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The text presents a systematic, geometry-based introduction to linear perspective aimed at painters, sculptors, and architects, beginning with clear definitions and the visual concepts of sight point, horizon, and distance-point. It then develops rules and indexed procedures that let one construct squares, cubes, pavements, interiors, and landscapes in both parallel and angular perspective, including methods for vanishing scales, reduced distances, and inaccessible vanishing points. Numerous geometric techniques are explained for measuring heights, depths, diagonal and square constructions, and for representing circles as true ellipses in projection. Practical examples and stepwise exercises emphasize reasoning so students can solve new perspective problems independently.

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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)

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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

What Is Perspective?

6

The Theory of Perspective:

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

The Practice of Perspective:

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.