Theory and Practice of Perspective

by G. A. Storey

Overview

Leonardo da Vinci declared that the first lessons for all aspiring artists should involve perspective, and this authoritative guide assists artists at all levels in following the master's advice. Its scores of concise chapters cover a vast range of subjects, offering a comprehensive view of one of art's most difficult challenges: the accurate re-creation of natural perspective.
Discussions of theory encompass definitions, both scientific and informal; the horizon and the points of sight and distance; and rules and conditions of perspective. The majority of the text examines the practice of perspective, featuring instruction on how to reproduce shape, distance, proportion, shade, shadow, reflection, and other aspects that endow two-dimensional works with lifelike qualities. More than 300 illustrations and diagrams make this an exceptionally clear and thorough treatment and an essential guide for students of art, architecture, and design.

Product Details

ISBN-13:	9780486147000
Publisher:	Dover Publications
Publication date:	03/05/2013
Series:	Dover Art Instruction
Sold by:	Barnes & Noble
Format:	eBook
Pages:	288
File size:	26 MB
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The Theory and Practice of Perspective

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By G. A. Storey

Dover Publications, Inc.

Copyright © 2006 Dover Publications, Inc.
All rights reserved.
ISBN: 978-0-486-14700-0

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CHAPTER 1

BOOK FIRST

THE NECESSITY OF THE STUDY OF PERSPECTIVE TO PAINTERS, SCULPTORS, AND ARCHITECTS

LEONARDO DA VINCI tells us in his celebrated Treatise on Painting that the young artist should first of all learn perspective, that is to say, he should first of all learn that he has to depict on a flat surface objects which are in relief or distant one from the other; for this is the simple art of painting. Objects appear smaller at a distance than near to us, so by drawing them thus we give depth to our canvas. The outline of a ball is a mere flat circle, but with proper shading we make it appear round, and this is the perspective of light and shade.

'The next thing to be considered is the effect of the atmosphere and light. If two figures are in the same coloured dress, and are standing one behind the other, then they should be of slightly different tone, so as to separate them. And in like manner, according to the distance of the mountains in a landscape and the greater or less density of the air, so do we depict space between them, not only making them smaller in outline, but less distinct.'

Sir Edwin Landseer used to say that in looking at a figure in a picture he liked to feel that he could walk round it, and this exactly expresses the impression that the true art of painting should make upon the spectator.

There is another observation of Leonardo's that it is well I should here transcribe; he says: 'Many are desirous of learning to draw, and are very fond of it, who are notwithstanding void of a proper disposition for it. This may be known by their want of perseverance; like boys who draw everything in a hurry, never finishing or shadowing.' This shows they do not care for their work, and all instruction is thrown away upon them. At the present time there is too much of this 'everything in a hurry'. and beginning in this way leads only to failure and disappointment. These observations apply equally to perspective as to drawing and painting.

Unfortunately, this study is too often neglected by our painters, some of them even complacently confessing their ignorance of it; while the ordinary student either turns from it with distaste, or only endures going through it with a view to passing an examination, little thinking of what value it will be to him in working out his pictures. Whether the manner of teaching perspective is the cause of this dislike for it, I cannot say; but certainly most of our English books on the subject are anything but attractive.

All the great masters of painting have also been masters of perspective, for they knew that without it, it would be impossible to carry out their grand compositions. In many cases they were even inspired by it in choosing their subjects. When one looks at those sunny interiors, those corridors and courtyards by De Hooghe, with their figures far off and near, one feels that their charm consists greatly in their perspective, as well as in their light and tone and colour. Or if we study those Venetian masterpieces by Paul Veronese, Titian, Tintoretto, and others, we become convinced that it was through their knowledge of perspective that they gave such space and grandeur to their canvases.

I need not name all the great artists who have shown their interest and delight in this study, both by writing about it and practising it, such as Albert Dürer and others, but I cannot leave out our own Turner, who was one of the greatest masters in this respect that ever lived; though in his case we can only judge of the results of his knowledge as shown in his pictures, for although he was Professor of Perspective at the Royal Academy in 1807—over a hundred years ago—and took great pains with the diagrams he prepared to illustrate his lectures, they seemed to the students to be full of confusion and obscurity; nor am I aware that any record of them remains, although they must have contained some valuable teaching, had their author possessed the art of conveying it.

