & GF, the distance should equal the length of square P, which has a height of Q; from points A & B, draw lines to the square's endpoints, noting the intersections of these lines with the wall DE & GF, which is also referred to as a curtain, glass, section, web, or board. You will find that lines RS and Television are equal, as well as lines XZ & YK; and so forth.

Explanation of the Lines of the Plan and Horizon, and of the Points of the Eye and Distance.

To help you better understand the Principles of Perspective, here’s a view of a Temple. On the inner Wall of this Temple, among other things, something will be painted in Perspective. The geometric layout of this Church is labeled A, the geometric elevation (or height) is B, and the width is C. In A, there's the spot from where a person sees the line DE, which represents the layout of the wall that will be painted. In B, the same person, from that same distance, looks at the line FG, which shows the elevation of the wall. In Fig. C, the person is positioned directly in front of that wall; this figure reflects, in a smaller size, the exact proportions and measurements taken from the actual wall.

The first line, therefore, HI, is called the Ground Line, or the Line of the Plan, where the building starts and on which it stands. The second line, NON, which runs parallel to the first, is called the Horizontal Line, where point O, the Point of the Eye, and point N, the Point of Distance, are located. Two Points of Distance are marked here so you can use whichever you prefer; just one side is enough for shortening figures in perspective. No optical drawing or perspective can be created without first establishing two parallels: one for the Plan, or Ground Line, and the other for the Horizon. In the Horizon line, mark the Point of Eye, or Sight, and the Point of Distance. It was also considered helpful to present the same thing in three schemes or designs, to show you that the viewpoint for figure C is point N, one of the right lines NO, which should be imagined as fixed at right angles to O; the distance ON being the same as that between A and DE in the Plan, or between B and GF in the Upright.

In pictures that take up a lot of space, the viewpoint should be positioned in the center of the horizontal line. If the height of the picture is greater than the width, the distance NO must be equal to the height. If the width of the picture exceeds the height, the distance NO should match the width. This way, the overall picture can be better understood and appreciated at a glance. And although the same distance may seem to be used differently in Plan A and Elevation B compared to C, the sections of the visual rays with the wall in Plan A and Elevation B correspond perfectly with the sections in Figure C.

Now, if we want the viewer at points A and B to see the farthest part of the work appear to pull away from the lines DE and GF just like square P does, whose height is Q, then we should draw visual lines from points A and B to the farthest points of squares P and Q. We should also note the sections they create with walls DE and GF, which some call the Veil, Transparent Medium, Section, Cloth, or Table. You'll find that RS is equal to TV and XZ is equal to YK, and the same goes for the rest.

Method for visually outlining a square.

Before describing the optical square A, which we imagine is drawn on a separate piece of paper, you need to draw two parallel lines; one is the horizontal line and the other is the vertical line, as we have already explained. Mark the point of the eye O on the horizontal line, and the point of distance E. Then, translate the width and height of square A onto the plan, so that line CB is equal to the width, and DC is equal to the height. From points B and C, draw visual lines BO and CO to the eye point; from point D, draw a straight line DE to the point of distance. Finally, where the visual line CO intersects the straight line DE, draw Girlfriend parallel to CB; you now have the square optically contracted.

Gathering of time and labor aspects, especially in diagrams that are filled with lines, if you fold the paper in the middle and use it to translate the width and length of the square into a flat line.

How to Draw a Square in Perspective.

Before the Square A, which needs to be drawn on a separate piece of paper, can be set up in perspective, two parallel lines must be drawn: one for the Plan and the other for the Horizon, as mentioned earlier; marking the Point of Sight O and the Point of Distance E on the Horizontal Line. Next, when the Length and Width of the Square A are transferred to the Line of the Plan, ensuring that the Line CB matches the Width and DC matches the Length, draw the visual lines BO and CO from points B and C to the Point of Sight O, and the straight line DE from Point D to the Point of Distance. Finally, where the Line DE intersects Visual CO, make GF parallel to CB, and you've got the Square optically contracted or shortened in perspective.

To save time and effort, especially with figures that have a lot of lines, fold your paper in half and use it to transfer the width and length of the square onto the line of the plan.

Optical outline of a rectangle, on the longer side.

Width BC of rectangle A should be set on a flat line, using a compass or folded paper; then, from points B and C, create lines to O, the point of perspective. Next, using another folded piece of paper, mark the length CD of the rectangle; then draw line DE to the distance point, and line FG parallel to BC, which will complete the optical representation of the rectangle.

This figure shows the cross-shaped complexity of the paper, which can be used to draw rectangles, whether their width is greater than their length, or vice versa; or whether the width and length are equal.

The Outline of a Rectangle in 3D.

Let the width BC of Square A be positioned along the line of the plan, using a compass or a folded piece of paper, and from points B and C, draw the lines to the point of sight O. Then, fold your paper in half, and mark CD as the length of the square, drawing line DE to the point of distance, and line FG parallel to BC, which will complete the optical depiction of the rectangular square.

The other figure shows how to fold the paper crosswise, which is useful for drawing squares that are wider than they are long, or vice versa, or where the length and width are the same.

Double square optical description.

You’ll begin to enjoy the summary of the folded paper. By moving it closer to the flat lines, you'll easily be able to mark points 1, 2, 3, 4, 5, 6, of the visual lines, which will lead to point O of perspective. Then, by folding the paper back in crosswise toward P, you will mark these points; 7, coinciding with point 6, unless the square is separated from the line of the flat; 8, 9, 10. Then, drawing straight lines from 8, 9, 10, to point E, where they intersect with visual points 6, 7, O will become parallel, and the outline will be complete.

In the middle of square B, another square can easily be drawn by connecting the diagonals or diameters from corner to corner, as shown in the figure.

The Optical Delineation of a double Square.

Here you’ll see the benefit of your folded paper; by applying it to the line of the plan, you can easily mark points 1, 2, 3, 4, 5, 6 of the visual lines that need to be drawn to the point of sight O. Then, folding the paper crosswise, as shown in P, you mark points 7, 8, 9, 10, positioning point 7 over point 6, unless you want the square to be moved inside the line of the plan. Next, from points 8, 9, and 10, draw lines to the point of distance E; where they cross the line 6, 7, O, draw parallels to the line of the plan, and your work is finished.

Within Square B, you can easily draw another square using the diagonals, as shown in the figure.

Footprints of squares, with elevations.

About the points we've already made about the optical contraction of squares, it's important to note that the distance from the first square to the flat plane line BA is contracted optically; because the line BD has a distance from the visual line AO that is equal to BA. Similarly, the second square is distanced from the flat plane line EA, and so on.

Velim notes that in all these squares, the lines of length are parts of the visuals, while the lines of width are parallel to the plane line, and in the first square, it's drawn from the points where the lines BD and CD, extending toward the point of distance, intersect the visual line AO.

Under each corner of the Squares, we’ve outlined completely similar ones, through which, with minimal effort, three bases can be created by raising two equal verticals as desired; and then drawing two lines to the point of sight O, along with the others, as shown in the figure. It should be noted that the geometric height of anything is derived from the normal lines to the plane line; just as the geometric width and length are derived from that same plane line.

Three additional lower bases are formed without hidden lines from the trace and from the elevation of lengths optically distorted, using only the heights and widths of the angles. By height, we mean the distance of any angle from the plane line; by width, we mean the distance of an angle from a line normal to the plane line; provided these normals have the same position relative to the bases and to the traces and elevations. Just as through the intersection of height FG and width Hey, one angle is found on one base using two compasses; so the others are found both on it and on the remaining ones.

Blueprints of Squares, along with their Heights.

Additionally to what has already been said about the shortening of squares in perspective, it's helpful to note that the base of the first square is positioned within the line of the plan by the same amount as the space BA is visually contracted; because the line BD has the distance BA from the visual AO. Similarly, the second square is set apart from the line of the plan by the space EA, and this pattern continues for the others.

I want you to notice in all these Squares that by the Length, I always mean part of the visual Lines, and by the Breadth, those that are parallel to the Ground-line; which in the first Square are drawn from the Points where the Lines BD and CD, pointing towards the Point of Distance, intersect the Visual AO.

Under the plans for these squares, there are three others similar to them, which can easily be turned into three bases by erecting, as desired, the first two perpendiculars of equal height, and then drawing two sight lines to the point of sight O, which also define the rest, as shown in the figure. Also, note that the geometric height of everything should be measured straight up from the ground line, or the plan line, just as the geometric length and width are also placed on that same line.

The three other bases below are created without using hidden lines, relying solely on the heights and widths of the angles taken from the perspective plan and upright. By height, I mean the distance of each angle or corner from the ground line; by width, I mean the distance of an angle or corner from any line that is perpendicular to the ground line, as long as these lines maintain the same position relative to the bases as they do in the perspective plan and upright. Just as the height FG and the width HI determine the corner of the first base using two compasses, the corners of the other bases are found in the same way.

Modus opticæ delineationis, absque lineis occultis.

In this sixth figure, I've placed the geometric point B separately from the geometric elevation A, as we will do next. The point B is optically contracted to E as NMRS; the contracted elevation of the length of the point is FTSN. Assuming that the heights FN, 1, 5, and 2, 6 are equal; the widths NM, 1, 2, and 5, 6 are equal; and the lines NM and 5, 6 are on line X of the plane; the lines FN and 1, 5 are perpendicular to V: angles 3 and 4 at base C have the same elevation or distance from the line X of the plane as angle T: angles 1 and 2 have the same elevation as angle F: angles 3 and 7 have the same width or distance from the perpendicular V as angle R: angles 2 and 6 have the same width as angle M.

How to design in Perspective without hidden Lines.

In this sixth figure, I’ve designed the Geometrical Plan B separately from the Geometrical Elevation A, and I will continue to do so from now on. The Plan B, when viewed in perspective, in E, is NMRS; the Elevation of its Length in Perspective is FTSN. Assuming the Heights FN, 1,5, 2,6 are equal, and the Widths NM, 1,2, 5,6 are equal; the Lines NM, 5,6, are along the Line of the Plan X; and the Lines FN, 1,5, are in the Vertical V: the Angles 3 and 4 of the Base C have the same Elevation or Distance from the Line of the Plan X as the Angle T does: the Angles 1 and 2 share the same Elevation as the Angle F: the Angles 3 and 7 have the same Width or Distance from the Vertical V as the Angle R: the Angles 2 and 6 have the same Width as the Angle M.

Aliud exemplum vestigii geometrici, cum elevatione longitudinis.

If the base is to be outlined and divided into four parts, create a footprint A with its divisions for length ED and width CD. This same width division will apply to EF for elevation B, reaching up to X. Additionally, for the optical contraction of the footprint, folded paper will be used for width & length, transferring the width and length of the footprint into the plane line. Then, the optical deformation of the elevation will occur seamlessly, as clearly shown in the figure. However, how the clear base is obtained from the footprint & elevation of reduced optical length without hidden lines is evident from the previous explanation. I would like you to diligently focus on practicing this method through consistent use of the compass; all ease of optical drawings depends on it.

Another Example of a Geometric Plan and Elevation, shown in Perspective.

To draw a pedestal or base in perspective, divided into four parts, start with Plan A, featuring its length divisions ED and width divisions CD; and the same width divisions EF in Elevation B, extended to X. Next, create the perspective plan by transferring the width and length onto the ground line using your paper folded crosswise. From this plan, the perspective upright is made quite easily, as shown in the figure. It's clear how the base below is formed from the perspective plan and upright without hidden lines, based on what has been discussed earlier. I encourage you to practice this method with a compass diligently, as the speed of perspective drawings largely relies on it.

Optical projection of the stylobate.

If you want to outline the base, with projections at the top & bottom, start with geometric elevation A, drawing the necessary hidden lines to it, then a vertical line L, and downwards to the geometric marker B, whose distances will transfer into space G. If the length measurements differ by space C from the width measurements, the distorted outline will appear to be offset from line K by the same distance C. In constructing optical elevation D, the visuals from the points of line L will provide width lines; the height lines will come from the contracted outline lines, as depicted in the figure. When forming the clear base EF, the angle point H will be given by the width intersection from line L to M, and height from line K to I. The intersection of both the height and width from L to O will provide angle N. Finally, you'll take the height of angle P from K to Q; the width from L to R.

The Projection of a Pedestal in Perspective.

If you want to draw a pedestal with the design of its top and bottom, start with the geometric elevation A by drawing the necessary hidden lines, both horizontally to the vertical line L and downward to create the geometric plan B. Transfer the measurements for length to the spacing C from those for width, and this will place the perspective plan within the ground line K as far back as the space C. In constructing the perspective elevation D, the lines of width come from the points on line L, while the lines of height are taken from the perspective plan lines, as shown in the figure. When outlining the finished pedestal EF, the intersection of the width from L to M with the height from K to I determines the exact position of the corner H. The intersection of that height with the width LO gives you the angle N. Finally, the angle P is found where the height KQ intersects with the width LR.

Optical Outline of the Architecture of Jacopo Barozzi; & first, about the Stylobate of the Etruscan Order.

Viewpoint shines most clearly in Architecture. Therefore, I present to you the Architecture of Jacobo Barozzi, known in his homeland as Il Vignola, perhaps more familiar to others; it contains the geometric elevation of the five Orders known as Etruscan, Doric, Ionic, Corinthian, and Roman or Composite, separately illustrating the parts of each Order in larger figures. We will add our trace to the geometric elevation; from the trace and the optically distorted elevation, we will derive the appearances of solids according to the established rule. For example, if you want to draw the square stylobate and the column of the Etruscan Order, besides the geometric elevation A, you must draw the geometric trace B; from both, the neatly contracted stylobate D is formed, with the anta and column existing on the side, taking heights from the plane line and widths from the perpendicular line to that plane. In another drawing, we placed the column facing the opposite way so that you can get accustomed to drawing them in every possible manner.

To avoid confusion with the lines, it will help if the figures are much larger: towards this goal, a scale of measures is added to each page. This refers to equal parts into which are divided the lines of width & height of geometric elevations; and the lines of width & length of geometric traces. If the measures are small, each one is divided into twelve parts; and depending on how large they are, they are further divided into thirty, sixty, or one hundred twenty parts. They split the Etruscan and Doric modules into twelve parts, while the others were divided into eighteen.

The Architecture of Vignola in Perspective; and first, of his Pedestal of the Tuscan Order.

Point of view is never more graceful than in architecture. That's why I'm sharing the perspective of James Barozzi from his country, commonly known as Vignola; which might be more widely used than any other. It outlines the geometric upright of each of the five orders, namely the Tuscan, Doric, , Corinthian, and the Roman or Composite; along with a separate drawing of the components of each order in larger figures. To this geometric elevation, we will add the plan, and from both of these, we'll create a perspective to illustrate the appearances of solids, following the previously established rule. For example, if you want to draw the square Tuscan pedestal and its pilaster, you should create the geometric plan B from the geometric elevation A. Then, from both of these reduced into perspective, draw the finished pedestal D, along with its pilaster on the side, by measuring the heights from the ground line and the widths from a line perpendicular to it. On the other side, we have placed the pilaster at the back so you can practice drawing them in any arrangement.

To avoid confusion with the lines, I recommend making the figures as much larger than ours as you can; for this reason, a scale of modules is attached to each figure. By this term, we mean the equal parts into which the lines of the width and height of the geometric uprights, and of the width and length of the geometric plans, are divided. If the modules are small, they are divided into twelve parts; and as they get larger, they are divided into thirty, sixty, or one hundred and twenty parts. I have divided the Tuscan cuisine and Dorick module into twelve parts, and the modules of the other orders into eighteen.

Optics of the distortion of the Doric stylobate; where it discusses how to avoid confusion in outlining the footprints.

Geometric height B of the Doric stylobate contains the same symmetry of parts found in Barozzi's work; from this, a geometric trace A is derived through hidden lines that descend from the terminal points of the main projections. The distances of these projections must be transferred to the line of elevation, marking the points necessary to shape the elevation of the stylobate's length.

If the proximity of the plane to the horizontal line causes the trace to become unclear, other planes can be established at a suitable distance below the plane, parallel to it, with their own traces. However, the benefit of a greater distance compared to a lesser one is shown by the trace E being clearer than the trace D. Each of these traces is created by marking the width and length measurements of trace A on the line of any plane and drawing lines to the same points of vision and distance.

We described the polished stylobate from section G, both out of necessity and to show that, for the distance FO, the distance Understood. Please provide the text to modernize. must be completely equal.

A Doric Pedestal in Perspective; with the Way to avoid Confusion in creating the Plans.

The Geometrical Elevation B has the same components and proportions as the Doric pedestal by Vignola; and the Geometrical Plan A is created by dropping hidden lines from the main projections of the upright structure. Hidden lines should also be extended to the perpendicular F, from the different components needed to raise the length of the pedestal in perspective.

When the ground line gets too close to the horizon, making the plan confusing, draw additional ground lines below, parallel to the first one, at a comfortable distance. Add the perspective plans as well. It’s clear that moving the ground line is beneficial, as shown by Plan E, which is much clearer than Plan D. Each plan is created by marking the width and length measurements of Plan A on its own ground line and drawing lines to the same points of sight and distance that were designated initially.

We have placed the finished pedestal on Side G, partly because of a lack of space, and partly to show that the point of distance G is used there, with GO being equal to FO.

Stylobatæ Ionici deformatio; where confusion in elevations should be avoided.

In the previous figure and again in this one, we show what needs to be done when the lines AA bend too much, which leads to confusion; especially in parallel lines that show widths. A similar challenge can arise in the elevation of lengths that appear distorted; because of their excessive angle, it's difficult to clearly see and define the heights of each projection. To address these issues, instead of using elevation B, we will use elevation C, which is clearer, along with two intermediate elevations D & E, due to its greater distance from the viewpoint.

In outlining the clear base, measurements will be taken from the last mark, placing one point of the compass on a vertical line closest to the letter O: heights will be taken from the height of C, placing one point of the compass on a flat line, as shown previously.

