The Theory and Practice of Perspective | Page 3

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

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]
[Footnote 1: Leonardo da Vinci's Treatise on Painting.]
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