However, we are here chiefly concerned with the necessity of this study, and of the necessity of starting our work with it.

Before undertaking a large composition of figures, such as the 'Wedding-feast at Cana', by Paul Veronese, or 'The School of Athens', by Raphael, the artist should set out his floors, his walls, his colonnades, his balconies, his steps, &c., so that he may know where to place his personages, and to measure their different sizes according to their distances; indeed, he must make his stage and his scenery before he introduces his actors. He can then proceed with his composition, arrange his groups and the accessories with ease, and above all with correctness. But I have noticed that some of our cleverest painters will arrange their figures to please the eye, and when fairly advanced with their work will call in an expert, to (as they call it) put in their perspective for them, but as it does not form part of their original composition, it involves all sorts of difficulties and vexatious alterings and rubbings out, and even then is not always satisfactory. For the expert may not be an artist, nor in sympathy with the picture, hence there will be a want of unity in it; whereas the whole thing, to be in harmony, should be the conception of one mind, and the perspective as much a part of the composition as the figures.

If a ceiling has to be painted with figures floating or flying in the air, or sitting high above us, then our perspective must take a different form, and the point of sight will be above our heads instead of on the horizon; nor can these difficulties be overcome without an adequate knowledge of the science, which will enable us to work out for ourselves any new problems of this kind that we may have to solve.

Then again, with a view to giving different effects or impressions in this decorative work, we must know where to place the horizon and the points of sight, for several of the latter are sometimes required when dealing with large surfaces such as the painting of walls, or stage scenery, or panoramas depicted on a cylindrical canvas and viewed from the centre thereof, where a fresh point of sight is required at every twelve or sixteen feet.

Without a true knowledge of perspective, none of these things can be done. The artist should study them in the great compositions of the masters, by analysing their pictures and seeing how and for what reasons they applied their knowledge. Rubens put low horizons to most of his large figure-subjects, as in 'The Descent from the Cross', which not only gave grandeur to his designs, but, seeing they were to be placed above the eye, gave a more natural appearance to his figures. The Venetians often put the horizon almost on a level with the base of the picture or edge of the frame, and sometimes even below it; as in 'The Family of Darius at the Feet of Alexander', by Paul Veronese, and 'The Origin of the "Via Lactea"', by Tintoretto, both in our National Gallery. But in order to do all these things, the artist in designing his work must have the knowledge of perspective at his fingers' ends, and only the details, which are often tedious, should he leave to an assistant to work out for him.

We must remember that the line of the horizon should be as nearly as possible on a level with the eye, as it is in nature; and yet one of the commonest mistakes in our exhibitions is the bad placing of this line. We see dozens of examples of it, where in full-length portraits and other large pictures intended to be seen from below, the horizon is placed high up in the canvas instead of low down; the consequence is that compositions so treated not only lose in grandeur and truth, but appear to be toppling over, or give the impression of smallness rather than bigness. Indeed, they look like small pictures enlarged, which is a very different thing from a large design. So that, in order to see them properly, we should mount a ladder to get upon a level with their horizon line (see Fig. 66, double-page illustration).

We have here spoken in a general way of the importance of this study to painters, but we shall see that it is of almost equal importance to the sculptor and the architect.

A sculptor student at the Academy, who was making his drawings rather carelessly, asked me of what use perspective was to a sculptor. 'In the first place,' I said, 'to reason out apparently difficult problems, and to find how easy they become, will improve your mind; and in the second, if you have to do monumental work, it will teach you the exact size to make your figures according to the height they are to be placed, and also the boldness with which they should be treated to give them their full effect.'

He at once acknowledged that I was right, proved himself an efficient pupil, and took much interest in his work.