The Ionick Pedestal in Perspective; with the Way to avoid Confusion, in Elevations.

As shown in the previous Figure, this one also illustrates what needs to be done, where the Plans AA are positioned at an angle that creates confusion, especially in the Parallel lines that indicate the Widths. A similar issue often arises when elevating the Lengths in Perspective; when they are too close to the Point of Sight, the edges of the various Mouldings can't be clearly detailed. To avoid this, instead of using B, you can use the Elevation C, which is not only clearer than the former but also better than either of the two intermediate ones D or E, as it is further away from the Point of Sight.

In designing the completed pedestal, the widths are taken from the lowest plan by setting one point of the compass on the vertical line OL; the heights are taken from the elevation C by placing one point of the compass on the baseline, as shown earlier.

Deformation of the Corinthian stylobate, with two columns.

Ornatus adds pilasters to the stylobate of Corinth, which are usually placed behind the columns. To make the pilasters stand out more clearly, one column has been omitted, and we haven't yet explained how to shape it. The measurements are all taken from Barozzi, as demonstrated by the schematic, where the geometric elevation of the stylobate is A; its geometric footprint is B: the pilasters are CC. The visually contracted footprint is D, and the visually contracted elevation of the stylobate is E, from which the polished stylobate with its pilasters will be derived using the usual method.

The Corinthian style Pedestal, with its Columns, in Perspective.

For the sake of decoration, we’ve added the Pilasters to this Corinthian Pedestal, which are typically placed behind Columns. To make them clearer, we've omitted the Column since we haven't yet shown how to represent it in Perspective. The diagram indicates that the measurements are based on Vignola; where the Geometrical Upright of the Pedestal is A, the Geometrical Plan of the same is B, and that of the Pilasters is CC. The Plan in Perspective is D, and the Elevation in Perspective is E; from which the finished Pedestal and Pilasters are drawn using the standard method.

Stylobate projection, Composite order.

Since the page could not hold the entire base of such a large structure, it was necessary to imagine that part of it was removed from the trunk; and the upper part of the base is supported by the lower part, not directly, but through four beams; and these were supplemented by suspended ropes from a pulley. The geometric elevation of the base is B; the geometric footprint is A. From these, the optical outline of the footprint C and elevation D is derived. And afterward, the precise base E is formed, taking widths from the footprint C and heights from the elevation D.

The Projection of a Pedestal, of the Composite Order, in Perspective.

Desiring space on this page to fully describe such a large pedestal, we imagine it has lost part of its trunk, and the top part is placed on the bottom; not directly, but on four crosspieces that sit in between; and we assume ropes and a pulley were used to lift it into position. The geometric elevation of the pedestal is B; its layout is A; from which we derive their projections in perspective D and C. Then, by taking the widths from layout C and the height from elevation D, you can complete the finished pedestal E.

Circle deformation.

That the stylobate may support columns with their bases and capitals, the method that must be followed in the optical projection of circles must be taught, both for single ones, as well as for double or multiple around the same center.

The geometric trace A consists of a square divided into four equal parts, with a circle inscribed within it, along with added diagonals; and where these intersect the circle, parallel lines to each side of the square are formed. Next, the square and all its divisions are optically diminished; and then through the four points where three straight lines intersect, and through the four endpoints of the other two diameters of the circle, a beautiful circumference of circle B will be drawn. If we want to add another circle, a different square will be inscribed into the geometric trace C; thus, an optical delineation of the double circle D will be obtained. The figures E & F demonstrate how a third can be described between the two, through eight sections of the squares. In short, circles are described through squares using sections visualized parallel to the plane line; and there is no point in the squares & circles A, C, E that cannot be found as a corresponding point in the squares & circles B, D, F through those sections. Nonetheless, when you need multiple circles, I advise you not to use multiple squares, as it will bring you more confusion than help.

Circles from a Perspective.

That to position Columns with their Bases and Capitals on Pedestals, you need to understand how to place Circles in Perspective; whether it's a single circle, double, or multiple concentric ones.

The Geometrical Plan A consists of a square with an inscribed circle, whose diameters divide it into four equal parts. Drawing the diagonals where they intersect the circle, continue lines parallel to each side of the square. The square, with all its divisions, is put in perspective; using the four extreme points of the diameters and those at the intersection of the diagonals, you can neatly trace the circumference B by hand. If you want to add another circle, you need to inscribe another square, as in Plan C; from this, you can find the double circle D in perspective. Between these two circles, you can describe a third circle using the eight intersections of the squares, as shown in Figures E and F. In short, all circles are created with the help of squares, tracing them through the intersections of the visual lines with those parallel to the ground line. There’s no point in either the squares or circles A, C, E, whose corresponding point can’t be easily found with such sections in the respective squares and circles B, D, F. However, when your work involves many circles, I recommend using as few squares as possible to avoid confusion.

Optical diagram of the column.

Descriptions a uniform cylindrical frustum I will have a height A, and a geometric footprint B, at least for half of it. From this optically distorted view, as you see in C, parallel lines must be drawn for both the width to the visual D and the height to the visual E; from which optically contracted circles F & L will be described, taking widths from the footprint C and heights from the perpendicular M; and using this method, the circles F & L are created without the aid of squares. Finally, perpendiculars G & H must be drawn, which will touch the circles F & L at the points defining maximum width.

There is no point on the line C for which a corresponding location cannot be found in circle F based on the latitude and elevation lines. For example, the location of point 7 is point 6. We determine this location through three lines, CD, DE, E7.

When outlining two cylindrical pieces, with the top and bottom ends, you must keep the same rule.

A Column from a Modern Viewpoint.

To explain part of the shaft of a pillar without projections, create the elevation A and the geometric plan B, at least up to the middle. From this, bring it into perspective as shown in C. You need to draw parallels for both width to the visual D and height to the visual E. From this, the circles in perspective F and L can be drawn, using the widths from the plan C and the heights from the perpendicular M. By following this method, circles F and L are created without the use of squares. Finally, draw the perpendiculars G and H at the points that mark the widest part of circles F and L.

There isn't a point in the Plan C that can't be found in the Circle F using the Lines of Breadth and Elevation. For example, the position of Point 6 is 7, which is determined by the three Lines CD, DE, E7.

In designing the two parts of a pillar, with the shaping of the fillet at the top and bottom, you must follow the exact same rule.

Etruscan optical projection basis.

From the geometric elevation, we derive the trace B. However, when deformed into C & D, the widths of the column, square, and triple base of the torus are obtained from the circles of the trace C; similarly, the widths of the square and the final base of the torus are derived from the trace D. From the greatest widths of the circles of the trace C, we erect perpendiculars to the parts corresponding to these widths in the base; this will help you identify which points represent the greatest width in those parts. These points (which are M & N on the largest circle of the trace C) will be found by touching the circumference of each circle with a ruler parallel to the perpendicular line E, as long as the figure is drawn accurately. The ruler will touch each of the three bases of the torus at points of maximum width on either side.

It will take more effort to find the heights of the four bases. However, if you carefully examine the distortion of elevation F and the other two (which were created, marked on the perpendicular line E with divisions taken from the geometric elevation A), it will be clear that there is no point in the tracing circles C for which a corresponding point can be found on the torus and its base square, as shown by the hidden lines that start from M and N. Each of these from the tracing C reaches the visual line and continues with the line of height from the visual to the elevation F, and with another line of latitude from the elevation F to the base. Furthermore, it is clear from the figure that the upper surface of the square is lowered from view by the column, and something from the back part of the torus that would otherwise be seen is hidden from the square. Therefore, the torus, bending back from points of maximum latitude, must be drawn to the extent it encounters the square covering it. It would be best for each part to be drawn so precisely, as if they were transparent; so that the parts not visible to the eyes perfectly integrate with the parts that are visible.

After you've finished the outline, if you look at your figure from the right angle at the proper distance, you'll easily spot any mistakes and fix them right away. Pay special attention to shaping and refining the rounded part, which has two curves: one that surrounds the column and the other that is smooth without corners, as shown in the geometric elevation in I.

The Tuscan Base in Perspective.

From the Geometrical Elevation A, we draw Plan B; which, when put into Perspective, as shown in C and D, allows us to determine the Widths of the Column, the List, and the Torus of the three Bases from the Circles in Plan C. Similarly, Plan D gives us the Width of the List and the Torus of the last Base. From the widest part of the Circles in Plan C, we have set up Perpendiculars to the corresponding Parts in the Base, so you can see where the Points land that define the widest part of those Sections. These Points (which in the largest Circle of Plan C are M and N) are found by drawing a Line parallel to the Perpendicular E that touches the Edge of the Circumference; if the Figure were accurate, that Line would touch every Torus of the three Bases at the farthest Points of their Width.

The heights of the four bases are somewhat more challenging to determine. However, if you carefully examine Elevation F, along with the other two, G and H (which are created by transferring the divisions of Elevation A onto Perpendicular E), it will clearly show that there is no point in the circles of Plan C that doesn't have a corresponding point in the Torus and the outline of the base. This is evident from the hidden lines that extend from M and N, each of which continues along three lines: the first is width from Plan C to the Visual; the second is height from the Visual to Elevation F; and the third is width from Elevation F to the Base. Now, although it’s clear from the figure that the body of the column obscures a significant part of the fillet, and the same fillet partially hides part of the Torus, which would otherwise be visible, the back part of the Torus is only extended until it meets it. Still, it's definitely best to draw every element completely, as if the work were transparent, so that the parts hidden from view can better align with those that are visible.

When your drawing is finished, if you look at it from the right distance and straight on, you'll easily spot and fix any mistakes. Your main focus will be on shaping the Torus, which is tricky because of its roundness on both sides; that is, in the outline of its molding, as shown in Elevation I, and in the loop it creates around the column.

Doric column base deformation.

To avoid the boredom created by excessive uniformity, we switch one of the bases. However, both bases are outlined using the method we presented in the previous figure. This same method is so clearly apparent from the hidden lines of widths and elevations that it would be unnecessary to repeat it.

The Dorick Base in Perspective.

So you don’t get bored by practicing the same thing, I’ve switched up one of the bases for variety. Both are created in the style explained in the previous figure; it's clear from the hidden lines of the plan and elevation provided here, so I think there's no need to elaborate further.

Optical definition of the Ionians.

From the multitude and variety of figures in this work, you will learn, dear Reader, how to distort both low and high objects, large and small. In this figure, the line that the bases of two columns rest on is a combined line of the plane and a horizontal line; the line that the bases of three columns rest on is a higher horizontal line. Just as, if the line of the plane is below the horizontal line, the lines that extend to the eye point and the distance point rise upward; so if the line of the plane is above the horizontal line, the lines that come to the eye point and the distance point go downward. If there are multiple planes on the same table, some of which are higher and others lower than the horizontal line, all the lines of the planes and the horizontal line are parallel to each other; thus from the line that intersects all of them normally, it can be immediately determined how each plane is positioned relative to the horizontal line. I would also like you to note that the width of the middle column is less than the width of the side columns; and the difference between these widths becomes greater the closer the distance point is to the eye point. What has been said about the columns must also be understood in relation to their bases and the optical depiction of both. Nevertheless, if the figure is viewed from the correct point, the painted columns will have the same appearance as solid columns that are equal to each other.

The Ionick Base in Perspective.

With the wide range of shapes in this work, the reader will learn how to depict things, regardless of their size or position. In this figure, the line that supports the two columns serves as both the horizontal and ground line, while the line for the three columns is positioned higher than the horizontal line. Just as, when the ground line is below the horizontal line, the lines leading to the points of sight and distance angle upwards; when the ground line is above the horizontal, the lines to the points of sight and distance angle downwards. If the same picture contains different ground levels, with some higher and others lower than the horizontal line, all those ground lines and the horizontal line remain parallel to each other; thus, by drawing a line that intersects them all perpendicularly, you can easily determine how each level compares to the horizontal line. Note that the width of the middle column is represented as smaller than that of the side columns due to perspective; this difference becomes more pronounced as the point of distance gets closer to the point of sight. The same principle applies to the bases and projections of all their parts in perspective. However, if the picture is viewed from the correct position, the columns will appear solid and equal to one another.

Optical reduction basis of Corinth.

This base is constructed according to traditional optical rules. Furthermore, the height of surface A is the same as the height of the visual line CD; the width of cross A is the same as the width of the cross of the second circle's outline B, starting from the minimum of all. Two lines normally fixed to the base show the maximum width that the column should have above the bottom shoulder. The maximum width of the upper torus and both astragali is the same as the maximum width of the third circle. The maximum width of the lower torus is the same as the maximum width of the last circle.

The Corinthian Base in Perspective.

This base is put into perspective by the rules outlined earlier. The height of surface A matches the height of the visual line CD; the width of the cross A is the same as that of the second circle of plan B, starting from the smallest. The two lines that stand perpendicular to the surface of the base show the greatest width of the column's shaft above the fillet. The extent of the upper Torus and the two astragals is the same as that of the third circle; and the extent of the lower Torus is the same as that of the outer circle.

Basis Acticurga optics diminished.

Foundation is particularly familiar to the Acticurga Pictoribus because it aligns remarkably well with almost all the other Orders. Furthermore, from the points E & F, the maximum width of the outermost circle of the footprint is defined by the largest width of the lower beam CDs. Other matters related to it and the beam AB should be sought from the discussions about the Etruscan base.

The Attic Base in Perspective.

The Attick Base is used more often by painters than any other type because it works well with most styles. The points E and F, representing the widest part of the outer circle of the perspective plan, provide the maximum width of the lower Torus CD. Anything else related to this or the upper Torus AB should be examined in the same way as demonstrated with the Tuscan Base.

Optical reduction of the Etruscan capital.

The same method should be used for drawing the capitals as for the others: since they also have their own square shape and are round. The line of the plane is usually made higher than the horizontal line: because when the capitals are placed on columns that are taller than a person, they generally appear higher to our eyes.

Tuscan Capital Perspective.

The method mentioned earlier about Bases is equally useful for drawing Capitals, since they also have their square Abacus and their round parts. The ground line for Capitals is usually positioned above the horizon, because when they are placed on columns taller than a person, they are typically seen from above eye level.

Optical projection of Doric capital.

The capitellum consists of several parts, making it more complex than the previous one. Nevertheless, a precise geometric drawing will flatten out all the difficulties.

The Projection of a Doric Capital, in Perspective.

This Capital, made up of more Members than the previous one, will be more challenging to visualize; however, a precise outline of the Geometrical Plan will definitely clarify many apparent difficulties.

Ionic capital deformation.

Capitellum Ionicum requires two distinct geometric elevations, one for the face and the other for the side; from these, a geometric trace A is formed, which is optically contracted by shifting to B points of latitude C, and to E points of longitude D in the usual manner: so that lines from B latitude points extend to the line of sight; and lines from E longitude points extend to the point of distance.

From the immediate shape of the capital, the elevation of the length must be drawn as shown in the figure. Additionally, according to tradition, both sides will create a polished capital, taking the widths from the shape and the heights from the elevation of the length. This will also provide the maximum width for each of the scrolls.

We'll provide a way to design the Ionic capital, where the helixes of the volutes are inclined, below in figure thirty.

The Ionick Capital in Perspective.

The Ionick Capital needs two separate geometric elevations, one for the front and one for the side. From both, you get the geometric plan A, which is visualized in perspective by moving the width points C into B and the length points D into E, as is typically done. This way, lines can be drawn from the width points B towards the vanishing point, and from the length points E towards the point of distance.

From the Capital Plan in Perspective, the Upright Length is to be derived, as shown in the Figure; and from both, as is customary, the finished Capital is created by taking the Widths from the Plan and the Heights from the Elevation; this provides the maximum Height, and that gives the maximum Width of each of the Volutes.

The method of describing the Ionian Capital, whose volutes are positioned obliquely, will be discussed in the Thirtieth Figure.

Corinthian capital optical projection.

You won't be able to finish the Corinthian capital unless you properly outline its geometric height and shape following Barozzi's guidelines.

To create from the remains of B the trace of E, necessary optical squares will form from four or at least three hidden lines; by aligning the divisions on line D of line C, and others, in the usual manner. Next, the hidden lines will outline the traces of the leaves, and the rest will be completed as placed in the trace of E.

To create the visual elevation of length F, all its divisions will be transferred vertically from elevation A to a perpendicular line H. This will be completed by straight lines drawn from the division points to the eye point, and by lines from the tops and depths of the circles, which will be parallel to line D and reach the visual G; from there, they will descend and be parallel to the perpendicular line H.

The shiny capital starts from the bottom circle I, showing the outline of the column. The successive leaves 1, 2, will have their widths taken from point E using a compass, with one point of the compass placed on line H; the heights will be taken from point F, with one point of the compass on line D. The same applies to leaves 3, 3, 4, 4, as well as leaf 5, and others, finally concerning the cymatium. The descent of the curve line of the cymatium will begin from point L.

The Corinthian Capital in Perspective.

There is no way to finish the Corinthian Capital unless you precisely outline its Geometrical Elevation and Plan, following the guidelines of Vignola.

Being to create Plan E from Plan B, you need to use hidden lines to make the squares necessary for bringing four, or at least three, of the circles into perspective; transferring the divisions of Line C into Line D, and the rest as usual. Then, with additional hidden lines, adjust the plans of the leaves, and complete what’s further needed in Plan E.

To create the visual elevation of length F, you need to move all the divisions from elevation A into the perpendicular H. Then, you complete it by drawing lines towards the point of sight until they meet their respective perpendiculars. These lines, originating from all parts of the circles parallel to line D, intersect the visual G. From there, they drop down parallel to the perpendicular H.

In working with the clean Capital, you should start with the lowest Circle I, which represents the Compass of the Column. Then create the Leaves 1, 2, by measuring their Widths from the Plan E using the Compasses, ensuring one Point is on the Line H; and their Heights from the Elevation F, keeping one Point on the Line D. The same process should be followed for Leaves 3, 3, 4, 4, as well as Leaf 5 and the others; and lastly, for the Abacus; the Indentation of the Horns corresponds to that of the visual Line L.

