The Theory and Practice of Perspective

by G. A. Storey

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