I cannot help thinking that the reason our public monuments so often fail to impress us with any sense of grandeur is in a great measure owing to the neglect of the scientific study of perspective. As an illustration of what I mean, let the student look at a good engraving or photograph of the Arch of Constantine at Rome, or the Tombs of the Medici, by Michelangelo, in the sacristy of San Lorenzo at Florence. And then, for an example of a mistake in the placing of a colossal figure, let him turn to the Tomb of Julius II in San Pietro in Vinculis, Rome, and he will see that the figure of Moses, so grand in itself, not only loses much of its dignity by being placed on the ground instead of in the niche above it, but throws all the other figures out of proportion or harmony, and was quite contrary to Michelangelo's intention. Indeed, this tomb, which was to have been the finest thing of its kind ever done, was really the tragedy of the great sculptor's life.

The same remarks apply in a great measure to the architect as to the sculptor. The old builders knew the value of a knowledge of perspective, and, as in the case of Serlio, Vignola, and others, prefaced their treatises on architecture with chapters on geometry and perspective. For it showed them how to give proper proportions to their buildings and the details thereof; how to give height and importance both to the interior and exterior; also to give the right sizes of windows, doorways, columns, vaults, and other parts, and the various heights they should make their towers, walls, arches, roofs, and so forth. One of the most beautiful examples of the application of this knowledge to architecture is the Campanile of the Cathedral, at Florence, built by Giotto and Taddeo Gaddi, who were painters as well as architects. Here it will be seen that the height of the windows is increased as they are placed higher up in the building, and the top windows or openings into the belfry are about six times the size of those in the lower story.

WHAT IS PERSPECTIVE?

PERSPECTIVE is a subtle form of geometry; it represents figures and objects not as they are but as we see them in space, whereas geometry represents figures not as we see them but as they are. When we have a front view of a figure such as a square, its perspective and geometrical appearance is the same, and we see it as it really is, that is, with all its sides equal and all its angles right angles, the perspective only varying in size according to the distance we are from it; but if we place that square flat on the table and look at it sideways or at an angle, then we become conscious of certain changes in its form —the side farthest from us appears shorter than that near to us, and all the angles are different. Thus A (Fig. 2) is a geometrical square and B is the same square seen in perspective.

The science of perspective gives the dimensions of objects seen in space as they appear to the eye of the spectator, just as a perfect tracing of those objects on a sheet of glass placed vertically between him and them would do; indeed its very name is derived from perspicere, to see through. But as no tracing done by hand could possibly be mathematically correct, the mathematician teaches us how by certain points and measurements we may yet give a perfect image of them. These images are called projections, but the artist calls them pictures. In this sketch k is the vertical transparent plane or picture, o is a cube placed on one side of it. The young student is the spectator on the other side of it, the dotted lines drawn from the corners of the cube to the eye of the spectator are the visual rays, and the points on the transparent picture plane where these visual rays pass through it indicate the perspective position of those points on the picture. To find these points is the main object or duty of linear perspective.

Perspective up to a certain point is a pure science, not depending upon the accidents of vision, but upon the exact laws of reasoning. Nor is it to be considered as only pertaining to the craft of the painter and draughtsman. It has an intimate connexion with our mental perceptions and with the ideas that are impressed upon the brain by the appearance of all that surrounds us. If we saw everything as depicted by plane geometry, that is, as a map, we should have no difference of view, no variety of ideas, and we should live in a world of unbearable monotony; but as we see everything in perspective, which is infinite in its variety of aspect, our minds are subjected to countless phases of thought, making the world around us constantly interesting, so it is devised that we shall see the infinite wherever we turn, and marvel at it, and delight in it, although perhaps in many cases unconsciously.

In perspective, as in geometry, we deal with parallels, squares, triangles, cubes, circles, &c.; but in perspective the same figure takes an endless variety of forms, whereas in geometry it has but one. Here are three equal geometrical squares: they are all alike. Here are three equal perspective squares, but all varied in form; and the same figure changes in aspect as often as we view it from a different position. A walk round the dining-room table will exemplify this.

It is in proving that, notwithstanding this difference of appearance, the figures do represent the same form, that much of our work consists; and for those who care to exercise their reasoning powers it becomes not only a sure means of knowledge, but a study of the greatest interest.