Optical description of the Composite capital.

From what we’ve discussed about the Corinthian capital, you will learn how to create a Composite capital. However, I want you to understand that when studying these rules set forth by the master, the use of a compass must always be combined. Only living masters can uniquely fill the void of knowledge.

The Composite Capital Today.

From what has been said about the Corinthian Capital, you can learn how to put the Composite into perspective as well. I wish I could persuade you to consistently combine your reading of the rules, which are basically just lifeless instructions, with dedicated practice using the compasses; this is the only way to make up for not having a live instructor.

Etruscan crown deformity.

After the capitals come the cornices, which, being square, have minimal height. Among the cornices, none is simpler or easier than the Etruscan style. From the geometric elevation, as usual, a geometric trace forms; from this, a similar elevation of length is derived optically. Finally, the shiny cornice is composed of elevation and trace. However, remember that there are two lines that define the width of the optical elevation. The higher line gives the height of the front face of the cornice, while the lower line gives the height of the back face. And it will be so in the future.

The Tuscan Entablature in Perspective.

After Capitals, we move on to Entablatures, which are square and therefore easier to work with than the previous ones. Among all Entablatures, the one from the Tuscan Order is the simplest and easiest to execute. From the Geometrical Upright, we draw the Geometrical Plan; from the Plan in Perspective, we create the Optic Elevation of the Length; and from both of these, we develop the clean Entablature needed. You’ll notice that there are two Lines that define the Width of the Perspective on either side. The Line coming from the upper Corner of the Visual indicates the Height of the most prominent Part, while the one from the lower determines the Height of the Back part. This process continues similarly moving forward.

Optical design of Doric crowns.

In making a Doric cornice, which requires more effort because of the little teeth and triglyphs, a common rule must be followed. However, if you would like to describe the clean cornice on paper separate from its preparations, that is certainly allowed, both in this and in any other design.

The Dorick Entablature in Perspective.

In creating the Dorick Entablature, which has more detail than the previous one due to its Dentils and Triglyphs, the standard rules should be followed. And if you want to draw the finished Entablature on a separate piece of paper from its preparations, you are free to do so, whether in this or any other illustration.

Preparation of the following figure.

In the twenty-eighth figure, which contains the outline and geometric elevations of the twenty-ninth figure, it was necessary to draw side C separately from face B; because the face shows the width of the building, while the side shows its length; and one is not equal to the other. In the geometric outline, the solid wall is A: the circles represent the upper part of the columns. The rest provide projections for the cornices, along with their multiples.

Before the following Figure.

In this twenty-eighth figure, which includes the plan and geometric elevations of the twenty-ninth figure, it was necessary to show the side C separately from the front B; because the front, indicating the width of the building, and the side, showing its length, are not equal to each other. In the geometric plan, the solid wall is A: the circles represent the tops of the pillar shafts. The remaining part is the projection of the cornice, along with its mutules.

Optical projection of a Doric building.

You’ve got in this figure twenty-nine, an optical representation of the footprint, & one of the elevations of figure twenty-eight; namely, the elevation of the length; from which is derived a clear image of the Doric Order building, with the tops & capitals of three columns; and its architrave, frieze, & cornice.

BO is the horizontal line; AC is the plane line; on which, from the lines D & C of the twenty-eighth figure, the points of latitude & longitude of the two elevations are transferred; extending towards C the plane line as required. However, you will work, as we mentioned, with the thirty-second figure; specifically, at point V, the width of the trail will end, and the length will begin; and from the points of latitude, the line will extend to the eye point; from the points of longitude, the hidden line will extend to the distance point. Where these lines cut the visual VO, they will become parallel to the line AC, along with the other necessary elements to complete the optical representation of the trail.

The elevation of the 28th figure will be visually contracted as usual, by aligning the divisions of line E or F along line AB, from which visual lines will be created to the point of view; and dropping perpendiculars from the visual line AO to the line AC, so that lines parallel to the plane line AC continue with other lines parallel to line AB.

This also includes the observation we mentioned earlier, shown in figure 26, about the lines that extend downward and terminate on either side of the optical elevation. From these, all projections of the crowns and capitals are derived.

A Projection of the Dorick Order in Perspective.

In this Twenty-ninth Figure, you see the Perspective Plan and one of the Uprights from the Twenty-eighth Figure; specifically, the Length; from which this finished piece of the Dorick Order is drawn, featuring the upper part and caps of three pillars, along with their architrave, frieze, and cornice.

BO is the horizontal line; AC represents the plan. From the lines D and C of the twenty-eighth figure, the points for width and length of the two elevations are transferred, first extending the line itself through C as much as needed. The work is then done as shown in the twenty-third figure; specifically, the divisions of the width of the plan end at point V, where the divisions of length begin. From the first, lines are drawn to the point of sight, and from the latter, hidden lines are directed to the point of distance. Where these intersect the visual VO, lines are drawn parallel to AC, along with any other necessary lines to complete the plan in perspective.

The Elevation C of the Twenty-eighth Figure is shown in perspective, as usual, by mapping the divisions of Line E or F onto Line AB in this Plate; from there, we draw lines of sight to the Point of Sight, which are crossed by perpendiculars dropped from those divisions of AO created by parallels to the ground line AC, and then continued parallel to the perpendicular AB.

The observation mentioned in the Twenty-sixth Figure is relevant here too. The lines that slope downward in the perspective elevation indicate the advancement and recess of the different parts of the work, and all the projections of the entablature and capitals are derived from them.

Optical projection of the Ionic building; where it discusses how to connect the artificial with the real.

If you are a painter and have the opportunity of a 40-hour setup, or for the burial of the Lord, if you feel like changing the architecture of a church temporarily by blending fiction with reality, as I have often done in Milan and Rome with great delight and admiration from the audience; I will show you briefly the method you should follow while working.

The section of the true crown, which, as I assume, should appear to be continuous with the painted crown on the tapestry, is A; the geometric elevation of the crown, and the others to be drawn, is B; the geometric outline is C. Furthermore, both the outline and the elevation will typically be contracted in length, as you see in C & B: from these, a polished crown will be formed on the tapestry along with a column & anta; and the tapestry itself will be painted, normally to be joined to the true crown.

To make it a part of the length that seems to continue the painted crown with reality, and cannot be extracted from a distorted elevation; you need to transfer section A to D, drawing visuals from the endpoint of the members of section D, until they meet the width lines of the same members. If colors are skillfully introduced into the fabric, the angle at E, although merely depicted, will appear real; and conversely, the angles created by the fabric itself with various crown edges will not be visible anywhere except in the flat plane; and the union of true architecture with the fictitious will not be discernible.

A Ionick Work in Perspective; showing how to blend the imaginary with real architecture.

If, as a Painter, you were asked to temporarily modify the structure of an altar piece during Holy Week by combining painting with the actual work, like I have often done in Rome and Milan, much to the satisfaction and surprise of the viewers: I will briefly explain the method to be followed in doing so.

The dissection of the solid cornice, which I assume will also be shown in the painting on the canvas, is A; the geometrical elevation of the cornice and other parts to be drawn is B; the geometrical plan is C. The plan and elevation of the length are represented in perspective as usual in C and B; from these, the finished cornice, along with the pillar and pilaster, are drawn on the canvas; and then the picture is joined at right angles to the actual cornice.

To adjust the Members so that the painted Cornice looks like it's a seamless continuation of the real one (which can’t be achieved through the Perspective Upright), you need to transfer Section A to D. From the ending Points of the various Members in that section, draw visual Lines until they intersect with those of their corresponding Members in the Perspective. If the Colors are applied by a skilled Artist, the Angle at E, although just painted, will appear to be real. Conversely, the Angles formed between the painted Cornice Members and the different Projections of the actual ones won’t be noticeable, except at the very top Fillet; however, the connection between the real and the painted Architecture will be completely undetectable.

Optical projection of the Corinthian crown, with the capital and top of the column.

In this diagram, the plane line is CIE, and the horizontal is DFO; the eye point is O, and the distance is D. The geometric height of the Corinthian capital with its crown is A, whose divisions are visible on the perpendicular CD. The geometric trace B has a length equal to its width: however, it appears reduced through the usual method. Indeed, by shifting the divisions of width & length onto the plane line CIE; the points of width create visual lines to the eye point; while the points of length create concealed lines to the distance point: this way, you have everything necessary for the optical contraction of the trace. For the lines of lengths are parts of the visuals, as seen in GN, HL: the lines of widths, parallel to the plane line, are created from points where the lines aiming at the distance point intersect the visual line HO, as you see in NL. Furthermore, if the horizontal line DO were extended so that it had two distance points equally spaced from O, the midpoints of the diagonals, which are in the larger square GNLH optically distorted, & in its smaller squares, would converge at one distance point; the other midpoint would lead to another distance point.

The elevation of length is visually narrowed by parallel lines to CE, which, when they reach the visual IO, continue with other parallels to IK. Furthermore, by transferring the divisions of the perpendicular line CD to the line IK, visual points are created from the division points to the eye, and each segment of the elevation is drawn, where the widths are parts of the visuals, and the heights are parts of the parallel lines to IK. Finally, from the outline and from the elevation of length, a shiny crown with a capital is formed. To make the modules easier to outline, they will first take on a square shape, as in M; then a suitable curve will be introduced to each.

The visual depiction of a Corinthian cornice, including the capital and part of the column.

In this figure, the line of the plan is CIE, the horizon line is DFO; the point of sight is O, and the point of distance is D. The geometrical height of the Corinthian capital with its entablature is A, and its divisions are visible in the perpendicular CD. The length and width of the geometrical plan B are equal, and the plan is presented in perspective using the usual method; specifically, by transferring the divisions of width and length into the line CIE; from the width points, drawing visual lines to the point of sight; and from the length points, drawing hidden lines to the point of distance: through these intersections, you have everything necessary to put the plan into perspective. The length lines are parts of visual rays, as shown by GN, HL; and the width lines are made parallel to the ground line, from the previously mentioned intersections, as seen in NL. Furthermore, if the horizontal line DO were extended to include another point of distance at an equal distance from O, half the diagonal lines of the large square GNLH, and the smaller squares contained within it, would converge at one point of distance, while the other half would converge at the other.

The elevation of the length is shown in perspective by extending the parallels to CE until they intersect the visual IO; then, from there, drop lines parallel to IK. Next, transfer the divisions of the perpendicular CD into IK, and from those, create visual lines to the point of sight, drawing the various parts of the upright. The widths are sections of the visuals, and their heights are sections of the perpendiculars or lines parallel to IK. Finally, from the plan and elevation of the length, you can sketch the finished cornice and capital. To make it easier to draw the modillions, first shape them into a square form, as shown in M, which will help you give each scroll a more pleasing curve.

Geometric outline of the crown, Composite Order.

To make this design larger and clearer, I’ve taken on just the middle part to outline. PN is a geometric trace. M is a solid wall. OO are the spaces for the columns. In H are the bases of the crowns. The geometric elevation of the building's width consists of the epistyle T, the frieze L, and the cornice V, above which rises the pinnacle S.

Let a center of arcs be found, where the distance AV is equal to the distance AC. Place one end of a compass at C, and extend the other to V: thus, arcs will be created, the last of which is BD, and all are concentric. Elevation F shows the length of the building from the side GI; elevation E shows its length from the side DR.

The Geometrical Design of a Cornice, of the Composite Order.

To make this figure clearer and more visible, I've only described half of it. PN is the geometrical layout. M is the solid wall. OO shows the locations of the columns. H indicates the extensions of the cornice. The geometrical elevation of the width of the front piece includes the architrave T, the frieze L, and the cornice V, topped by the pediment S.

For finding the center of the curved lines of the pediment, make the distance AC equal to the distance AV; then, place one point of the compass at C and extend the other to V to draw the arc. The other arcs, with BD being the outermost, all share the same center. The elevation F shows the length of the work on the side GI. The upright E shows the length of the same on the front DR.

Deformation of the Composite Crown.

This figure will seem less difficult for you if you first sketch the half that corresponds to the trace PN and the elevation BR of the thirty-second figure; excluding the top part, after you have completed the rest. The line BV is horizontal. The point of sight is V, and the point of distant sight is from V through the space BV, adding fourteen and a half modules. The plane line is AR, where the width P is transferred from Q towards A; from Q towards R is transferred the length N, with all its divisions; so that the width points become visual to the point of sight; and the length points become hidden to the point of distance. From this, you have everything necessary for the optical projection of the trace, as we showed in the thirty-first figure. By the same method we used there, you will derive the elevation P of the crown's length: and from that, as well as from the trace, the shining crown will be produced as usual.

To outline the peak, the divisions from the elevation of the thirty-second figure must be aligned with line AB and visual lines should be drawn to the viewpoint, including boundary lines for each section, which will be taken from the distorted optical trace at Q. The center O of the clear peak arcs is located halfway between the top of the crown and the distance from the square nails that support the peak itself. Therefore, if you derive various heights of the peak's members from elevation P, and take the widths from the trace at Q, you will successfully complete your work.

A Composite Cornice in Perspective.

This Thirty-third Figure will be easier to understand if you first focus on the Half that corresponds to PN in the Plan, and BR in the Upright of the Thirty-second Figure; save the Pediment for last after everything else is completed. The Line BV is the Horizontal. V is the Point of Sight; the Point of Distance is fourteen and a half Modules beyond Point B, which is more than the Interval BV. The Line of the Plan is AR, where from Q towards A you have the Divisions of Width from the previous Plan P; and from Q to R are the Length divisions N: From the first, Visuals are drawn to the Point of Sight; and from the second, hidden Lines to the Point of Distance. From these, you have everything needed to create the Plan in Perspective, as demonstrated in the Thirty-first Figure. Using the method shown, you can also draw the Perspective-Elevation of the Length P; and from this, along with the Plan, you can create the finished Cornice in the usual way.

To create the Pediment, transfer the divisions of Elevation F from the thirty-second figure to line AB, and draw visuals from those points to the Point of Sight. This will give each section its proper outline and contour, which can be referenced from the Perspective Plan Q. The center O of the arches in the finished Pediment is placed below the upper member of the cornice, as far down as half the height of the upper fillet from which the Pediment originates. By measuring the various heights of the sections from Elevation P and the widths from Plan Q, you will successfully finish your work.

Preparation for figure thirty-five.

If you want to compare the thirty-third shape with the current thirty-fourth figure, you'll notice how the trace and height of the Composite crown change here, specifically by swapping the length for the width and the width for the length. Therefore, this shape only occupies as much space as to require it to be outlined separately from the shiny crown.

Latitude divisions start from V towards R, and they are the same as those of the rectangular IG of the thirty-second figure. Longitude divisions start from V towards S, and they are the same as the divisions of the rectangular IP multiplied by two. Latitude divisions create visuals to the point of sight; longitude divisions create lines to the point of distance; along with the other elements necessary to complete the trace AVDC.

The elevation of the length of the coronic and the peak is visually reduced along parallel lines to the plane line AS; when they reach the visual AC, they continue with other parallels to the perpendicular P, as we outlined in figure thirty-one. From figure thirty-two, the straight divisions DR are transferred to the same perpendicular P; along with the heights that the points KXZ have above the line VA; these will create visuals at the eye point: the sections of the visuals with the parallels to the perpendicular P will provide six points of the peak, corresponding to the duplicated points KXZ in figure thirty-two; and a supreme arch is to be formed from their guidance. The same technique will produce all the others.

The crown will be easier to outline, as the visual lines mostly occupy the point of the eye: furthermore, all the parts, except for the summit, are common to the crown and the apex. Thus, similar points on the end lines of each part, from which the bases and claws of the shining figure are derived, are parallel to the vertical P.

Preparing for the Thirty-fifth.

If you compare the Thirty-third Figure with this Thirty-fourth Figure, you'll see that the Plan and Elevation of this Composite Cornice are shown differently. Specifically, the Length of that one is the Breadth of this one, and the Breadth of that one is the Length of this one. Because of this, this Figure takes up so much space that we had to draw the finished Cornice on a separate sheet of paper.

The divisions of width in the plan start from V to R and are the same as those of the line IG in the thirty-second figure. The divisions of length are set from V to S and match those of the line IP in the thirty-second figure, which is halved and then doubled here. Lines are drawn from the divisions of width to the point of sight, and from the divisions of length to the point of distance, along with the additional requirements for completing the plan AVDC in perspective.

The Upright of the Length of the Cornice and Pediment is created by drawing parallels to the Ground-line AS until they meet the Visual AC; then continuing lines parallel to the Perpendicular P, as directed in the Thirty-first Figure. The divisions of the line DR from the Thirty-second Figure are transferred into the same Perpendicular P; as well as the heights that the points KXZ are above VA in the same Figure. From all this, visuals are drawn to the Point of Sight; when these intersect the Perpendiculars, they create six Points on the Cima of the Pediment, corresponding to the points KXZ of the Thirty-second Figure, doubled. This is how the outer arch is formed. Using the same method, you can find points for all the others.

You will find it easier to draw the Cornice, as most of it is made up of visual lines leading to the point of sight. Additionally, all the parts, except for the upper Cima, are common to both the Cornice of the Entablature and the Pediment. Therefore, the matching points in the outlines of their various parts, from which the breaks and contours of the finished piece are derived, are located along the same parallels to the vertical P.

Deformatio coronicis Compositæ, ad latus inspectæ.

The process of creating a smooth crown, based on the shape and elevation of the 34th figure, isn’t different from what has often been taught. Therefore, assuming that the horizontal plane line, eye points, and distances are positioned the same way in this diagram as they are in the previous one; using two compasses, the distances that necessary angles for the complete drawing of the crown have from the plane line and from the line normal to the plane line will be found. By drawing visual lines and other lines parallel to the perpendicular, along with the ends and bends that correspond to each section, the drawing will be completed.

