Chapter IV: 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