Perspective is said to have been formed into a science about the fifteenth century. Among the names mentioned by the unknown but pleasant author of The Practice of Perspective, written by a Jesuit of Paris in the eighteenth century, we find Albert Dürer, who has left us some rules and principles in the fourth book of his Geometry; Jean Cousin, who has an express treatise on the art wherein are many valuable things; also Vignola, who altered the plans of St. Peter's left by Michelangelo; Serlio, whose treatise is one of the best I have seen of these early writers; Du Cerceau, Serigati, Solomon de Cause, Marolois, Vredemont; Guidus Ubaldus, who first introduced foreshortening; the Sieur de Vaulizard, the Sieur Dufarges, Joshua Kirby, for whose Method of Perspective made Easy (?) Hogarth drew the well-known frontispiece; and lastly, the above-named Practice of Perspective by a Jesuit of Paris, which is very clear and excellent as far as it goes, and was the book used by Sir Joshua Reynolds. But nearly all these authors treat chiefly of parallel perspective, which they do with clearness and simplicity, and also mathematically, as shown in the short treatise in Latin by Christian Wolff, but they scarcely touch upon the more difficult problems of angular and oblique perspective. Of modern books, those to which I am most indebted are the Traité Pratique de Perspective of M. A. Cassagne (Paris, 1873), which is thoroughly artistic, and full of pictorial examples admirably done; and to M. Henriet's Cours Rational de Dessin. There are many other foreign books of excellence, notably M. Thibault's Perspective, and some German and Swiss books, and yet, notwithstanding this imposing array of authors, I venture to say that many new features and original problems are presented in this book, whilst the old ones are not neglected. As, for instance, How to draw figures at an angle without vanishing points (see p. 141, Fig. 162, &c.), a new method of angular perspective which dispenses with the cumbersome setting out usually adopted, and enables us to draw figures at any angle without vanishing lines, &c., and is almost, if not quite, as simple as parallel perspective (see p. 133, Fig. 150, &c.). How to measure distances by the square and diagonal, and to draw interiors thereby (p. 128, Fig. 144). How to explain the theory of perspective by ocular demonstration, using a vertical sheet of glass with strings, placed on a drawing-board, which I have found of the greatest use (see p. 29, Fig. 29). Then again, I show how all our perspective can be done inside the picture; that we can measure any distance into the picture from a foot to a mile or twenty miles (see p. 86, Fig. 94); how we can draw the Great Pyramid, which stands on thirteen acres of ground, by putting it 1,600 feet off (Fig. 224), &c., &c. And while preserving the mathematical science, so that all our operations can be proved to be correct, my chief aim has been to make it easy of application to our work and consequently useful to the artist.

(Continues...)

