The Project Gutenberg eBook of The Theory and Practice of Perspective
Title: The Theory and Practice of Perspective
Author: G. A. Storey
Release date: December 22, 2006 [eBook #20165]
Language: English
Credits: E-text prepared by Louise Hope, Suzanne Lybarger, Jonathan Ingram, and the Project Gutenberg Online Distributed Proofreading Team (http://www.pgdp.net)
E-text prepared by Louise Hope, Suzanne Lybarger, Jonathan Ingram,
and the Project Gutenberg Online Distributed Proofreading Team
(http://www.pgdp.net/c/)
Lines in the sample drawings are not always parallel. In some cases this may be an artifact of the scanning process, but more often the pictures were not positioned evenly in the original book. Page numbers shown in brackets [ ] held illustrations without text. They will sometimes be out of sequence with adjoining page numbers.
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HENRY FROWDE, M.A.
PUBLISHER TO THE UNIVERSITY OF OXFORD
LONDON, EDINBURGH, NEW YORK
TORONTO AND MELBOURNE
THE
THEORY AND PRACTICE
OF PERSPECTIVE
BY
G. A. STOREY, A.R.A.
TEACHER OF PERSPECTIVE AT THE ROYAL ACADEMY
‘QUÎ FIT?’
OXFORD
AT THE CLARENDON PRESS
1910
OXFORD
PRINTED AT THE CLARENDON PRESS
BY HORACE HART, M.A.
PRINTER TO THE UNIVERSITY
DEDICATED
TO
SIR EDWARD J. POYNTER
BARONET
PRESIDENT OF THE ROYAL ACADEMY
IN TOKEN OF FRIENDSHIP
AND REGARD
PREFACE
It is much easier to understand and remember a thing when a reason is given for it, than when we are merely shown how to do it without being told why it is so done; for in the latter case, instead of being assisted by reason, our real help in all study, we have to rely upon memory or our power of imitation, and to do simply as we are told without thinking about it. The consequence is that at the very first difficulty we are left to flounder about in the dark, or to remain inactive till the master comes to our assistance.
Now in this book it is proposed to enlist the reasoning faculty from the very first: to let one problem grow out of another and to be dependent on the foregoing, as in geometry, and so to explain each thing we do that there shall be no doubt in the mind as to the correctness of the proceeding. The student will thus gain the power of finding out any new problem for himself, and will therefore acquire a true knowledge of perspective.
CONTENTS
| BOOK I | ||
| page | ||
The Necessity of the Study of Perspective To Painters, Sculptors, and Architects |
1 | |
| 6 | ||
| I. | Definitions | 13 |
| II. | The Point of Sight, the Horizon, and the Point of Distance. |
15 |
| III. | Point of Distance | 16 |
| IV. | Perspective of a Point, Visual Rays, &c. |
20 |
| V. | Trace and Projection | 21 |
| VI. | Scientific Definition of Perspective | 22 |
| Rules: | ||
| VII. | The Rules and Conditions of Perspective | 24 |
| VIII. | A Table or Index of the Rules of Perspective |
40 |
| BOOK II | ||
| IX. | The Square in Parallel Perspective | 42 |
| X. | The Diagonal | 43 |
| XI. | The Square | 43 |
| XII. | Geometrical and Perspective Figures Contrasted |
46 |
| XIII. | Of Certain Terms made use of in Perspective |
48 |
| XIV. | How to Measure Vanishing or Receding Lines |
49 |
| XV. | How to Place Squares in Given Positions | 50 |
| XVI. | How to Draw Pavements, &c. | 51 |
| XVII. | Of Squares placed Vertically and at Different Heights, or the Cube in Parallel Perspective |
53 |
| XVIII. | The Transposed Distance | 53 |
| XIX. | The Front View of the Square and of the Proportions of Figures at Different Heights |
54 |
| XX. | Of Pictures that are Painted according to the Position they are to Occupy |
59 |
| XXI. | Interiors | 62 |
| XXII. | The Square at an Angle of 45° | 64 |
| XXIII. | The Cube at an Angle of 45° | 65 |
| XXIV. | Pavements Drawn by Means of Squares at 45° |
66 |
| XXV. | The Perspective Vanishing Scale | 68 |
| XXVI. | The Vanishing Scale can be Drawn to any Point on the Horizon |
69 |
| XXVII. | Application of Vanishing Scales to Drawing Figures |
71 |
| XXVIII. | How to Determine the Heights of Figures on a Level Plane |
71 |
| XXIX. | The Horizon above the Figures | 72 |
| XXX. | Landscape Perspective | 74 |
| XXXI. | Figures of Different Heights. The Chessboard |
74 |
| XXXII. | Application of the Vanishing Scale to Drawing Figures at an Angle when their Vanishing Points are Inaccessible or Outside the Picture |
77 |
| XXXIII. | The Reduced Distance. How to Proceed when the Point of Distance is Inaccessible |
