The Theory and Practice of Perspective

by G. A. Storey

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, andArchitects]		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 inParallel Perspective	53
[XVIII.]	The Transposed Distance	53
[XIX.]	The Front View of the Square and of the Proportions of Figures atDifferent Heights	54
[XX.]	Of Pictures that are Painted according to the Position they are toOccupy	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 whentheir Vanishing Points are Inaccessible or Outside the Picture	77
[XXXIII.]	The Reduced Distance. How to Proceed when the Point of Distance isInaccessible	77
[XXXIV.]	How to Draw a Long Passage or Cloister by Means of the ReducedDistance	78
[XXXV.]	How to Form a Vanishing Scale that shall give the Height, Depth, andDistance 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 aLighthouse, &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 InclinedPlane	88
[XLI.]	How to Find the Distance of a Given Figure or Point from the BaseLine	89
[XLII.]	How to Measure the Height of Figures on Uneven Ground	90
[XLIII.]	Further Illustration of the Size of Figures at Different Distances andon 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 GeometricalPlane	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 intoPerspective	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 ProportionateParts	107
[LIX.]	How to Divide a Diagonal Vanishing Line into any Number of Equal orProportional 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 ArtSchools	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 ofDistance	118
[LXVIII.]	How to Draw a Cube on a Given Square, using only One VanishingPoint	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 ofDiagonals	121
[LXXI.]	How to Divide a Square Placed at an Angle into a Given Number of SmallSquares	122
[LXXII.]	Further Example of how to Divide a Given Oblique Square into a GivenNumber 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 ofPoints 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 AngularPerspective, 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 DrawnTherein	138
[LXXXV.]	To Draw an Oblique Square in Another Oblique Square without UsingVanishing-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 SixteenGuiding Points	152
[XCIV.]	How to Divide a Perspective Circle into any Number of EqualParts	153
[XCV.]	How to Draw Concentric Circles	154
[XCVI.]	The Angle of the Diameter of the Circle in Angular and ParallelPerspective	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 LadderPlaced 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 VanishingPoint	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.