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Table of Contents

Book I:
The Necessity of the Study of Perspective to Painters, Sculptors, and Architects
What is Perspective?
The Theory of Perspective:
I. Definitions
II. The Point of Sight, the Horizon, and the Point of Distance
III. Point of Distance
IV. Perspective of a Point, Visual Rays, &c.
V. Trace and Projection
VI. Scientific Definition of Perspective
Rules:
VII. The Rules and Conditions of Perspective
VIII. A Table or Index of the Rules of Perspective
Book II:
IX. The Square in Parallel Perspective
X. The Diagonal
XI. The Square
XII. Geometrical and Perspective Figures Contrasted
XIII. Of Certain Terms made use of in Perspective
XIV. How to Measure Vanishing or Receding Lines
XV. How to Place Squares in Given Positions
XVI. How to Draw Pavements, &c.
XVII. Of Squares placed Vertically and at Different Heights, or the Cube in Parallel Perspective
XVIII. The Transposed Distance
XIX. The Front View of the Square and of the Proportions of Figures at Different Heights
XX. Of Pictures that are Painted according to the Position they are to Occupy
XXI. Interiors
XXII. The Square at an Angle of 45°
XXIII. The Cube at an Angle of 45°
XXIV. Pavements Drawn by Means of Squares at 45°
XXV. The Perspective Vanishing Scale
XXVI. The Vanishing Scale can be Drawn to any Point on the Horizon
XXVII. Application of Vanishing Scales to Drawing Figures
XXVIII. How to Determine the Heights of Figures on a Level Plane
XXIX. The Horizon above the Figures
XXX. Landscape Perspective
XXXI. Figures of Different Heights. The Chessboard
XXXII. Application of the Vanishing Scale to Drawing Figures at an Angle when their Vanishing Points are Inaccessible or Outside the Picture
XXXIII. The Reduced Distance. How to Proceed when the Point of Distance is Inaccessible
XXXIV. How to Draw a Long Passage or Cloister by Means of the Reduced Distance
XXXV. How to Form a Vanishing Scale that shall give the Height, Depth, and Distance of any Object in the Picture
XXXVI. Measuring Scale on Ground
XXXVII. Application of the Reduced Distance and the Vanishing Scale to Drawing a Lighthouse, &c.
XXXVIII. How to Measure Long Distances such as a Mile or Upwards
XXXIX. Further Illustration of Long Distances and Extended Views
XL. How to Ascertain the Relative Heights of Figures on an Inclined Plane
XLI. How to Find the Distance of a Given Figure or Point from the Base Line
XLII. How to Measure the Height of Figures on Uneven Ground
XLIII. Further Illustration of the Size of Figures at Different Distances and on Uneven Ground
XLIV. Figures on a Descending Plane
XLV. Further Illustration of the Descending Plane
XLVI. Further Illustration of Uneven Ground
XLVII. The Picture Standing on the Ground
XLVIII. The Picture on a Height
Book III:
XLIX. Angular Perspective
L. How to put a Given Point into Perspective
LI. A Perspective Point being given, Find its Position on the Geometrical Plane
LII. How to put a Given Line into Perspective
LIII. To Find the Length of a Given Perspective Line
LIV. To Find these Points when the Distance-Point is Inaccessible
LV. How to put a Given Triangle or other Rectilineal Figure into Perspective
LVI. How to put a Given Square into Angular Perspective
LVII. Of Measuring Points
LVIII. How to Divide any Given Straight Line into Equal or Proportionate Parts
LIX. How to Divide a Diagonal Vanishing Line into any Number of Equal or Proportional Parts
LX.-LXI. Further Use of the Measuring Point O
LXII. Another Method of Angular Perspective, being that Adopted in our Art Schools
LXIII. Two Methods of Angular Perspective in one Figure
LXIV. To Draw a Cube, the Points being Given
LXV. Amplification of the Cube Applied to Drawing a Cottage
LXVI. How to Draw an Interior at an Angle
LXVII. How to Correct Distorted Perspective by Doubling the Line of Distance
LXVIII. How to Draw a Cube on a Given Square, using only One Vanishing Point
LXIX. A Courtyard or Cloister Drawn with One Vanishing Point
LXX. How to Draw Lines which shall Meet at a Distant Point, by Means of Diagonals
LXXI. How to Divide a Square Placed at an Angle into a Given Number of Small Squares
LXXII. Further Example of how to Divide a Given Oblique Square into a Given Number of Equal Squares, say Twenty-five
LXXIII. OF Parallels and Diagonals
LXXIV. The Square, the Oblong, and their Diagonals
LXXV. Showing the Use of the Square and Diagonals in Drawing Doorways, Windows, and other Architectural Features