77 |
| XXXIV. | How to Draw a Long Passage or Cloister by Means of the Reduced Distance |
78 |
| XXXV. | How to Form a Vanishing Scale that shall give the Height, Depth, and Distance of any Object in the Picture |
79 |
| XXXVI. | Measuring Scale on Ground | 81 |
| XXXVII. | Application of the Reduced Distance and the Vanishing Scale to Drawing a Lighthouse, &c. |
84 |
| XXXVIII. | How to Measure Long Distances such as a Mile or Upwards |
85 |
| XXXIX. | Further Illustration of Long Distances and Extended Views. |
87 |
| XL. | How to Ascertain the Relative Heights of Figures on an Inclined Plane |
88 |
| XLI. | How to Find the Distance of a Given Figure or Point from the Base Line |
89 |
| XLII. | How to Measure the Height of Figures on Uneven Ground |
90 |
| XLIII. | Further Illustration of the Size of Figures at Different Distances and on Uneven Ground |
91 |
| XLIV. | Figures on a Descending Plane | 92 |
| XLV. | Further Illustration of the Descending Plane |
95 |
| XLVI. | Further Illustration of Uneven Ground | 95 |
| XLVII. | The Picture Standing on the Ground | 96 |
| XLVIII. | The Picture on a Height | 97 |
| BOOK III | ||
| XLIX. | Angular Perspective | 98 |
| L. | How to put a Given Point into Perspective |
99 |
| LI. | A Perspective Point being given, Find its Position on the Geometrical Plane |
100 |
| LII. | How to put a Given Line into Perspective |
101 |
| LIII. | To Find the Length of a Given Perspective Line |
102 |
| LIV. | To Find these Points when the Distance-Point is Inaccessible |
103 |
| LV. | How to put a Given Triangle or other Rectilineal Figure into Perspective |
104 |
| LVI. | How to put a Given Square into Angular Perspective |
105 |
| LVII. | Of Measuring Points | 106 |
| LVIII. | How to Divide any Given Straight Line into Equal or Proportionate Parts |
107 |
| LIX. | How to Divide a Diagonal Vanishing Line into any Number of Equal or Proportional Parts |
107 |
| LX. | Further Use of the Measuring Point O | 110 |
| LXI. | Further Use of the Measuring Point O | 110 |
| LXII. | Another Method of Angular Perspective, being that Adopted in our Art Schools |
112 |
| LXIII. | Two Methods of Angular Perspective in one Figure |
115 |
| LXIV. | To Draw a Cube, the Points being Given | 115 |
| LXV. | Amplification of the Cube Applied to Drawing a Cottage |
116 |
| LXVI. | How to Draw an Interior at an Angle | 117 |
| LXVII. | How to Correct Distorted Perspective by Doubling the Line of Distance |
118 |
| LXVIII. | How to Draw a Cube on a Given Square, using only One Vanishing Point |
119 |
| LXIX. | A Courtyard or Cloister Drawn with One Vanishing Point |
120 |
| LXX. | How to Draw Lines which shall Meet at a Distant Point, by Means of Diagonals |
121 |
| LXXI. | How to Divide a Square Placed at an Angle into a Given Number of Small Squares |
122 |
| LXXII. | Further Example of how to Divide a Given Oblique Square into a Given Number of Equal Squares, say Twenty-five |
122 |
| LXXIII. | Of Parallels and Diagonals | 124 |
| LXXIV. | The Square, the Oblong, and their Diagonals |
125 |
| LXXV. | Showing the Use of the Square and Diagonals in Drawing Doorways, Windows, and other Architectural Features |
126 |
| LXXVI. | How to Measure Depths by Diagonals | 127 |
| LXXVII. | How to Measure Distances by the Square and Diagonal |
128 |
| LXXVIII. | How by Means of the Square and Diagonal we can Determine the Position of Points in Space |
129 |
| LXXIX. | Perspective of a Point Placed in any Position within the Square |
131 |
| LXXX. | Perspective of a Square Placed at an Angle. New Method |
133 |
| 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 |
134 |
| LXXXII. | How to Draw Solid Figures at any Angle by the New Method |
135 |
| LXXXIII. | Points in Space | 137 |
| LXXXIV. | The Square and Diagonal Applied to Cubes and Solids Drawn Therein |
138 |
| LXXXV. | To Draw an Oblique Square in Another Oblique Square without Using Vanishing-points |
139 |
| LXXXVI. | Showing how a Pedestal can be Drawn by the New Method |
141 |
| LXXXVII. | Scale on Each Side of the Picture | 143 |
| LXXXVIII. | The Circle | 145 |
| LXXXIX. | The Circle in Perspective a True Ellipse |
145 |
| XC. | Further Illustration of the Ellipse | 146 |
| XCI. | How to Draw a Circle in Perspective Without a Geometrical Plan |
148 |
| XCII. | How to Draw a Circle in Angular Perspective |
151 |
