Chapter I: Front Matter

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| Transcriber’s Note |
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| In the original book the author used lowercase italic letters and |
| lowercase small capitals to label the geometric diagrams. These |
| have been here transcribed as lowercase and uppercase italic |
| letters respectively (_aA_). |
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| This file should be read using a font that supports the following |
| Unicode characters: |
| ∠ angle, ∶ ratio, ∷ proportion, ∴ therefore, ′ prime, and |
| ″ double prime. |
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| Library Edition |
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| THE COMPLETE WORKS |
| OF |
| JOHN RUSKIN |
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| ELEMENTS OF DRAWING AND |
| PERSPECTIVE |
| THE TWO PATHS |
| UNTO THIS LAST |
| MUNERA PULVERIS |
| SESAME AND LILIES |
| ETHICS OF THE DUST |
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| |
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| NATIONAL LIBRARY ASSOCIATION |
| NEW YORK CHICAGO |
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THE ELEMENTS OF PERSPECTIVE

ARRANGED FOR THE USE OF SCHOOLS

AND INTENDED TO BE READ IN CONNECTION WITH THE
FIRST THREE BOOKS OF EUCLID.

CONTENTS.

PAGE
Preface ix

Introduction 1

PROBLEM I.
To fix the Position of a given Point 10

PROBLEM II.
To draw a Right Line between two given Points 13

PROBLEM III.
To find the Vanishing-Point of a given Horizontal Line 17

PROBLEM IV.
To find the Dividing-Points of a given Horizontal Line 23

PROBLEM V.
To draw a Horizontal Line, given in Position and Magnitude,
by means of its Sight-Magnitude and Dividing-Points 24

PROBLEM VI.
To draw any Triangle, given in Position and Magnitude, in a
Horizontal Plane 27

PROBLEM VII.
To draw any Rectilinear Quadrilateral Figure, given in
Position and Magnitude, in a Horizontal Plane 29

PROBLEM VIII.
To draw a Square, given in Position and Magnitude, in a
Horizontal Plane 31

PROBLEM IX.
To draw a Square Pillar, given in Position and Magnitude,
its Base and Top being in Horizontal Planes 34

PROBLEM X.
To draw a Pyramid, given in Position and Magnitude, on a
Square Base in a Horizontal Plane 36

PROBLEM XI.
To draw any Curve in a Horizontal or Vertical Plane 38

PROBLEM XII.
To divide a Circle drawn in Perspective into any given
Number of Equal Parts 42

PROBLEM XIII.
To draw a Square, given in Magnitude, within a larger
Square given in Position and Magnitude; the Sides of the
two Squares being Parallel 45

PROBLEM XIV.
To draw a Truncated Circular Cone, given in Position and
Magnitude, the Truncations being in Horizontal Planes,
and the Axis of the Cone vertical 47

PROBLEM XV.
To draw an Inclined Line, given in Position and Magnitude 50

PROBLEM XVI.
To find the Vanishing-Point of a given Inclined Line 53

PROBLEM XVII.
To find the Dividing-Points of a given Inclined Line 55

PROBLEM XVIII.
To find the Sight-Line of an Inclined Plane in which Two
Lines are given in Position 57

PROBLEM XIX.
To find the Vanishing-Point of Steepest Lines in an Inclined
Plane whose Sight-Line is given 59

PROBLEM XX.
To find the Vanishing-Point of Lines perpendicular to the
Surface of a given Inclined Plane 61

APPENDIX.

I.
Practice and Observations on the preceding Problems 69

II.
Demonstrations which could not conveniently be included in
the Text 99