In the peaks, the visuals are completely hidden: however, similar points like H and L, from which the peak begins to curve inward, fall into one and the same visual. I say the same about other similar points. For all straight lines that are parallel to the plane line in the thirty-third figure are parts of the visual lines in the thirty-fourth and thirty-fifth figures.

A Side-View of the Composite Cornice, in Perspective.

The way to draw this finished cornice, based on the previous plan and elevation, is the same as what has been shown to you many times. So, if we assume that the lines of the plan and horizon, along with the points of sight and distance, are positioned exactly as they were in the previous scheme, all the angles needed to outline the entire cornice can be easily found using two pairs of compasses. Measure one distance from the ground line and the other from a line perpendicular to it. Then, draw the visual and perpendicular lines while maintaining the placement and shape of the various moldings, and you'll complete your design.

In the Pediment, the visual lines are completely hidden; and the points H and L, where the Pediment starts to recede, are at the same height and can be seen in the same visual. The same applies to all points that are at equal heights from the plan; all the straight lines, which in the Thirty-third Figure are parallel to the ground line, are parts of the visual lines in the Thirty-fourth and Thirty-fifth Figures.

Preparation for Figure 37.

In geometric tracing C, & in its elevation AB, I only noted the main lines to avoid confusion in the figure, & to leave something for the diligence of the students. The plane line EG has width divisions P, & length divisions Q, in the geometric tracing C. From the width points, visual lines are drawn in the usual manner to the O eye point; from the length points, hidden lines will be created to the distance point, which extends beyond the line AB by fourteen modules: & where the hidden lines from the length divisions intersect the visual line FO, they become parallel to the plane line EF, using sections of such parallels with visuals, to complete the deformation of the tracing.

The same lines that are distorted in the trace are parallel to EF, extending to the visual EO, and continuing with others parallel to the perpendicular DE. Visuals are also created at the eye point from the divisions of elevation AB shifted to the perpendicular DE; using sections of these parallels with visuals to complete the distortion of the elevation length.

Preparing for the Thirty-seventh.

In the Geometrical Plan C, and in the Elevation AB, I've only marked the main lines to avoid confusion in the figure and to leave some work for the diligent. The line of the plan EG has the width divisions P and the length divisions Q of Geometrical Plan C. From the width points, visual lines are drawn to the point of sight O; from the length points, hidden lines are extended to the point of distance, which is fourteen modules beyond the line AB. Where the hidden lines from the length divisions intersect the visual line FO, parallels are drawn to the ground line EF; from the intersections of those parallels with the visuals, you complete the perspective drawing of the plan.

The lines in the plan that run parallel to EF, when extended to Visual EO, continue parallel to the perpendicular DE. From the divisions of AB, extended to DE, visual lines are drawn to the point of sight. These lines intersect the aforementioned perpendiculars, allowing you to determine the length of the elevation in perspective.

Deformation of Etruscan column.

From the preparation we presented in figure thirty-six, this shiny column of the Etruscan Order is visually narrowed by the widths and heights of the individual parts; these are measured using two compasses, as mentioned before.

A Tuscan Column in Perspective.

From the preparation shown in the Thirty-sixth Figure, this complete piece of the Tuscan Order is rendered in perspective using the widths and heights of the different parts, precisely measured with the compass, as has often been stated.

Preparation for the thirty-ninth figure.

This figure is very similar to the thirty-sixth figure. Right at the foot of the P column, the prominence of the crown is R; however, the crown at the stylobate is T. The solidity of the stylobate is V. The circumference of the column at the bottom is X, and at the top Z.

Preparing for the Thirty-ninth.

This Figure is very similar to the Thirty-sixth. In Plan P, the highest point of the Cornice is R; the top of the Pedestal is T; the body of the Pedestal is V; the bare Shaft of the Column at the bottom is X, and at the top is Z.

Doric building deformation.

You've got in this place a Doric building, with the addition of one statue for decoration. However, I would like you to take some figure from these, to sketch it, changing at least something in the position of the eye points or the distance. In this way, you'll make greater progress in this art; and if anywhere the sculptor goes astray, you won’t feel any loss from his mistake.

A Piece of Dorick Architecture in Perspective.

In this plate, you have a Doric composition, featuring a single statue as an additional ornament. However, I recommend that when you start working on any of these designs, you should adjust the points of sight and distance a bit from what's shown here. This practice will significantly enhance your progress in this art and help avoid any issues that might come from an engraver's mistake.

Doric order building geometry.

Vermont for the students who have diligently practiced the methods taught so far and aspire to greater things, I have taken on the task of outlining the midpoint of an arc with three columns and three locations for statues. To avoid confusion, only the parts that we noted in figure thirty-eight will be sketched, showing the characters A, B, C, D, E.

The Geometric Plan of a Design, of the Doric style Order.

For the benefit of those who are eager to learn and have already put into practice the rules established so far, I have taken on the task of illustrating half an arch embellished with three columns and three niches for statues. To keep things clear, I have provided complete lines only for the parts mentioned in the Thirty-eighth Figure, which are marked here with the letters A, B, C, D, and E.

Geometric elevation of the Doric building.

This geometric elevation shows the length of our building. And so this figure, the forty-first, whose dimensions are all taken from Barozzi, matches the length of the fortieth figure.

The Geometric Elevation of the previous Design.

This Upright is based on the previous Geometrical Plan; and therefore all the Parts of this Design, whose Measurements are taken from Vignola, perfectly match those of the Fortieth Figure.

Modus vitandi confusionem, in contractione vestigiorum, & elevationum.

The contractions of the forty-foot shape, and the elevation of the first forty-foot shape, are quite confusing due to their excessive slant. However, we will address this issue as we did with the tenth and eleventh shapes. The chart shows, in a small format, this second forty-foot shape and the four that follow.

How to Avoid Confusion When Converting Plans and Elevations into Perspective.

The Reducing into Perspective the Plan of the Fortieth Figure, and the Upright of the Forty-first Figure, would become very confusing due to the great angle of the Rays. We have therefore fixed the issues of both by the methods explained in the Tenth and Eleventh Figures. This Plate contains a summary of what is described in more detail in this and the four following Figures.

Contracting the footprint of forty.

The aircraft is much further from the horizontal line in this diagram than in the previous one. Thus, this trace avoids any confusion. The rest is clear from what has been mentioned before and from examining this figure. However, it is necessary to extend straight lines parallel to the plane line all the way to the visual TO (which falls outside the page) so that the elevation of the length of our building can be determined, which we will discuss in figure forty-four.

The Layout of the Fortieth Figure in Perspective.

By positioning the ground line much farther from the horizontal than in the previous figure, we avoid any confusion here. The rest is clear from what has often been discussed on this topic and a simple look at the figure. However, lines parallel to the ground line must still extend to the visual top, which is off this page; from them, we can establish the elevation of the length of this design, which we will address in the next figure.

Contract of the 41st figure.

Straight parallels to the line of the figure in the forty-third plane, where they reach the visual TO, should be continued, as usual, with parallels to the perpendicular line. Moreover, it is necessary to transfer all divisions from Barozzi that relate to the elevation of this order; and to draw visual lines. The way this elevation is completed with the help of visuals & parallels is evident from the figure and more clearly illustrated in the chart of the forty-second figure. Numbers 1, 2, 3, 4, doubled, show the centers & heights of semicircles or arcs of the forty-fifth figure; specifically, the lower number indicates the center, while the upper number indicates the height of the semicircle.

The Elevation of the 41st Figure in Perspective.

When the parallels to the ground line in the forty-third figure are extended to the visual top, they should then, as usual, continue as parallels to the perpendicular. On this perpendicular, the divisions provided by Vignola for the proportions of this order should be transferred, and visuals should be drawn from them to the point of sight. How these visuals and parallels raise the elevation in perspective is partly shown in this figure, but is clearer in the forty-second figure. The numbers 1, 2, 3, 4, which you see doubled here, represent the centers and heights of semicircles of the arches in the forty-fifth figure; the lower numbers indicate the centers, and the upper numbers indicate the heights of the semicircles of the same.

Half of the building is visually distorted.

For this purpose figure's drawing, we have borrowed several aspects from the fortieth figure and the heights from the forty-fourth. Now, it's necessary to skillfully add lights and shadows to each part of the building.

One Half of the Dorick Design in Perspective.

The previous figures set the stage for this one, with the widths taken from the forty-third figure and the heights from the forty-fourth figure. All that's left is to skillfully arrange the light and shadows for each part of the work.

Other half of the building.

Supersede I could outline the other half of our building. But I didn’t hold back in showing the variety of light & shadows that complement parts that are otherwise completely similar.

The other half of the same design.

I might be able to. very well have left out this half of the design, but I spared no effort to show the variety of lights and shadows that should be applied to those parts of the work that are similar in other respects.

Remnants of Ionic architecture.

Geometric path A of the Ionic building has its deformation B beneath it. To make this clearer, we extended a horizontal line, which will represent the distance PE from the horizontal OE, downwards in CD, as we did in figures forty-two and forty-three. The visual line OM serves the same purpose as the visual line OT in figure forty-three; specifically, it defines the parallels to the horizontal line from the components of the trace B, continuing the same way with other parallels to the line EC, to represent the altered elevation we will show in figure forty-nine.

The Plan of an Ionic Building.

The geometric layout of this Ionick work is A, with its perspective view shown below as B. To make this clearer, the ground line, which in the following figures only shows the distance PE from the horizontal EO, is moved down to CD, just like it was done in the forty-second and forty-third figures earlier. The visual line OM serves the same purpose as the line OT in the forty-third figure; that is, to complete the lines drawn from the elements of plan B parallel to the ground line. From there, they continue parallel to the perpendicular EC, to create the perspective view for the elevation shown in the forty-ninth figure.

Geometric elevation of Ionic building.

From this elevation, which clearly shows the parts of the entire building according to the length dissected, one can derive the heights and terminations of each part. However, more experienced individuals often tend to skip this figure because the terminations can be gathered from the footprint of figure A of the forty-seventh figure, while the heights must once again be established with the next figure.

The Geometrical Upright of the previous Ionick Design.

From this figure (which clearly shows the composition of the entire work regarding its length) are taken the heights and terminations of the different parts. However, those who are skilled in this craft usually skip drawing these elevations because the terminations can be taken from Plan A in the forty-seventh figure, and the heights will be repeated in the next figure.

Deformation of Ionian building elevation.

This shape, which contains the deformation of the previous elevation, is completed using the method we demonstrated in figure forty-two; specifically, from the trace of B in figure forty-seven, we need to draw parallels to the plane line CD. When these reach the visual OM, they should be extended with other parallels to the line EC. The same parallels transferred into this shape intersect with visuals from the straight line AB, where the heights of the Ionic building are situated, taken either from the previous figure or from Barozzi. However, there is no point in the elements of this elevation that cannot be found through the intersections of visuals from line AB, along with parallels to that same line.

The Elevation of the Ionick Design in Perspective.

This plate shows the perspective of the upright mentioned earlier, and it's created using the method described in the forty-second figure. Specifically, from the plan B of the forty-seventh figure, parallels to the ground line CD are extended to the visual OM; then, parallel lines are continued to the perpendicular EC. These are transferred into this figure and intersected by the visual lines coming from AB, which represent the heights of this Ionick composition, in accordance with the previous figure and the rules provided by Vignola. Now, there’s no point on any part of this upright that cannot be located by the intersection of the visual line from AB with its corresponding perpendicular.

Ionic Architecture.

From the remnants of the forty-seventh figure, and from the elevation of the forty-ninth figure, this Ionic building is derived, which could serve as either the base of a bell tower or the foundation of some triumphal arch. I fear that the sculptor has not sufficiently demonstrated his diligence in this design. However, you will easily uncover his mistakes, and you will carefully avoid them with all your effort.

A Design of Ionic Architecture.

From the Plan of the 47th Figure, and from the Upright of the 49th Figure, is drawn this Ionick Piece; which could definitely work for the lower part of a Tower, or for part of a Triumphal Arch. I worry the Engraver hasn't been as precise in this design as he should be; but you'll easily notice his mistakes and be careful to avoid them.

Corinthian Order.

This page contains a detailed summary of the structure of the Corinthian Order, along with its preparations. The mark A shows a wall positioned behind the columns like a channel. The same mark is optically distorted in D: with the geometric elevation omitted, the elevation is projected through its heights noted on the line BC; and using the usual method, the building is composed from the mark & elevation, with the addition of one decorative statue.

A Corinthian Design in Perspective.

This Plate shows the Perspective of a Corinthian Work, along with its Preparations. The Geometrical Plan A reveals the Wall carved out behind the Columns. The Perspective Plan is D: and omitting the Geometrical Elevation, the Perspective is described by mapping the Heights from the former into the Line BC. The Design is completed in the usual way from the Perspective-Plan and Upright, including the addition of a single Statue as an ornament.

Spiral column layout, Composite Order.

Posita the geometric elevation of the straight column, and dividing it into twenty-four equal parts, the spiral column is resolved through parts of the circumference of circles, whose diameters are equal at various widths of the straight column, as shown in figure A. For the optical projection of the elevation, four hidden lines must be noted, which descend from the terms of convexity and concavity of the lower spirals of the same elevation A, and end in two circles of geometric tracing B. The tracing itself appears optically reduced in C: these are the maximum widths on both sides, both in the larger circle and in the convexity of the lower spirals of the column; they are the same maximum widths, both in the smaller circle and in the concavity of the spirals; as you can discern by applying the rule to the spirals and circles. From the four points of maximum width of the two circles, four lines parallel to the plane line begin, which, when they reach the visual line ED, should be extended with parallels to the perpendicular line DF. On the same line DF, you must transfer twenty-four equal parts of the height of the column from elevation A, and draw visuals to point O, the observer's eye. Through the intersection of the visuals with the aforementioned four parallels to line DF, wavy lines MN, PQ are drawn, from which the boundary lines of the polished spiral column are obtained on both sides. From line GH the front face of the stylobate, column, and cornice is obtained; from line IL the back face is obtained.

The Description of a Wreathed Column, of the Composite Order.

After creating the geometrical elevation of a straight column and dividing the height of its shaft into 24 equal parts, the wreathing is described using parts of the circumference of circles, whose diameters match the various widths or diameters of the straight column, as shown in Figure A. To put the upright in perspective, four straight hidden lines are helpful; these descend from the extent of the bulges and indentations of the lower wreaths of Column A and end at two circles in the geometrical plan B. The plan laid out in perspective is C. The farthest extent of the larger circle determines the convex parts of the lower wreaths, while the widest point of the smaller circle determines the hollow parts of those wreaths, which can be seen by applying a ruler from the wreaths to the circles of the plan. From the four points of greatest width in those circles, four lines parallel to the ground line are extended to the visual ED and then continued parallel to the perpendicular DF. From elevation A, the 24 equal parts of the column's height are transferred to line DF, with visuals drawn from each to the point of sight O. The intersections of those visuals with the aforementioned four perpendiculars create the wavy lines MN and PQ, from which the outlines of the finished column are drawn. However, the front part of the pedestal, column, and cornice is taken from line GH; the back part comes from line IL.

Ordines Architecturæ, taken from Palladio & Scamozzio.

On the Orders of Architecture, besides Barozzi, have been excellently written by Palladio and Scamozzi; and each, rightfully, has their followers and patrons. Therefore, in accordance with the principles of the most esteemed Authors, I wanted to showcase all the Orders on this page, as they appear in their Books.

The Orders of Architecture, taken from Palladio and Scamozzi.

Also, Vignola, Palladio, and Scamozzi have also written very well about the Orders of Architecture, and each of them has rightfully earned their Followers and Admirers. To help you create Designs in Perspective, based on the Proportions of the most renowned Masters, I have included in this Plate the Measurements of all the Orders, as presented by them in their Books.

Three methods for outlining spiral columns.

Columns of the upper figure lack the elegance that the famous bronze spiral columns of Sir Bernini have at the tomb of St. Peter in the Vatican. Therefore, I present a threefold method for reducing the height of the entire column.

1. Let line OA be equal to the height of the column AB. Also, let line OB be made, and an arc AP drawn from the center O, divided into twelve equal parts, by drawing lines that end at the vertical column at the division points; and finally, let parallel lines be drawn to the base: The spaces between these parallels will create openings for circles for equilateral triangles and for spirals, as shown in column 1.

2. Translate from the third part of the height of the column from its base, the compass should have an opening CD; and with one leg initially placed at D, then at C, create two small arcs to E: the intersection of those arcs will be the center of arc DC, which should be divided into twelve equal parts, and from the division points, draw parallels to the base. Then, by dividing the spaces between the parallels into four equal parts, three of those parts will provide the length of the legs for isosceles triangles; the vertices of the triangles will be the centers of individual spirals, as shown in column 2.

3. Draw a line from the middle of the summit G straight to GF, transfer the distance HF to I, and create a straight line IL that is parallel to the base HF; transfer the distance IL to N, and create NM, and so on. In small columns, triangles can be drawn with negligible error using diagonals: however, in larger columns, it is necessary to use one of the previously explained methods.

Three different ways to outline decorated columns.

The decorated columns shown in the Fifty-second Figure, divided into twenty-four equal parts, lack a lot of the elegance in shape seen in the brass pillars created by the famous designer Bernino for St. Peter’s tomb in the Vatican. Therefore, I present to you three different methods for reducing the spaces throughout the entire height of the column.

1. Make the line OA the same length as AB, which represents the height of the column; then draw the line OB. From the center O, create the arch AP as you wish, dividing it into twelve equal parts. From these divisions, draw straight lines from the center O to the column line, and then extend the same parallels down to the base. The spaces between these parallels will form the sides of equilateral triangles that you will use to create the column's wreath, as shown in Column 1.

2. After establishing the height of the column's third part, from the bottom of the shaft to point C, use the distance CD from centers D and C to outline the arches that meet at E. At center E, using the same distance, create the arch DC, dividing it into twelve equal sections. From the points of those divisions, draw parallel lines to the base. Then, divide each space between the parallels into four equal parts; three of those parts will form the sides of the isosceles triangle, with the vertex being the center where each wreath of column 2 will be drawn.