| XCIII. | How to Draw a Circle in Perspective more Correctly, by Using Sixteen Guiding Points |
152 |
| XCIV. | How to Divide a Perspective Circle into any Number of Equal Parts |
153 |
| XCV. | How to Draw Concentric Circles | 154 |
| XCVI. | The Angle of the Diameter of the Circle in Angular and Parallel Perspective |
156 |
| XCVII. | How to Correct Disproportion in the Width of Columns |
157 |
| XCVIII. | How to Draw a Circle over a Circle or a Cylinder |
158 |
| XCIX. | To Draw a Circle Below a Given Circle | 159 |
| C. | Application of Previous Problem | 160 |
| CI. | Doric Columns | 161 |
| CII. | To Draw Semicircles Standing upon a Circle at any Angle |
162 |
| CIII. | A Dome Standing on a Cylinder | 163 |
| CIV. | Section of a Dome or Niche | 164 |
| CV. | A Dome | 167 |
| CVI. | How to Draw Columns Standing in a Circle |
169 |
| CVII. | Columns and Capitals | 170 |
| CVIII. | Method of Perspective Employed by Architects |
170 |
| CIX. | The Octagon | 172 |
| CX. | How to Draw the Octagon in Angular Perspective |
173 |
| CXI. | How to Draw an Octagonal Figure in Angular Perspective |
174 |
| CXII. | How to Draw Concentric Octagons, with Illustration of a Well |
174 |
| CXIII. | A Pavement Composed of Octagons and Small Squares |
176 |
| CXIV. | The Hexagon | 177 |
| CXV. | A Pavement Composed of Hexagonal Tiles | 178 |
| CXVI. | A Pavement of Hexagonal Tiles in Angular Perspective |
181 |
| CXVII. | Further Illustration of the Hexagon | 182 |
| CXVIII. | Another View of the Hexagon in Angular Perspective |
183 |
| CXIX. | Application of the Hexagon to Drawing a Kiosk |
185 |
| CXX. | The Pentagon | 186 |
| CXXI. | The Pyramid | 189 |
| CXXII. | The Great Pyramid | 191 |
| CXXIII. | The Pyramid in Angular Perspective | 193 |
| CXXIV. | To Divide the Sides of the Pyramid Horizontally |
193 |
| CXXV. | Of Roofs | 195 |
| CXXVI. | Of Arches, Arcades, Bridges, &c. | 198 |
| CXXVII. | Outline of an Arcade with Semicircular Arches |
200 |
| CXXVIII. | Semicircular Arches on a Retreating Plane |
201 |
| CXXIX. | An Arcade in Angular Perspective | 202 |
| CXXX. | A Vaulted Ceiling | 203 |
| CXXXI. | A Cloister, from a Photograph | 206 |
| CXXXII. | The Low or Elliptical Arch | 207 |
| CXXXIII. | Opening or Arched Window in a Vault | 208 |
| CXXXIV. | Stairs, Steps, &c. | 209 |
| CXXXV. | Steps, Front View | 210 |
| CXXXVI. | Square Steps | 211 |
| CXXXVII. | To Divide an Inclined Plane into Equal Parts—such as a Ladder Placed against a Wall |
212 |
| CXXXVIII. | Steps and the Inclined Plane | 213 |
| CXXXIX. | Steps in Angular Perspective | 214 |
| CXL. | A Step Ladder at an Angle | 216 |
| CXLI. | Square Steps Placed over each other | 217 |
| CXLII. | Steps and a Double Cross Drawn by Means of Diagonals and one Vanishing Point |
218 |
| CXLIII. | A Staircase Leading to a Gallery | 221 |
| CXLIV. | Winding Stairs in a Square Shaft | 222 |
| CXLV. | Winding Stairs in a Cylindrical Shaft | 225 |
| CXLVI. | Of the Cylindrical Picture or Diorama | 227 |
| BOOK IV | ||
| CXLVII. | The Perspective of Cast Shadows | 229 |
| CXLVIII. | The Two Kinds of Shadows | 230 |
| CXLIX. | Shadows Cast by the Sun | 232 |
| CL. | The Sun in the Same Plane as the Picture |
233 |
| CLI. | The Sun Behind the Picture | 234 |
| CLII. | Sun Behind the Picture, Shadows Thrown on a Wall |
238 |
| CLIII. | Sun Behind the Picture Throwing Shadow on an Inclined Plane |
240 |
| CLIV. | The Sun in Front of the Picture | 241 |
| CLV. | The Shadow of an Inclined Plane | 244 |
| CLVI. | Shadow on a Roof or Inclined Plane | 245 |
| CLVII. | To Find the Shadow of a Projection or Balcony on a Wall |
246 |
| CLVIII. | Shadow on a Retreating Wall, Sun in Front |
247 |
| CLIX. | Shadow of an Arch, Sun in Front | 249 |
| CLX. | Shadow in a Niche or Recess | 250 |
| CLXI. | Shadow in an Arched Doorway | 251 |
| CLXII. | Shadows Produced by Artificial Light | 252 |
| CLXIII. | Some Observations on Real Light and Shade |
253 |
| CLXIV. | Reflection | 257 |
| CLXV. | Angles of Reflection | 259 |
| CLXVI. | Reflections of Objects at Different Distances |
260 |
| CLXVII. | Reflection in a Looking-glass | 262 |
| CLXVIII. | The Mirror at an Angle | 264 |
| CLXIX. | The Upright Mirror at an Angle of 45° to the Wall |
266 |
| CLXX. | Mental Perspective | 269 |
| Index | 270 | |
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.’1
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.