LXXVI. How to Measure Depths by Diagonals
LXXVII. How to Measure Distances by the Square and Diagonal
LXXVIII. How by Means of the Square and Diagonal we can Determine the Position of Points in Space
LXXIX. Perspective of a Point Placed in any Position within the Square
LXXX. Perspective of a Square Placed at an Angle. New Method
LXXXI. On a Given Line Placed at an Angle to the Base Draw a Square in Angular Perspective, the Point of Sight, and Distance, being given
LXXXII. How to Draw Solid Figures at any Angle by the New Method
LXXXIII. Points in Space
LXXXIV. The Square and Diagonal Applied to Cubes and Solids Drawn Therein
LXXXV. To Draw an Oblique Square in Another Oblique Square without Using Vanishing-points
LXXXVI. Showing how a Pedestal can be Drawn by the New Method
LXXXVII. Scale on Each Side of the Picture
LXXXVIII. The Circle
LXXXIX. The Circle in Perspective a True Ellipse
XC. Further Illustration of the Ellipse
XCI. How to Draw a Circle in Perspective Without a Geometrical Plan
XCII. How to Draw a Circle in Angular Perspective
XCIII. How to Draw a Circle in Perspective more Correctly, by Using Sixteen Guiding Points
XCIV. How to Divide a Perspective Circle into any Number of Equal Parts
XCV. How to Draw Concentric Circles
XCVI. The Angle of the Diameter of the Circle in Angular and Parallel Perspective
XCVII. How to Correct Disproportion in teh Width of Columns
XCVIII. How to Draw a Circle over a Circle or a Cylinder
XCIX. To Draw a Circle Below a Given Circle
C. Application of Previous Problem
CI. Doric Columns
CII. To Draw Semicircles Standing upon a Circle at any Angle
CIII. A Dome Standing on a Cylinder
CIV. Section of a Dome or Niche
CV. A Dome
CVI. How to Draw Columns Standing in a Circle
CVII. Columns and Capitals
CVIII. Method of Perspective Employed by Architects
CIX. The Octagon
CX. How to Draw the Octagon in Angular Perspective
CXI. How to Draw the Octagonal Figure in Angular Perspective
CXII. How to Draw Concentric Octagons, with Illustration of a Well
CXIII. A Pavement Composed of Octagons and Small Squares
CXIV. The Hexagon
CXV. A Pavement Composed of Hexagonal Tiles
CXVI. A Pavement of Hexagonal Tiles in Angular Perspective
CXVII. Further Illustration of the Hexagon
CXVIII. Another View of the Hexagon in Angular Perspective
CXIX. Application of the Hexagon to Drawing a Kiosk
CXX. The Pentagon
CXXI. The Pyramid
CXXII. The Great Pyramid
CXXIII. The PYramid in Angular Perspective
CXXIV. To Divide the Sides of the Pyramid Horizontally
CXXV. Of Roofs
CXXVI. Of ARches, Arcades, Bridges, &c.
CXXVII. Outline of an Arcade with Semicircular Arches
CXXVIII. Semicircular Arches on a Retreating Plane
CXXIX. An Arcade in Angular Perspective
CXXX. A Vaulted Ceiling
CXXXI. A Cloister, from a Photograph
CXXXII. The Low or Elliptical Arch
CXXXIII. Opening or Arched Window in a Vault
CXXXIV. Stairs, Steps, &c.
CXXXV. Steps, Front View
CXXXVI. Square Steps
CXXXVII. To Divide an Inclined Plane into Equal Parts--such as a Ladder Placed against a Wall
CXXXVIII. Steps and the Inclined Plane
CXXXIX. Steps in Angular Perspective
CXL. A Step Ladder at an Angle
CXLI. Square Steps Placed over each other
CXLII. Steps and a Double Cross Drawn by Means of Diagonals and one Vanishing Point
CXLIII. A Staircase Leading to a Gallery
CXLIV. Winding Stairs in a Square Shaft
CXLV. Winding Stairs in a Cylindrical Shaft
CXLVI. Of the Cylindrical Picture or Diorama
CXLVII. The Perspective of Cast Shadows
CXLVIII. The Two Kinds of Shadows
CXLIX. Shadows Cast by the Sun
CL. The Sun in the Same Plane as the Picture
CLI. The Sun Behind the Picture
CLII. Sun Behind the Picture, Shadows Thrown on a Wall
CLIII. Sun Behind the Picture Throwing Shadow on an Inclined Plane
CLIV. The Sun in Front of the Picture
CLV. The Shadow of an Inclined Plane
CLVI. Shadow on a Roof or Inclined Plane
CLVII. To Find the Shadow of a Projection or Balcony on a Wall
CLVIII. Shadow on a Retreating Wall, Sun in Front
CLIX. Shadow of an Arch, Sun in Front
CLX. Shadow in a Niche or Recess
CLXI. Shadow in an Arched Doorway
CLXII. Shadows Produced by Artificial Light
CLXIII. Some Observations on Real Light and Shade
CLXIV. Reflection
CLXV. Angles of Reflection
CLXVI. Reflections of Objects at Different Distances
CLXVII. Reflections in a Looking-glass
CLXVIII. The Mirror at an Angle
CLXIX. The Upright Mirror at an Angle of 45° to the Wall
CLXX. Mental Perspective