3. From the top of Column G, draw line GF, then make HI the same length as HF and draw IL parallel to the base HF. Next, make IN the same length as IL and draw NM parallel as well, and continue this process. For smaller pillars, the centers of the diagonals in these spaces can be used to outline the wreaths without significant error, but for larger columns, one of the other two methods is preferable.

Remnants of the Corinthian Order.

Description of the octagonal Corinthian building, we present here the footprint of one of the four columns that will support the arch in the style of a dome, so it will take the form of the fifty-eighth figure. For easier description, I placed the geometric footprint of the stylobate at the bottom of the page, and the geometric footprint of the cornice at the top, along with the widths and lengths of each individual element; so that by transferring them to the plane line in the usual manner, both footprints will be optically distorted. To avoid confusion, it will first be necessary to note the points related to the elements closest to the solid wall, and then the others.

The Plan of a Design of the Corinthian style Order.

To describe an Octangular Corinthian Work, I've included the Plan of one Quarter of the Composition, which has a vaulted structure in the shape of a Cupola, as shown in the Fifty-eighth Figure. To make the Plan clearer, I've provided the Geometrical Plan of the Pedestal at the bottom of the Plate, and at the top, that of the Cornice, along with the Widths and Lengths of each Component. By transferring these into the Ground-line, in the usual way, you can draw each Plan in Perspective. To avoid confusion, it's essential first to transfer the Points of those Components that are closest to the Wall's solidity, then proceed to the others.

Elevation of the Corinthian building.

The geometric height of the octagonal building aligns with its two previous shapes. However, since the elevation of the wall hides the second of the four columns, which will be visible in the deformed building; therefore, it was necessary to represent it with hidden lines.

The Geometric Elevation of a Corinthian Work.

The Geometrical Elevation of this Octagonal Design completely matches the two Plans of the previous Figure: However, since the Wall in this Upright obscures the view of the second of the four Columns, which is still visible in the finished Perspective that follows, it’s necessary to illustrate it using hidden Lines, as shown in the Figure.

Deformation of footprints & elevation of the Corinthian building.

In this figure, I wanted the plane line to align with the horizontal line. Therefore, the lower trace couldn't be seen unless I otherwise drew the plane line downward, while here I would raise the horizontal line upward, which I set as the midpoint between the plane lines of both traces, so that both projections would be equally distinct. In the elevation, the second column, which, as I mentioned, is hidden by the wall, should be indicated with hidden lines.

The Perspective Plans and Structure of the Corinthian style Design previously mentioned.

In this figure, I made the ground line match up with the horizon, which means the lower plan can’t be seen unless the ground line is lowered, as mentioned earlier; or on the other hand, the point of sight is raised higher, as I have done here, keeping it in the middle between the ground lines of the two plans so that the perspective of both is equally clear. In the elevation, the second column, which I said would be hidden by the wall, should be drawn with dashed lines.

Overview of the following figure.

I created this outline separately so you can see how to make the overall depiction by using the heights of each limb from the elevation and the widths and lengths from the footprints. All of this is clearly shown in the diagrams.

The rough draft of the following figure.

I’ve got separated this Figure so you can see how to outline the entire Work by measuring the Heights of the different parts from the Elevation, and their Widths and Lengths from the Plans; all of which is very clear upon looking at the Figure.

Corinthian octagonal building.

So far we have described the ancient piles on the left side of the Corinthian building. Here is the right half of the entire structure. You will have the complete building shaped like a sixty-sided figure.

Part of an Eight-Sided Work of the Corinthian Style.

So far the closest left side of this Corinthian design has been described. In this plate, you can see the right side of the whole work; and in the sixtieth figure, the complete perspective.

Remnants of the octagonal tent.

Predictions of octagonal shapes are more complex than squares: therefore, I didn't hold back on the details in explaining them. The mass whose traces you see in A & B shares many similarities with the figure we created in the fifty-eighth. The visual CD captures the perpendicular sections, which serve as the basis for the elevation of the next figure, as has been mentioned before. If the inner face needs to be drawn separately from the front face, you'll complete it using lines CE, and this one using lines FD.

The Plans of an Eight-Sided Tabernacle.

Eight-sided figures are harder to put in perspective than squares; I'll do my best to make the method as clear as possible. The design shown in A and B is similar to the one described in the Fifty-eighth figure. The visual CD receives the sections, from which perpendiculars are drawn for the elevation and profile of the next figure, as has often been mentioned. If you want to draw the back part separately from the front part, you can do the back part using line CE, and the front part using line FD.

Octagonal tabernacle.

I have used this structure multiple times for the presentation of forty hours. If the colors are applied skillfully in two rows of fabric, while cutting away everything that doesn't relate to the structure itself, it will impress the viewers and appear solid. However, it will be necessary to extract the model of the outer face from the section DF of the footprint and elevation; the model of the inner face should be extracted from the section EC, following all the rules we have discussed so far.

An Octagonal Tabernacle in Perspective.

I’ve got sometimes used this Tabernacle for the Exposition of the Forty Hours. If the colors are applied by a skilled hand, on two layers of fabric, and the frame is cut away according to the outline of the work, they will remarkably deceive the eye and look solid; but then the outer layer must be drawn according to the plan and elevation of the part DF in the previous figure; and the inner layer after that of EC; always following the rules given so far.

Modus of setting up machines that consist of multiple levels of looms.

From inspecting the figures, you’ll learn how to set up machines that consist of multiple layers of fabric. Our tent only needs two layers; the closer fabrics depict the outer appearance, while the farther ones show the inner look. To avoid hiding the poles that support the fabric, we've omitted half of the fabrics. The line LS is a straight plane line, while DG is a horizontal line; the distance point that falls outside the page along the extended line CG should be set back from point C, just like, at the top of the figure for the fifty-ninth, the distance point is set back from the eye point. The same horizontal line DG is intersected normally at C by the line EF, which is the section of the tent's outer face, and from C, the divisions into equal parts for the front fabric’s network begin, as we will show in the sixty-second figure. The line IL, which is the section of the tent's inner face, can be spaced freely from the line EF to which it is parallel. Furthermore, through the divisions on line EF (as you see in M, N, O), visual lines should be drawn from the distance point to the line IL for the network of other fabrics: the distance DC requires an increase in what is painted on the fabrics, otherwise, they would appear too small. Thus, you’ll understand why the arc that reaches the front fabrics only goes to B, while in the back, it rises up to H.

In the following figure, we will show how to sketch the inner surface of the fabric using the grid from the outer surface. To understand this method, draw a straight line HP parallel to DC, and divide the line BC into the same number of equal parts as the line desktop computer has been divided.

How to build machines that consist of multiple rows of frames.

By looking at the diagram, you'll quickly understand how to set up the different rows of frames. This tabernacle I've just described only needs two of them; the frame closest to you shows the outer face, while the frame behind represents the inner face. I've only shown half the width of these frames so you can see the poles and braces that support them. The line LS is the plan line or ground line; the line DG represents the horizon; and the point of distance, which is outside the page along CG extended, is as far from point C as the point of distance is from the point of sight at the top of figure fifty-nine. The horizontal line DG is intersected perpendicularly at C by line EF, which indicates the section of the outer face of the tabernacle. From point C, the equal divisions for the netting of the front frame begin, as shown in figure sixty-two. The line IL, which is the section of the inner face of the tabernacle, can be positioned closer to or farther from line EF, to which it runs parallel. Using the divisions of line EF (like M, N, O), lines are drawn from the point of distance to the perpendicular IL for the netting of that frame; this is because the distance DC requires the parts of D to be painted larger; otherwise, they will look smaller than they should. And from this, you can understand why the arch, which in the front frame reaches only to B, rises up to H in the back frame.

In the following figure, the method of outlining the inner frame from the outer face's network is shown. To better understand this, make the line HP in this figure parallel to DC, and divide the line BC into as many equal parts as the line PC was.

De reticulandis telariis, quæ repræsentant ædificia solida.

You’ve got two models of the tabernacle that need to be outlined separately, which you can find together in A. Both share the same grid, which we have marked with their respective numbers. Once you've defined the size of the entire structure, you can layout the flooring in B in a way that fits the entire design, using the same numbers as the model: and with the help of this grid, there will be guideline lines on the flooring corresponding to how many panels will represent the outer appearance of the tabernacle. When these are prepared, each piece will be arranged precisely in its designated spot on the flooring; and with black-dyed strings, the same grid will be repeated in the panels, adding as many visual elements as needed. As the panels are painted separately, straight lines can be drawn leading to the vanishing point or perspective. Another grid is also necessary on the flooring for the inner face of the tabernacle: and the two flooring grids will maintain the same proportions as the divisions of the lines IL, EF, of the sixtieth figures. Following this grid will create the guideline lines for the panels along with the others, as we've indicated before.

Following this method, you can't draw the boundary lines of the inner face unless you create a new net on the floor, replacing the old one, which would be quite labor-intensive. Once you have extracted two copies from the shape of the 50-sided figure, transfer the line PC to the external face copy, and transfer the line BC to the internal face copy. If the line computer is divided into fifteen equal parts, then BC should also be divided into fifteen equal parts, and both copies will need to be gridded accordingly. Furthermore, although the squares in the grid of the external face copy may be larger than those in the internal face copy, the same grid will still be used to guide the boundary lines of both faces. What has been said about the two copies applies to any number of others. For example, if you want to create five rows of weavers, you will need five copies on paper. If the same grid is used in all copies, you will need to create five different grids on the floor. However, if there are five different grids in the copies, then a single grid on the floor will be sufficient.

It is important that the squares you create on your grid are precise, and that all their corners are right angles. The fastest way to make right angles is as follows. Place one leg of a compass at point F on the straight line EF, and the other leg anywhere at O, which will create the circle GFI, and from point G, draw the diameter GI. If line HF passes through points I and F, it is perpendicular to EF.

On creating the network on frames to represent the architecture as solid.

You have together in A, the two designs of a Tabernacle, which should be drawn separately; the same network can be used for both, marked with numbers. Once you have decided on the size of your work, create a network on the floor of a room large enough to accommodate it, and label it with the numbers as in your reference. With this, you can outline all the components needed for the outer frame of the Tabernacle on the floor. After that, place the frame exactly where it should go on the floor and draw the same network with a black line; you can add as many visual lines as you want, which will be helpful for drawing lines to the vanishing point when you come to paint the frames separately. Another network on the floor is also necessary for the inner face of the Tabernacle, which should be proportionate to this one, similar to how the divisions of line IL relate to those of EF in the sixty-first figure; this way, the outlines of the inner frame, &c. can be drawn, as has already been shown.

Thus, the outline of the inner face can't be described without erasing the first network and creating a second one on the pavement, which would be very troublesome. Therefore, from the plan of the fifty-ninth figure, take the two designs and transfer line PC from the sixty-first figure on the outer face and line BC on the inner face. Then, if PC is divided into fifteen equal parts, BC should be divided in the same way, and use these divisions to create the network on each design. Although the squares on the outer face are larger than those on the inner face, the same network can still serve to outline both. What has been stated about these two designs can also apply to many others. For instance, if five rows of frames are required, five designs must be created on paper. If the same network is used in all the designs, then five separate networks must be created on the pavement; however, if the designs are different, then one network on the pavement will be enough.

You need to be very careful that all the squares in the grid are divided perfectly and at right angles. A simple way to create a right angle is as follows: Place one end of the compass at point F on line EF and the other end anywhere at point O to draw circle GFI; then draw the diameter GI from point G. The line FH drawn from points FI will be perpendicular to line FE.

Square building remnants.

The geometric path of this building has its deformation in B. The difference between columns C & D arises from the fact that column C has traces of the stylobate, while column D has traces of the cornice.

The Plan of a square Design.

The geometric layout of this Design A is shown in perspective in B. The difference between parts C and D comes from the fact that the plan of the pedestals is situated in C, while that of the cornice is in D.

Square building.

From the deformation of the footprint and elevation, the traditional method produces an image of the entire building, which can serve as a model for the high altar of any church. I have used this device, not without common approval, several times in the setup for the forty hours; it occupies a place in the middle of the empty area filled with Angels and clouds, adding several figures in the lower part. The method for creating in more remote weavings from the eye is derived from what we have shared regarding the projection of circles.

A square design in perspective.

From the plan and upright perspective, this finished piece of the entire work is depicted in the usual way and can serve as the design for a grand altar in a church. Sometimes, for the solemnity of the Forty Hours, I have displayed this painted on a frame, receiving general admiration; angels with clouds occupy the upper part of the hemisphere, and groups of figures are in the lower part. The way of designing on the inner frame, that part of the said dome which you see here, is based on what has been previously mentioned about placing circles in perspective.

Imminent optical reduction of the round building.

Those who have not put diligent effort into shaping circles and have failed to describe them with minimal work will struggle in vain to discard the remnants of round buildings. To avoid confusion, it will help to first mark the hidden lines of the main components; by transferring these into elevation, you can gradually add the remaining parts. I have personally used this method in this plan. However, after I learned through experience how intense these descriptions can be, I have long started applying another rule, which we mentioned above and reserve for another work.

The Plan of a Circular Work in Perspective.

Those who haven’t put in the effort to understand how to put circles into perspective, and who haven’t practiced consistently to make the task second nature, will struggle to create plans for round buildings. To avoid confusion, it’s a good idea to first mark the hidden lines of the main components; once those are transferred to the vertical view, you can move on to the rest, just as I did in this illustration. However, after experiencing the challenges of depicting these round forms, I’ve since adopted a different method, which, as I mentioned before, is saved for another book.

Design of a circular building.

Awesome images of round objects captivate the eyes if all unrelated elements are precisely outlined and depicted. This design must be worked out using the usual method, and I constructed it in the Church of St. Ignatius at the Roman College for the holy days of the 5th and 6th weeks of Lent. Inside the arch, above the altar, there was a place for a burial urn, along with the Blessed Sacrament. Under the altar, there was a statue of Christ taken down from the Cross; in the middle of the columns, the image of the Sorrowful Virgin; above the balustrades, angels mourning, holding instruments of the Savior's torment.

A Circular Design in Perspective.

The appearance of round objects, when designed well, skillfully painted, and framed to match the shape of the artwork, can really trick the eye. This figure is based on the usual plan and was created by me in the Church of S. Ignatius of the Roman College for the Thursday and Friday of Holy Week. Above the altar, there was a sepulchral urn holding the Holy Sacrament. Beneath the altar, a figure of our Savior Christ was displayed as if taken down from the cross. In the center of the tambour, there was a picture of the Blessed Virgin in deep sorrow, and on the balustrade, angels were mourning, holding the instruments of the Passion.

Vestigium geometricum, and the first preparation for the seventy-first figure.

I gave a presentation a remarkable structure and created such an impressive machine back in 1685 for a 40-hour prayer session at the Farnese Temple that I decided to make it accessible to scholars by making the image of the entire building public. I’ve included the footprints and elevations, all drawn with such care as if the work wasn’t meant to be colored with a brush, but built with stones. The dark areas represent the solidity of the walls and columns. The other lines show the bases of the stylobates and the crowns. The drawing will start from those parts from which the hidden lines originate in A, (and those discussed here should be understood as pertaining to another set) so that the multitude of lines doesn’t cause confusion. In B, the hidden curved lines represent the trace of the dome that completes the top of the structure. The trace in C shows the interior corridor. However, we omitted the trace of the theater because the page’s narrowness doesn’t accommodate it.

The Geometrical Plan, and first Preparation for the Seventy-first Figure.

The Machine I built in 1685, in the Church Farneze, or Jesuits Church at Rome, for the Devotions of the Forty Hours; had such an amazing effect and deceived the eye so well, that I decided to satisfy those who study this by providing not just a general view, but also the plans and elevation of it; all done with such precision that the work itself seemed to be made of solid stones rather than created by a painter's hand. The shaded part indicates the solidity of the walls and columns. The other shows the breaks and projections of the pedestals and cornices. To avoid confusion from too many lines, start with those parts that create the hidden lines on Side A; this also applies to the other half. In B, the hidden curved lines are the plan of the Cupola that tops this structure. Plan C is for the inner vestibule, but the plan for the theater is omitted here due to lack of space on the page.

Elevating the geometric outline of the previous mark, and the second preparation for the seventieth figure.

In this diagram, you have the building's elevation drawn out in length, which we will project optically in a seventy-degree angle: you will also see that the distorted elevation is made up of the same components as the geometric elevation. From this, you will learn to design such machines, understanding that the knowledge of architecture is just as necessary for a painter as it is for an architect building solid structures.

The Geometric Elevation of the above Plan, and the second Preparation for the Seventy-first Figure.

In this figure, you can see the elevation of the structure displayed lengthwise; the perspective is shown in the seventieth figure. You’ll notice that both representations consist of the same components. This shows that when designing these types of structures, the artist should have just as much skill in architecture as is needed for the construction of solid works.

Deformation of the figure of the sixty-seventh and preparation for the figure of the seventy-first.

The display of this artifact has been explained by us in the figure of the forty-second square. Clearly, to keep the parallels spaced apart, we’ve extended a line down the plane so that you can immediately recognize it from the figure.

The Plan of the 67th Figure in Perspective, and the third Preparation for the 71st Figure.

The technique used to create the perspective of this plan has already been shown in the forty-second figure; specifically, to give the appearance of greater distance between the parallels, the ground line is drawn much lower than its actual position, which is clear upon looking at the figure.

Deformation of the elevation of the thirty-eighth figure, and the fourth preparation for the seventy-first figure.

What has been said about the projection of our building's footprint applies to the elevation. Indeed, to keep them notably separated in parallel, we used the technique we outlined in figure forty-two.

The View of the Rise of the Sixty-eighth Figure, and the fourth Preparation for the Seventy-first Figure.

