Chapter 3

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