What has been said about the Perspective-Plan of this Structure is also applied here in the Elevation; that is, to ensure the Parallels are clearly defined, the Perpendiculars are drawn farther away from the Point of Sight, as demonstrated in the Forty-second Figure.

Theater representing the Wedding at Cana in Galilee, built in Rome, in the year 1685, during the exposition of the Venerable Sacrament in the Farnese Temple of the Society of Jesus.

From the earlier preparations, we developed the design of this noble Architecture, which captivated the eyes with both the daylight and especially the light of candles; many were openly displayed, while others were entirely hidden, illuminating six different levels of the tapestry that made up the entire structure, not including the tapestries depicting clouds filled with angels worshiping the Venerable Sacrament in the center of the main arch. We omitted these clouds to avoid obscuring parts of the interior buildings. In organizing the tapestry layers, we followed the method I illustrated with the figures sixty-one and sixty-two; moreover, in choosing their spacing, care was taken to position the candles at the back of the tapestries, ensuring they illuminated the front of the inner tapestries. Furthermore, the number of main components in the two major facades matched the number of distinct tapestries, making it difficult to discern their connections; some pairs of these were joined with iron hooks, allowing them to be unfolded and folded for easier handling and longer-lasting maintenance.

Those who have followed me this far can be sure that they will continue on their journey successfully; and in our work, they will discover greater and better things.

A theater showcasing the Wedding at Cana in Galilee, built in the Jesuits Church in Rome, in the year 1685; for the special occasion of displaying the Holy Sacrament.

From the preparations mentioned above, the perspective of this impressive piece of architecture comes to life. It catches the eye in daylight, but is especially striking by candlelight; several candles are visible, while others remain hidden, illuminating the six different ranges of scenes that make up the entire work. Not to mention, in the center of the grand arch are clouds filled with angels worshipping the blessed Sacrament. Those clouds are left out here so that the inner parts of the work can be more easily seen. In arranging the various ranges of scenes, the same method was used as described in the sixty-first and sixty-second figures. Great care was also taken with their distances, ensuring that the candles placed at the back of one illuminated the front of the one behind it. Additionally, each scene was made up of as many parts as there were main elements in the two larger façades, making the joints nearly invisible. Some pairs were connected with hinges, allowing them to fold and unfold for easier handling and maintenance.

I have no doubt that those who have followed me this far will be encouraged to continue their studies so they can create even greater and more impressive works than mine.

In theater settings.

Theaters that we have outlined are similar to stage theaters: however, it is not so easy to find the focal point or perspective in these. Furthermore, due to the angle of the channels in which the scenes move, the straight lines that should appear parallel to the plane line need to be slanted rather than parallel, making their depiction quite challenging. This issue could be avoided by using parallel channels to the stage, as is sometimes done, especially in Germany. Nevertheless, the Italian method provides this advantage, allowing those responsible for suggesting to the actors, moving the scenes, and overseeing other similar tasks to blend in more easily and perform their roles more freely.

To give you a brief summary of what we will explain more thoroughly later, take a look at this diagram. 1, 2, 3, 4 illustrates a space that is 120 Roman palms in length and 60 palms in width; this is shown by the scale S of 30 palms. The theater occupies half of the area, while platforms and audience spaces take up the other half. O is the point where the visual lines converge, D is the location for apparent things that are farther away. BC indicates the spot for the stage. HH are the angled channels, whose width is double that of the stages. FG is the front and face of the theater. AO denotes its depth or length. E is the space for singers, pipers, and musicians. K is the area for spectators. I shows the trace of the platforms. L represents the steps of the platforms. N indicates their elevation. M refers to the slope of the flooring, along with the layout and elevation of the theater and the scenes seen from the side, which align with their channels, as shown by the hidden lines. OO is the normal line to the horizontal line. P & Q show the elevation of the observed stages, which curve inward; they align in width with the channels indicated by B, and in height with the sections of elevation M; as demonstrated by the hidden lines. In the same elevation M, part of the height is assigned to the stages, and part to the ceilings R, through which each pair of curtains is joined. VV are the lines used to check if there is a gap between the stages and ceilings, or between the stages, or between the ceilings. In some scenes, instead of ceilings, clouds and air are painted.

Stage Scene Ideas.

Stage scenes have a lot in common with those described recently, but finding the right perspective in these isn't as straightforward. Because the tracks where the scenes move are angled, the lines that should look parallel to the plan must actually be drawn at an angle, which can be tricky. This can be avoided by making the tracks parallel to the backdrop, as is common in some places, especially in Germany. However, the Italian style has the advantage that those responsible for prompting the actors and changing the scenes, & c., are less visible while doing their jobs.

In this figure, I've provided a summary of the details that will be explained further later on. The numbers 1, 2, 3, and 4 indicate the area of a hall that's 120 Roman palms long and 60 palms wide, as shown on the scale marked S with a measurement of 30 palms. Half of this space is occupied by the stage, while the other half is for the audience. O is the point where the visual lines converge. D is where things intended to seem most distant are placed. BC is the positioning of the backdrop. HH are the angled grooves, which are twice the width of the scenes. FG is the front of the stage, and AO is its depth or length. E is where the musicians are. K refers to the area for spectators. I shows the layout of the galleries, and L indicates the stairs to them. N represents the height of the galleries. M illustrates the slope of the floor, with side views of the stage and scenes, corresponding to their respective grooves, as the hidden lines show. OO is a line that is vertical to the horizon line. P and Q show the height of the scenes viewed from the front, curling inward, with widths matching the lengths of the grooves in plan B and heights that correspond to the sections in elevation M, as shown by the hidden lines. In this profile M, part of the height is attributed to the scenes and part to their soffits or ceilings, R; where each pair of these frames are connected. VV are the lines used to identify any gaps between the scenes and their ceilings, between the scenes themselves, or between their respective ceilings; although in some scenes, the place of the latter is filled by painting the sky with clouds, &c.

Aliud vestigium theatri, ubi de modo inveniendi ejus punctum.

If the scenery of an already built theater is to be rendered, it will need to outline a geometric footprint taken directly from it (like the footprint you see on this page), to determine the length of the theater, or the distance from its point to point A: this can be done easily by taking the distances BC between the front channels and DE between the back, and drawing visual lines MO, NO: for the theater will have a length of AO, and the perspective point on the theater's footprint will be O. Additionally, you need to know the length and width of the channels, their number, distances, and bends; and it is especially important that although they may be slanted to the line MN, they remain parallel to each other on each side, and each touches the lines MO, NO. Now, if the straight line AO is made equal to the straight line FA, point F will be the distance point: therefore, if the theater has been depicted according to our method, it will appear to the observer standing at F as if it were a painted picture according to the laws of perspective, placed at A.

Another layout of a theater, with the way to determine the viewpoint within it.

If you need to paint the scenes of a theater that's already built, you must first carefully draw its geometric plan (as shown in this plate) to determine the theater's length or the distance from its point to point A. You can easily find this by measuring the interval BC of the first grooves and DE of the latter, then drawing the visuals MO and NO. In this case, AO represents the length of the theater, and the point of sight, or perspective, is O. Additionally, you need to know the length and width of the grooves, as well as their numbers, spacing, and angles. Be especially careful to ensure that, even if they are angled relative to line MN, each side remains parallel to itself and that they all touch lines MO and NO. If you make AO equal to FA, the point of distance will be F; and if you paint the theater according to the rules provided later, it will appear to the viewer at F as a regular piece of perspective placed at A.

Theater Scene Section.

Beyond the outline of the theater lies the section of the stage. Therefore, if we take the measurements of the height from point A, where the stage starts, and point D of the proscenium, which are above the horizontal plane FV, let there be drawn from the vertical NV both the line ADO, which reveals the inclination of the stage, and the line NO, which is parallel to FV and equal to the line AO of the seventy-third figure; the point of the theater at elevation is O; in the proscenium, however, the point of the theater is Q. If the maximum height of the stages is EB, the line OE gives the height of all the others. However, the true height of any stage is that of the major line, while from the minor one it can be seen how much the inclination of each stage appears to reduce the height of that extreme line. Furthermore, the excess by which the major line surpasses the minor one at both the top and the bottom must be carefully noted, for this is essential for understanding the seventy-fifth figure. The point M, which is as far from N as point F in the seventy-third figure is from A, indicates the location from which the theater should be observed, as we noted there.

When constructing a floor, the following rule is usually followed: the height of point O should be equal to the height of the eyes, and the elevation from A to D should be about one-ninth or one-tenth of the length of AD. It would also help to move the scenes more easily if the floor F is lower than the floor G, allowing someone to walk upright under the platform.

The Section or Profile of Scenes for Theaters.

Additionally to the Theater Plan, the Scene Section also needs to be mapped out to find the Theater's Point in Elevation. Therefore, by setting the heights of Point A, where the Stage Floor begins, and Point D of the Poscene, in relation to the Level of the Horizontal FV; from the Perpendicular NV, draw the straight Line ADO, which shows the Stage's slope; then make NO parallel to FV, equal to AO from the seventy-third figure: The Theater's Point in Elevation is O; the corresponding Point on the Poscene is Q. If EB is the highest point of the first Scene, the Line OE establishes the Height for all the others. The longer of the two Lines indicates the true Height of each Scene, while the shorter shows how much Height is lost from the Sight on the Out-line due to the angled Position of the Scenes. Additionally, pay close attention to the difference between the longer Line and the shorter, both at the top and bottom, as this is crucial for correctly understanding the seventy-fifth figure. The Point M, which is the same distance from N as F is from A in the seventy-third figure, marks where the Stage should be viewed, as mentioned there.

In setting up the Stage Floor, this rule is usually followed: the Height of Point O should match Eye Level, and the Rise of the Floor from A to D should be around one-ninth or one-tenth of the Length AD. It’s also necessary, for easier scene changes, that the Pavement F is lower than G so that a person can walk upright beneath the Floor.

Elevatio scenarum coram inspectarum: where it teaches the technique so that slanted scenery appears straight.

The clips you see in S have their width from the trace of the figure seventy-third, height from the elevation of the figure seventy-fourth, and are considered upright and inserted into the channels, all of which are also represented by the figure seventy-second in P & Q. Please note how much the floor is raised at the beginning of A, in the proscenium D, & at the theater point O. Similarly, one must observe the elevation of individual scenes, which are inclined inward due to the slant of the channels: therefore, the lines BL, AI, part C, do not appear parallel to the line of the plane, as they actually are; and the visual LF does not extend to the eye point O, but to point F. If the apparent excess that the straight line BK has at the top & bottom above the line LI is transferred to the side E of the scenes, (the same excess can also be derived from the figure seventy-fourth) and straight lines LG, IH are drawn, those lines will appear parallel to the line of the plane. If line LO is drawn, which, in conjunction with LG, makes angle GLO equal to angle BLF, the same LO will extend precisely to the eye point O, and it will be used as the visual one.

In P, we assume the scenes M & N are laid out on the floor one on top of the other, and that the two lines RT have the same distance as the two LI, and this applies to the other scenes as well. It should be noted that the lines RS and Television are the same as the lines LG and IH of scene E; however, the lines RS and Television are not parallel, while LG and IH appear to be parallel. Therefore, if a straight line RL is drawn and angles SRL and GLO are equal, the straight line RL will serve as a visual reference point for scene L, which will be the accidental eye point for painting scenes N. The lines RS and Television will be treated as parallel: anything beyond those lines on the canvas will be considered negligible and will be painted as sky or something else. The accidental eye point for painting scenes M will be at I.

The Elevation of Scenes in Front, and how the angled Scenes are made to look straight-on.

The scenes in S get their width from the layout of the seventy-third figure and their height from the elevation of the seventy-fourth figure; they are supposed to stand straight in their grooves. This is also shown in P and Q of the seventy-second figure. I want you to notice how much the floor rises from its edge A to the position D and to the theater point O. Also, pay attention to the height of each scene, which, because of the angle of the grooves, tilts inward. As a result, the lines BL and KI of part C don’t appear parallel to the ground line, even though they actually are. The visual line LF doesn’t point to the point of sight O, but to point F instead. However, if you take the apparent excess that the line BK has at the top and bottom above the line LI and transfer it to the side of the scenes E (this excess can also be taken from the seventy-fourth figure), and then draw the lines LG and IH, those lines will look parallel to the plan line. Then, by drawing the line LO so that angle GLO is equal to angle BLF, LO will point directly to the point of sight O, serving as a visual line.

In P, I assume that Scenes M and N are stacked on top of each other on the floor, and that the two lines RT are the same distance apart as the lines LI; and the same goes for the others. Please note that the lines RS and TV are the same as the lines LG and IH of Scene E; however, the lines RS and TV are not parallel, even though LG and IH appear to be. Therefore, if you draw the line RL so that angles SRL and GLO are equal, the line RL will act as a visual line, with L representing the accidental point of sight for painting the scenes on the side N; and the lines RS and TV will be used as parallels. Anything beyond those lines in the frame is considered irrelevant; you can paint it with air or whatever you like. The accidental point of sight for painting the scenes on the side M is I.

Method for outlining scenarios.

Again we have outlined the scenes set up on the stage; in B naked, in A depicted, with added projections of crowns & other decorations. The deformation of the scenes A is revealed through the usual method from the trace C, where you will see the line of the plane extended downward. The geometric trace is in D.

The Way to Outline the Designs of Scenes.

In this Plate, you have another design of scenes set up on the floor; the bare scenes are B; the painted ones are A; along with the added projections of cornices and other decorations. The draft of the scenes A is created from the plan C, following the usual method; in which you can see the ground line is lower than its actual position, for the better distinction of the parallels. The geometrical plan is D.

Modus reticulandi & pingendi scenas theatri.

After you accurately arrange the stage and the other scenes in order, each one overlapping the next as we've shown in figure seventy-five, you'll create a horizontal line where three perspective points need to be marked: one in O for painting the stage and two others on either side, specifically for the scenes on the opposite side. Now, assuming that in a small model A, there is a grid created through perfect squares; the proportional division will happen both in the line Hi of the first scene B and in the line CDs. Then, from point E, using each point of division on line Hey, you'll create visuals by using a string dipped in black dye; with these, as the figure shows, you'll need to grid scene B and then move it to the scene beneath it, and in the same way, continue to do this for additional scenes; finally, by the divisions made in line LM from point E, you'll complete the grid of the stage, which should consist of perfect squares, unlike the squares of the scenes. At the bottom of the page, the two scenes G & F show the decorations that can be painted in the scenes. However, I want you to note both the cross lines of the crown, which are not parallel to each other, and the visuals which extend to the opposite points. For such lines contain two specific difficulties in theatrical projections; to overcome them, the rules we've outlined must be precisely followed.

How to create the network or squares and paint the scenes of theaters.

After you have arranged the backdrop on the ground with great precision, placing the other elements one on top of the other as mentioned in the Seventy-fifth Figure, draw a horizontal line and mark three points of view: the point at O for the backdrop's use, and the points on the sides for the respective opposite scenes. Next, assuming that the grid of the small drawing of the first scene A consists of perfect squares, transfer those same divisions along the lines HI and CD of the first scene B. Then, using a black line, draw the visual lines from point E through the division points of HI; with the help of these visual lines, create the grid for scene B as shown in the figure. Once that’s done, set it aside and repeat the process for the next scene and so on. Finally, using the divisions made by the visual lines from point E on the perpendicular LM, complete the grid on the backdrop, which consists of perfect squares, even though the grids of the other scenes do not. The two scenes at the bottom of the plate, G and F, show what variety of ornamentation the painter can incorporate. I also want you to pay special attention to the transverse lines of the cornice, which are not parallel to one another, and to the visuals directed toward their opposite points: because the greatest challenge in describing theatrical designs lies in these two aspects; to overcome this, it is crucial that you carefully follow the rules already provided.

On horizontal projections.

Just like it's easier to shape the tops of lying columns than standing ones; (because the lines in the former are vertical, while in the latter they are visual, and no circle loses its shape) horizontal projections, which we need to draw on ceilings, are actually quicker and easier than the vertical ones we've covered so far. In order for the bases and columns to appear upright, they should be painted as if they are lying down.

We anticipate horizontal deformations from the arches, as the columns and bases are repeatedly placed on them to enhance their visibility. However, due to the difference in appearance between the side of the arch and its front, we present separate geometric representations of both in this figure.

Of horizontal perspective.

Since it's easier to describe Perspective Columns that are lying flat on the ground than those that are standing up (the lines in the latter being perpendicular, whereas in the former they are visuals, where no circle loses its shape), the horizontal projections of perspective that are suitable for ceilings, contrary to what painters usually think, are done with more ease and speed than the vertical ones we’ve discussed so far. This is because the pedestals and columns that need to look upright are painted as if they're lying on the ground.

I have introduced these horizontal designs alongside the corbels because they typically appear to support the pedestals and columns, making them more visible. Since the side of this corbel differs from its front, I have included a geometric description of each one separately.

Trace and elevation projections of the mound.

Facial features mutuli that we outlined in the 78th figure shows the feature of the footprint here; the side shows the feature of elevation. This is demonstrated by the hidden lines that extend from the facial divisions to the eye point and from the side divisions to the distance point (the eye and distance points in this and following figures are located outside the page). Lines are drawn from the intersections of these lines that define each part of the distorted footprint; using this, the elevation of the side is determined, and with the usual method, the widths and lengths of the solid mass are derived from the footprint, with heights coming from the elevation. Here and onward, we will use terms of length and height as if the plane of any perspective were vertical; in this assumption, IL would be the width of the mass, SR the height, and RL the length: when SR is truly the length, RL is the height. For a clearer description of this figure, it is important to note that the straight lines IL, LM, GH on this page contain divisions of the straight lines DC, FE, AB, in the 78th figure.

The Plan and View of a Corbel in Perspective.

The Face of the Corbel shown in the Seventy-eighth Figure acts as a Plan, while the Side functions as the Elevation; this is clear from the hidden Lines that extend from the Divisions of the Face toward the Point of Sight, and from those of the Side toward the Point of Distance; both Points, in this and the following Figure, are located outside the Plate. From the Intersections of these Lines, additional lines are drawn that define each part of the Perspective-Plan; using this method, the Elevation of the Side is also created, and the Widths and Lengths of the solid Corbel are derived, as usual, from the Plan, with the Heights taken from the Elevation. From this point forward, the terms Length and Height will be used as if the Plan of each Perspective is vertical; under this assumption, IL represents the Width of the Corbel, SR the Height, and RL the Length; although, in reality, SR is the Length and RL is the Height. To better understand this Figure, note that the Lines IL, LM, GH in this Plate have the same Divisions as DC, FE, AB in the Seventy-eighth Figure.

Horizontal projection of shaded vault.

In this form, we added our shadows to it: and if you lift it high above your eye, and look at it from the distance we gave it; you'll definitely be amazed at how it suddenly transformed into something much more beautiful.

The Horizontal Projection of a shaded Corbel.

In this figure, you have the corbel finished with its proper shades; if placed above eye level and viewed from the distance indicated here, you'll be quite surprised by the sudden and very pleasant change you’ll notice.

Stylobates of Corinth contracted horizontally.

In shaping these stylobates, we used the projection of footprints & elevation, as shown in figure twelve; this will clearly show that figure when compared with that one. Moreover, we mentioned that stylobates are usually depicted leaning on mules, as seen in figure seventy-eight.

Corinthian Pedestals in a Horizontal View.

In outlining these Pedestals, I used the Plan and Upright shown in the Twelfth Figure; this will become clear when you compare that Figure with this one. I already mentioned, in the Seventy-eighth Figure, that when painting these Pedestals, they are generally thought to be supported by Corbels.

Corinthian column horizontally distorted.

Trace & elevation of the stylobate, which we illustrated in figure twelve, provides the dimensions for the pillars being altered here, allowing us to determine the contraction of the column. We have also added its own shadows so that the method & craftsmanship of the entire operation can be more clearly seen. From these, you can see that squares & circles maintain their shape in the horizontal perspective, only gradually being confined & constricted: anything contrary to this, as some painters have taught, both in words & with their brushes.

A Corinthian Column in Side View.

The Plan and Elevation of the Pedestal shown in the Twelfth Figure also provides the measurements for creating a perspective of these Pilasters; this is where the shortening of the Column comes from. I’ve only shaded this last element so that the overall design stands out more clearly. From this, you can see that Squares and Circles in Horizontal Perspective always keep their shapes, with no changes except for gradually becoming smaller; despite what some painters have taught and practiced to the contrary.

Capitella Corinthia contracted horizontally.

You’ve got on this page the deformations of the footprint & elevation of the Corinthian capital, which we took from geometric drawings, transferring their measurements to the horizontal lines AB and elevation AC, so that it can be easily recognized where each part of the elegant capitals originates. I have no doubt that you will find horizontal deformations easier to understand than the vertical ones we've shown in figure twenty-four. For in the horizontal views, the circles of leaves are enclosed, whose centers change their latitudes from their footprints at points 1, 2, 3, 4; while the heights come from the capitals’ elevation at points 5, 6, 7, 8.

A Corinthian Capital in Perspective.

You have in this plate both the plan and elevation of the Corinthian capital, created from the geometrical descriptions, by transferring their measurements onto the ground line AB and the elevation line AC. This way, you can easily see where each part of the finished capital comes from. I have no doubt you'll find these horizontal perspectives much easier than the vertical one presented in the twenty-fourth figure. In these, the outline of the leaves is defined by perfect circles, with their centers measured from the plan at points 1, 2, 3, 4, and their heights taken from the capitals of the elevation at points 5, 6, 7, 8.

Coronix Corinthia.

If you are making crowns that have corners, the geometric elevation A will represent one side, while the section will represent the other side, B. However, you must ensure that the edges of the parts we want to shape do not interfere with the neat arrangement of the brackets. To reduce the elevation of A and section B, you need to transfer the points of different widths that they have in elevation A from the caps of the beam, frieze, and crown by drawing lines to the eye point; on the other hand, for section FH, you need to transfer the points of length by drawing lines to the distance point. With this effort, you will accomplish both deformations, one serving as a footprint and the other as elevation. In both cases, you will mark the boundary lines of the crown parts, as well as sections C & D.

A Corinthian Cornice.

If you want to describe cornices with angles, consider Elevation A to represent one side and Section B the other. However, be careful that the breaks in these parts, which are supposed to be positioned directly over the columns, do not interfere with the proper arrangement of the modillions. To create a perspective view of Elevation A and Section B, you need to transfer the points of the various widths created by the projections of the architrave, frieze, and cornice from Elevation A to the ground line EF and the elevation line EG; then draw lines to the vanishing point. On the segment FH of the line FE, mark the points of length, and draw lines from these points to the vanishing point. This process allows you to complete both contractions, where one serves as a plan and the other as an elevation. It's also necessary to draw the outline of the cornice members on each side of the angle, along with Sections C and D.

Coronix Corinthia shortened horizontally.

The power of the crown is established through the study and elevation of the eighty-fourth figure. Here, however, we set a limit on the aspects of things in order to prepare for the construction of complete buildings.

A Corinthian cornice in horizontal view.

The strength of this cornice, along with all its projections, is derived from the plan and elevation of the earlier figure. With this, I will wrap up the description of individual parts and move on to the discussion of complete structures.

Horizontal projection of column.

After we have individually described the base, the stylobate, the column, and the cornice, it seemed right to bring all these together: this way, it will be clearer how to arrange the geometric drawings so that horizontal projections can be derived from them.

The plane line is CD, and the perpendicular is CI. At A is the geometric elevation of the column length, (we assume the column is drawn as if lying on the ground.) At B is its geometric footprint, with divisions of width on the line ER. Length points will be transferred to the plane line CG, and height points EC will be transferred to CF, drawing straight lines from divisions CG to the distance point and from divisions CF to the eye point. Through the visual section CO, perpendiculars will be raised, and the elevation H will be completed, from which the shiny column L will emerge.

If you want to shape another column based on the footprint of column M, you should take its width from column B; and the section should extend into N, so that column P can be derived from this as if from an elevation. If you wish to add another column at the corner, you can easily complete it using sections HN.

A Column in Horizontal View.

After the individual descriptions of a corbel, pedestal, column, and cornice, I've combined them all here so you can better understand how to arrange geometric elevations for the purpose of horizontal perspective.

The line of the plan is CD, the perpendicular is CI; the geometric elevation of the length of the column, assumed to be lying on the ground, is A. The geometric plan is B, with the divisions of its width on the line ER. The length points are transferred to the plan line CG, and the height points EC into CF; from the divisions of CG, lines are drawn to the point of distance, and from those of CF to the point of sight. From the sections of the visual CO, perpendiculars are raised, and the elevation H is completed, from which the finished column L is derived.

If you want to outline another column on Plan M, the widths must be taken from Column B, and you should design another profile in N, which acts as an elevation for creating Column P. If another column is needed at the angle, the profiles HN will help you accomplish that easily.

Practical preparation needed for the following shape and for horizontal projections on ceilings or domes.

This figure in AA shows one of the four walls of the hall, whose true height IH you can seemingly raise up to L, by painting on the ceiling or dome a series of balusters. In B is the geometric mark of a quarter of the ceiling. In C, there's the elevation of half the width. In D is the section of the crown and mutules. In E is the elevation of half the length. In F is the eye point, and in G is the distance point; thus the total distance is GF.

The preparation needed for the following figure, and for all other horizontal perspectives, whether on flat or vaulted ceilings.

The Figure AA shows one of the four walls of a hall, which you would want to look raised to L by painting a balustrade on the ceiling. B is the geometric plan of the fourth section of that ceiling; C is the elevation of half the width; D is the section of the cornice and corbels; E is the elevation of half the length. F marks the point of sight, and G marks the point of distance; thus, the distance itself is FG.

Horizontal projection of the pomegranates in figure seventy-eight, with a short distance.

For clarity, the entire layout is divided into four parts. The first includes the contraction of the footprint and elevation, which are completed using the standard method. The line AOV is horizontal, and Before Christ is the plane line. The eye point is O, at a distance of E. The second part includes section L, which provides projections of the beams and other parts, derived from section D of the seventy-eighth figure, distorting it at angles B & C. The third part includes the complete drawing without shadows: the final part includes the same drawing with shadows.

Due to the angle of view being slightly away from the eye, this drawing seems overly large and oddly shaped. However, if you look at the figure from the distance EO, all awkwardness will disappear.

To avoid confusion for the inexperienced, it's important for a skilled painter to create two copies of their works, where the differences are minimal; one is clearly displayed, where the distance point is far enough from the viewer's eye to avoid any unpleasantness. The other, however, is to be used in secret within the work itself.

If turtles are to be trapped, a special net must first be made for them; since this is difficult and cannot be easily explained to a few, it is reserved for another work.

The horizontal projection of the balustrade of the eighty-seventh figure, viewed from a short distance.

To better illustrate this figure, I’ve divided the entire ceiling into four parts. The first part shows the plan and elevation in perspective, using the standard approach; AOV represents the horizontal line, BC shows the plan line, O is the point of sight, and E is the distance point. The second part includes section L, which displays the projections of the corbels and other elements taken from section D of the eighty-seventh figure, drawn at angles B and C. The third part outlines the perspective without shadows, while the fourth part presents the same view completely shaded and finished.

Through the close approach of the Point of Distance to the Point of Sight, you might think this drawing looks too wide and might have a negative effect. But once you see it from the proper distance EO, you'll find that all those doubts disappear.

When you're working with people who aren't experienced in these matters and need to create something for a short distance, your best option is to create two sketches: one for public display, where you can set the vanishing point further from the viewer's eye to avoid distortion; and the other you can use privately while doing your work.

If you're going to paint arched or vaulted ceilings, you first need to create a specific type of net or lattice work in them. This task is complicated and can't be explained in just a few words, so I will cover it in another volume.

Horizontal projection of architecture in a square ceiling.

If the square is distant from the eye, it will be possible to depict an architecture similar to it. A is the geometric elevation; however, it is distorted in B and C, taking on the role of a trace and elevation. Half of one of the four parts can be useful in the entire work, either by pressing the paper or by perforating it, allowing finely ground charcoal to be inserted through the holes.

A horizontal projection of architecture on a square ceiling.

If the ceiling is square and far from your view, you can paint something like this architecture in it. A shows the geometric elevation; the same design reduced into perspective in B and C serves as a plan and elevation. Half of one of the four parts may be enough for the draft of the entire work, either by tracing over the lines on the paper or by poking small holes in it and applying finely powdered charcoal through them.

Horizontal projection of the dome.

The start of this process will start with a geometric outline, where two series of circles represent the columns; other lines represent the stylobates, projections, bases, and the crown. The baseline is AB, the horizontal line is CD, and the vertical is AD. The eye point is O, at a distance of D; therefore, this figure should have a height of Do above the eye. The eye point is placed outside the dome so that those observing it are less fatigued and can see more of the architecture and craftsmanship; it would be the opposite if the eye point were in the middle. Thus, the points on line EF will be transferred to part AG of line AD. The center I of the outline will be transferred to H, and from all these points, visual lines will be drawn to O. Then, using the height of the dome and the divisions of its individual parts and the lantern, transferred to line AB, straight lines will be drawn to the distance point D. Where these intersect with the visual line AO, vertical lines will rise, and their intersections with the visual HO will provide the centers for each circle. From the visuals AG, it is necessary to draw the limit lines for the columns and the crown; as would be the case if the outline had a geometric elevation extracted. With this established, you will proceed to the optical delineation of the dome, transferring into the perpendicular EO using centers with the help of the parallels Hey, LN; and with a radius of LM, a circle NP will be created for the top of the crown: with a radius of ST, circle QR Code will be made, and so forth for the others. How the crown's tops are related to the eye point through straight lines from the angles of the outline is shown by numbers 1, 2, 3, 4; the side lines of the tops extend towards their respective circle centers, as seen in N 3, 4. In the outline, to avoid taking too much space, we have omitted minor details.

From this, it’s clear that it’s necessary to create a geometric outline of the entire dome, and it’s not enough to just outline a single column, since each one requires its own specific adjustments. When the actual work is being drawn and painted, you won’t be able to take it from a small model using a grid. Instead, you will need to lead visual lines to their respective positions and find the centers of all the circles. By marking a string at each center, you can easily complete all the circumferences.

A Cupola in horizontal view.

In carrying out this work, you should start with the geometric plan; in which the two rows of circles represent the columns, and the other lines indicate the pedestals, along with the projections and breaks of the bases and cornices. The line of the plan is AB, the horizon line is CD, and the perpendicular line is AD. The point of sight is O, and the point of distance is D; therefore, this figure should be placed as high above the eye as the height DO. I positioned the point of sight slightly outside the dome to reduce eye strain when viewing the work, allowing for a broader perspective of the architecture than if the point of sight were in the center. The points on line EF are transferred to AG, which is part of line AD. The center of plan I is extended to H, and visual lines are drawn from all these points to O. Then, position the heights of each part of the dome and lantern on line AB; from those division points, draw lines to the point of distance D, and where they intersect the visual line AO, erect perpendiculars that meet line HO; these points become the centers of the various circles. On the visuals, between AG, outline the columns and cornices just as you would when lifting a geometric upright from a plan. Once that's done, you can begin illustrating the dome itself in perspective by transferring the various centers of HO into the perpendicular EO, using parallels to HI, such as LN, &c. At the center, with the interval LM, draw the circle NP for the nose of the cornice, and with the semi-diameter ST draw the circle QR, and so on for the rest. The numbers 1, 2, 3, 4 indicate how the breaks of the cornice are determined by lines extending from the corners of the geometric plan toward the point of sight until they intersect the circle. The returns of these breaks are made by lines pointing to the centers of their respective circles, as evident from N 3 and N 4. In this plan, I have left out the corbels so as not to overcrowd the work.

Hence, there's a need to create a complete geometric plan of the entire dome, as a plan of a single column isn't enough; each one needs its specific outline. When you're preparing the actual work for painting, you can't just rely on a small sketch made with a grid or net; instead, the visual lines should be accurately placed, and the various centers determined. By securing strings, you can easily outline the circumferences of all the circles.

Tholus figure ninety, with lights and shadows.

The framework you see on this page promises itself a longer life than the one I painted on the flat canvas of significant size in 1685 at the Church of St. Ignatius at the Roman College. Therefore, if some misfortune should take it away, there will be those who will restore it to a better state. Some architects were amazed that I placed the front columns on the brackets, as they wouldn’t do that in solid buildings. However, my dear friend the Painter freed them from all worry and pledged for me that he would immediately repair any damage if the brackets were to weaken and cause the columns to collapse.

The Dome of the Ninetieth Figure, with its Lights and Shadows.

The Cupola in this Plate will likely last longer than the one I painted on a very large Table for the flat Ceiling of the Church of S. Ignatius of the Roman College, anno 1685. If that one gets damaged for any reason, this one can serve as a better replacement. Some Architects didn’t like my idea of placing the advanced Columns on Corbels, claiming it’s not something done in solid Structures; however, a certain Painter, who is a Friend of mine, put their concerns to rest by saying that if at any point the Corbels became overloaded with the weight of the Columns and risked collapsing, he would cover the repair costs himself.

Tholus octangularis.

From the circle, an octagon will be formed by taking half of the quadrant of the circle, so that each side of the octagon is obtained. On these sides, the geometric outline of the entire architecture will be distributed, with the projections of all the parts, according to the method we maintained in the circular boundary of the ninetieth figure. It would also be useful to elevate the geometry of the entire Work; although due to space constraints, I have overlooked it. Then, with one point of the compass placed at the center of the circle, the other point will stretch to the height of the individual projections between the space A & B, as you see here: and with the help of parallels, everything will be transferred onto line CD, to create the optical distortion that the elevation section requires, along with other preparations, as shown in the previous figure. Here too, using circles, we need to find the extreme points in the protrusions of each architectural part: so that by connecting the points with straight lines, which will shape the faces of the octagon, the entire Work will be completed.

An Octagonal Cupola.

From the Circle, outline the Octagon by taking half the Quadrant of the Circle for each Side of the Octagon. On these Sides, the entire Geometric Plan of the Architecture should be laid out, with the Projections of all its Parts, just like in the circular Border of the Ninetieth Figure. It would also be helpful to create the Geometric Elevation of the entire Project, although I've left it out here due to space constraints. Next, place one Point of the Compass in the Center of the Circle and extend the other to the Height of the various Projections between A and B, as illustrated in the Figure; then, using Parallel Lines, transfer them all into the Line CD, to put the Profile of the Upright into Perspective, and draw the other Necessary Elements, as shown in the previous Figure. In this case, too, the Circles reveal the extreme Points of the Projections of the different Parts of the Architecture; by connecting these Points with straight Lines that match the Shape of the Octagon, the entire Work is finished.

Vestige of the Temple of St. Ignatius in the city of Louis.

I've decided to conclude this book with the figure of ninety-two; however, to satisfy the requests of friends who wish to learn the method of optical networks used on irregular surfaces, I have decided to make public the method of constructing it with the figure eighty-eight. By means of this very network, I have outlined not only the building that will soon be represented but also all the figures of the turtle of the Louisian temple, which I am currently working on illustrating. This same network, which will be the final figure of this book, will give our work its completion; for there is no surface where those studying can’t complete their outlines according to the rules of Perspective.

This figure shows the outline of the entire temple. Even though I only need the turtle between the main entrance and the dome, it will still benefit those interested in architecture to contemplate the elegance and symmetry of the whole work at their leisure.

The Geometric Layout of the Church of St. Ignatius in Rome.

I have once decided to finish this book with the Ninety-second Figure, but at the request of some friends who wanted to learn how to create perspective networks for irregular surfaces, as mentioned in the Eighty-eighth Figure, I decided to share how to do that. With this network, I was able to illustrate not only the architecture we're discussing but also every figure in the vault of the Church of S. Ignatius, which I'm currently painting. The method is explained in the last figure of this book, fully completing it; there is no surface, no matter how irregular, that a dedicated person can’t describe using these rules for any perspective they need.

This figure shows the entire layout of the church. Although my current plan only required the vault of the nave, spanning from the main entrance to the dome, I thought it would still be interesting for architecture enthusiasts to see the complete design, which is well-known for its elegance and proportion.

Orthography of the Louisian Temple.

Vermont I'm more pleased to present to you the detailed drawings of the architecture or elevation of the Ludovician temple, along with all the measurements that are commonly referenced; I've added the dome based on the author's idea. However, in place of it, I've placed a tapestry in A & B featuring the depicted dome, as mentioned earlier in figures ninety and ninety-one.

The Spelling, or Geometric Layout of the Interior of S. Ignatius’s Church.

To enhance your understanding, I’ve provided a lengthwise section of the Church’s geometric structure along with all its measurements that match the design plan. I’ve also included the cupola designed by the author. Since it hasn’t been constructed yet, you’ll find the painted cupola mentioned earlier between A and B in the ninetieth and ninety-first figures.

Aliæ præparationes ad figuras 98. & 99.

From this figure divided into four parts, you will learn from one glance the method I used to depict the optical representation of the Louisian temple. The first part shows the right side of the dome between the temple entrance and the vault. The second part contains the outline of the same dome, marked by arches and crescent shapes. The third part includes the right side of the dome up to the top of the windows, where the architecture we illustrate in the arch begins. The fourth part represents the geometric outline of the arch, highlighting the projection of the arches at the top of the previously mentioned windows. We assume that the solidity is the same for both the depicted building and the temple's nave; only the columns that correspond to the temple's pillars extend outside the building.

Other Preparations for the Ninety-eighth and Ninety-ninth Figures.

By this figure divided into four parts, you will quickly notice the method I used to start the perspective design of this Church of S. Ignatius. The first part shows the right-hand side of the vault between the door and the dome. The second contains the plan of the same vault, with its arches and lunettes. The third part represents the same right-hand side, up to the top of the windows, where the architecture painted on the vault begins. The fourth part contains the geometrical plan of the painted section of the vault, along with the lunettes created by the arches above the heads of the mentioned windows. The arrangement of the painted architecture above is the same as that of the nave of the church, except that, corresponding to the pilasters below, I have imagined columns projecting over the work.

Aliæ præparationes ad figuras 98 & 99.

The first part of this figure is divided into three sections, representing the geometric elevation of the temple's side above the cornice, and the building in the dome painting. The second part includes the largest dome arch and the geometric elevation of its facade. The third part shows the outline of the entire building to be painted in the dome, which is the same size as the width of the nave, as we mentioned earlier. Furthermore, the geometric outline is just as essential for painting the building as it is for constructing it from solid materials, as we noted elsewhere.

Other Preparations for the Ninety-eighth and Ninety-ninth Figures.

In this figure, which has three parts, the first shows the geometric elevation of the right side of the nave above the cornice and the design painted on the vault. The second includes the large arch of the vault and the geometric elevation of the front of that design. The third part displays the overall plan of the work painted on the vault, which has the same extent and layout as that of the nave, as mentioned earlier. The geometric plan, as I mentioned before, is just as essential for painting a design in perspective as it is for constructing a solid structure.

Alia preparation for figures eighty-eight and eighty-nine.

To make the optical projection of the outline and elevation of the fourth part of the entire work clearer, I quadrupled the measurements of each individual part, maintaining the same method in this drawing, which was explained in figures eighty-six, eighty-seven, eighty-eight, and eighty-nine. The eye point is located in the center of the church nave; the distance point is on the line from which the arch of the dome begins.

Another Preparation for the Ninety-eighth and Ninety-ninth Figures.

To make the perspective of the fourth part of the plan and elevation of this work clearer, I've made the measurements of each part four times larger than before; and I've used the same method in this depiction as described in the eighty-sixth, eighty-seventh, eighty-eighth, and eighty-ninth figures above. I've placed the viewpoint in the center of the church nave, and the point of distance is on the line from which the arch of the vault starts.

Quadrants of horizontal architecture in the arch, with lights and shadows.

You got on this page a diagram of the entire work, extracted in the usual manner from the previous one: namely, perpendicular lines are taken from the angles of the outline using a compass; meanwhile, parallel lines are drawn from the angles of elevation, along with visual lines to the eye point.

A fourth part of the architectural design, painted on the vault of St. Ignatius's Church; featuring its lights and shadows.

In this figure, you have a quarter of the entire work, created based on the previous figure, in the usual way; specifically, by using the compass to take the vertical lines from the corners of the plan, the horizontal lines from the elevation, and the sight lines to the viewpoint.

Change the whole project.

Thinking about the differences between the two quadrants, both in length and in light & shadows, I thought it best to treat each separately; that way, I could remove any difficulty you might have in illustrating them.

Another part of the entire design.

Due to the difference between the two parts, both in length and in their lights and shadows, I decided to describe them separately so that you would have no trouble understanding the entire work.

Tortoise networking methods.

In sketches made on flat surfaces, there are two grids, as is well known. One is drawn on a template, and the other is on the surface where the actual work is to be painted. However, turtles require three grids. The first is on the template, which we assume has been drawn according to the rules of horizontal perspective. The second grid consists of strings and is suspended; you can see its geometric shape in M. The spots where the pegs that hold the strings are to be placed are represented by the straight lines AB, EF: the optical distortion of the grid is in N. The point of view is O, with a distance of LO. Therefore, if you imagine, during nighttime, the light of a candle or lamp existing at O, and from the grid of strings, shadows are cast onto the turtle, then those same lines will be colored with a brush, and this will provide the third grid necessary for painting the turtle.

I said, imagine that in a covered shell on a surface, far from the net and even more from the light, shadows cannot be cast or appear clear and defined as they should. So, where the distance is too great, place the end of the line at point O; from there, extend it towards the shell, using it like a ray and the light from a candle to mark the location of the shadow. It will also help if you move the line close to the light of a candle that you hold near it. With these and other supports, along with your effort, you will bring colors to the shadowy lines, and thirdly, you will complete the network. You could also stretch a net of threads at a small distance from the crown, say at GH, where the base of the building begins; that way, the shadows in the arch are more distinct and visible.

You will carefully ensure that the sample measurements don't differ at all from the turtle's measurements: that the net intersects at angles, arcs, or the turtle's crevices, precisely matching the sample net. Lastly, if there are flaws that can't be fixed, you shouldn't worry about them; just know that all the rules of horizontal perspective must be strictly followed, whether in painting humans or animals, or in columns or crowns.

The method for drawing the grid or lattice work on vaults.

For works on a flat surface, two grids are enough, as mentioned earlier: one drawn on the reference image and the other on the surface to be painted. But for arched surfaces or vaults, three are needed: one created on the reference image, which should be drawn according to the rules of horizontal perspective. The second is a frame made of small cords or threads that will be hung up, shaped like an M. The lines AB and EF show where this frame should be fixed, similar to the perspective N. The point of sight is O; the distance is LO. So, if you picture a lamp or candle placed at point O during the night, the shadows of the threads cast onto the vault, traced with a pencil, create the third grid needed for painting.

I say, if you picture a lamp positioned like this; because either the scaffolding to the vault, or the significant distance of the vault from the net, or a combination of both from the light, may prevent the shadows from appearing at all, or at least make them so faint that they're not clear enough for the purpose. So, when this happens, instead of the light, attach one end of a thread at point O; and stretching the other end to the vault, use it as a ray from the lamp or candle to outline the location of the shadows. It will also be very helpful to complement the movement of the thread with the light of a candle you have on the scaffolding, holding it close to the thread itself. With this and other tips that your own effort will suggest, you can lay these shadows in colors and complete the third network required. The frame of threads can also be set closer to the vault at some distance above the cornice, like at GH, where the painted architecture starts; this way, the shadows cast on the arch will become more visible and distinct.

You need to be very careful that the measurements of your copy match exactly with those of the vault, so that the network placed in the angles, arches, and lunettes of the vault aligns perfectly with your copy. Finally, to avoid serious mistakes, make sure that all these rules of horizontal perspective are followed as strictly for figures of people or animals as they are for painting columns, cornices, and similar structures.

Explication of the lines of the plane, & horizon, points of the eye, & distance; on this last point in more detail.

Three lines with different names and functions, along with two essential points, are needed for any optical representation: the first is called the plane line, the second is the horizontal one where the eye point is located; I will talk about the third in elevations: one of the two points is assigned to the eye, commonly known as the eye point; the other is assigned to the distance, from which it gets its name. The eye point is well known, whereas the distance point is not as familiar; therefore, I will focus on explaining this and to clarify what it is and how it should be formed, I selected a geometric description of a church, divided into three parts: the footprint, the section, and the interior face, on which someone wants to paint or depict something optically, so that it extends to the measurement of the opening of square P, as you have in the footprint, and to the measurement of the depth Q, which you have in the section.

On the surface CCCC, which you consider to be a representation, you have a method to arrange the aforementioned points and lines. Hi will be the plane line: NON will not be a horizontal line, which typically is situated at a distance from the plane line corresponding to a person's height, as you can see in B. The eye point will be at O; the distance point will be at N, whichever side you prefer. This point N should be as far from point O as you wish it to be in order to perceive the depth of that square PQ, as you can see in the example of the footprint and section; where I present the object as if in its natural state; here point N is as far from O as a person is from A to DE, and person B in the section is from FG, where there is a wall to be painted or drawn.

If you look further into this detailed description, you will see how well the square P corresponds in the plane, and the elevation Q, to the natural state of the object in the sectional perspective presented on face CCCC, which is the drawing. You will observe the visual lines that intersect the area RS, and similarly intersect the area Television in elevation: and the segment of the visuals XZ in the section corresponds to YK in elevation, which is not without demonstration.

A Breakdown of the Lines of the Plan and Horizon, and of the Points of View and Distance; but especially this last one.

To start any design in perspective, you mainly need three lines and two points: One line where the feet are placed, called the line of the plan or ground line; the second line where the eye is located, called the horizontal line; I’ll explain the third line in the elevations. One of the points corresponds to the eye, and the other to the distance. The first point is widely recognized, while the second is not as well understood, even though it’s very useful for showing the space or depth of each object. Therefore, I will spend some time explaining the point of distance; to clarify what it is, I have chosen the geometrical description of a church, which is divided into three parts: viz. the plan, profile, and inner face; in the center of which face, one would paint a piece of perspective that seems to recede just as much as the square P in the plan and the depth Q in the profile.

On the Face CCCC, which represents the Design, you can see how the two Lines and the two Points are arranged. HI is the Ground line. NON is the horizontal line, usually set at a person's height above the Ground line, like in B. The Point of Sight is O, and the Point of Distance is N, on whichever side you choose. This Point N must be as far from O as the Distance you decide to place yourself to view the Depth of the Square PQ; as shown in the Plan and Profile, where you see everything in its natural Position. In those, N is as far from O as the Man in A is from DE; or the Man B in the Profile is from FG, which is the Wall that needs to be drawn or painted on.

If you take a closer and more detailed look at this Description, you'll notice how well the Square of the Plan P and the Elevation Q match up, almost as if they were naturally put into Perspective on the Face CCCC, which is the Draft. You can see that the Visuals intersecting Space RN in the Plan also cut through the same Space TV in the Upright. Additionally, the Segment of the Visuals XZ in the Profile corresponds to that of YK in the Elevation, which doesn't require any proof.

Optically outlined square.

After you’ve drawn a separate geometric square A on paper, create two parallel lines that are spaced apart at the height you’ve set for the eye point. The lower line will be the plane line, while the upper line will be the horizontal line, on which the eye points O and the distance E will be placed, whichever side you prefer: the distance line should not be shorter than the size of the things you’re describing. Next, use a compass to transfer the width of square A to CB, along with the visuals to the point O; similarly, transfer the length of the square to DC, drawing a line from point D to the distance point E, crossing through the visual CO, and where that intersects, you will have the endpoint of the optical square GFCB, drawing a parallel to the plane line at F.

To wrap this up more quickly, I folded the paper several times, just like you have in A.

A Square in Perspective.

After you've drawn the Geometrical Square A on a separate piece of paper, make two parallel lines, spaced apart as high as you want the eye level to be. The lower line is the ground line, and the upper line is the horizon, where you'll place the points of sight O and distance E on whichever side you choose. The distance line shouldn't be shorter than the extent of the object you're trying to depict in perspective. Then, using your compass, set the width of Square A on CB, and draw lines to point O. From the length of the square transferred to DC, draw a line from point D to distance E. Where that line intersects the visual line CO, draw a line parallel to GF; this will give you the square in perspective GFCB.

For quicker processing of this, I usually fold the paper like you see in A.

Rectangular on one side longer visually.

Whatever you saw in the nearby square, you will do in the present. You transfer the latitude Before Christ into BC, and the longitude into CD, leading the latitude BC to the eye point O, and the longitude CD to the distance point E. Where this line intersects the visual CO, it will be the boundary of the aforementioned rectangle FG, BC leading parallel, as before.

An Oblong Square in Perspective.

What was done in the previous step, repeat in this Third Figure. Transfer the Width BC into BC, and the Length into CD, drawing the Width BC to the Point of Sight O, and the Length CD to the Point of Distance E. Where this intersects the Visual CO, complete the Square FG, BC, by drawing the Parallel, just like before.

Double optical square.

Similarly, construct the double square A by transferring with a compass or by doubling a paper, the width of any line, as you see at points 1, 2, 3, 4, 5, 6, on the plane line at the same numbers, and transfer those visuals to the point O. Then transfer the lengths 7, 8, 9, 10, on the plane line at the same numbers, and draw lines from these to the distance point E. Where these lines intersect the line 6, 7, O, they become parallel lines to the plane line, and a square is formed; you will create the same construction for the second and third squares, easily from what has been said.

A double square in perspective.

The double Square A is created in the same way as the previous one, by measuring the width of each line using either Compasses or folded paper, as shown by the points 1, 2, 3, 4, 5, 6 on the baseline marked with the same numbers; then, draw lines to the Point of Sight from these. Next, transfer the length points 7, 8, 9, 10 onto the baseline, as indicated by the same numbers; and direct their lines to the Point of Distance E. Where these intersect the lines 6, 7, O, draw parallels to the baseline, and the Square is finished. The same process applies to drawing the middle Square and the one on the other side.

Quadrant footprints with elevations.

This figure is divided into two parts; in the upper part, you see three optical squares lightly shaded, spaced apart as indicated along the line of the plane. BC will be the first square. The second will be at EF. So, if you place the length of the square at BCE and extend it to the distance, it will intersect at DD with the visual AO. If you similarly place another length of that same square at EF and extend it to the distance line, you will have the second square visually. You will do the same for the third and for any others that need to be distributed.

In the second part. If you want to create the same outlines for the elevations of cubes and stylobates, as you see in the lower part of the figure, it will be enough to raise hidden and visible lines from every corner of the outlines, determining the height of face L of the first cube, and the angles of that face will give the height of all the others.

Actually, you can also create the same number of cubes without hidden lines, just by using the visible ones, as you see in the three presented as shaded and bright, whose verticals are taken from the corners of the marks, as shown in the upper figure in H, and the flat lines are translated from the angles of elevation, as it appears in F.

Various designs of squares, along with their elevations.

I’ve split this Figure into two Parts. In the top part, you see three Squares in Perspective, slightly shaded and spaced apart according to where they sit on the Ground-line. BC is the first Square, and EF is the second. If you mark the Length of a Square on BC and draw Lines to the Point of Distance, they will meet the Visual AO at DD. Similarly, if you mark another Length of that Square on EF and draw to the Point of Distance, you'll get the second Square in Perspective. You can do the same for the third Square and as many as you need.

In the second part, you can see that if the elevations of cubes or pedestals are needed based on the plans mentioned earlier, it would be enough to raise the hidden and visible lines from every angle of the plan. By determining the height of the face L of the first cube, the angles of that face drawn to the viewpoint provide the height of all the others.

You can create the same cubes without hidden lines, drawing only the ones that are visible, as you see in the three completed and shaded cubes. The vertical lines are measured with a compass from the corners of the plan, as shown in HI of the upper figure, and the horizontal lines are transferred from the corners of the elevation, as in FG of the same figure.

Modus delineandi opticè sine lineis occultis.

Wanting an easy way to explain this concept, I will provide a method for lifting bodies without hidden lines, as I mentioned earlier; I will show here how to obtain five shaded cubes from their outlines and elevations.

You need to make two preparations, if you'd like, on separate sheets of paper. The first will be to create a geometric outline and elevation, as you see in B & A. The second will involve distributing the width of the outline B along the line of the plane, say at NM, and in the two adjacent ones: Its length MX drawn to the distance D intersects visual MO at R. The slanted space E is also useful for the other two squares positioned on the same line of the plane; their angles, shifted by the distance B, will give the same angles between visuals NO, MO. With this established, draw a perpendicular line to angle N, which is always necessary in geometric elevations; this is the third line I mentioned earlier. Then transfer the height A to NF, using visuals FO, NO, and you'll find the height ST. The same will happen with the others.

You should know how to use the aforementioned preparation to build shadowy and unadorned stylobates.

So, arrange another sheet with two lines, clearly horizontal and flat, along with the point of view O, and a perpendicular V, of the same measurement as the preparation mentioned earlier, and you can see how I did it. Next, use a compass NF to check if 1, 5, and 2, 6 are equal. Measure ST as well, and you'll find that 7 and 3 are equal; then, draw flat and visual lines to the point of view, and you'll have the upper plane of the cube at 1, 2, 3, 4. You need to do the same for the others. In short: the angles of the steps will give you perpendicular lines, and the angles of elevation will give you flat lines; and this will always be the case.