[piii]
]THE ELEMENTS OF PERSPECTIVE
ARRANGED FOR THE USE OF SCHOOLS
AND INTENDED TO BE READ IN CONNECTION WITH THE
FIRST THREE BOOKS OF EUCLID.
[pv]
]CONTENTS.
| PAGE | |
|---|---|
| [ix] | |
| [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 aHorizontal Plane | [27] |
| [PROBLEM VII.] | |
To draw any Rectilinear Quadrilateral Figure, given inPosition and Magnitude, in a Horizontal Plane | [29] |
| [PROBLEM VIII.] | |
To draw a Square, given in Position and Magnitude, in aHorizontal Plane | [31] |
| [pvi] ][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 aSquare 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 givenNumber of Equal Parts | [42] |
| [PROBLEM XIII.] | |
To draw a Square, given in Magnitude, within a largerSquare given in Position and Magnitude; the Sides of thetwo Squares being Parallel | [45] |
| [PROBLEM XIV.] | |
To draw a Truncated Circular Cone, given in Position andMagnitude, 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 TwoLines are given in Position | [57] |
| [p vii] ][PROBLEM XIX.] | |
To find the Vanishing-Point of Steepest Lines in an InclinedPlane whose Sight-Line is given | [59] |
| [PROBLEM XX.] | |
To find the Vanishing-Point of Lines perpendicular to theSurface of a given Inclined Plane | [61] |
APPENDIX. | |
| [I.] | |
Practice and Observations on the preceding Problems | [69] |
| [II.] | |
Demonstrations which could not conveniently be included inthe Text | [99] |
[p ix]
]PREFACE.
For some time back I have felt the want, among Students of Drawing, of a written code of accurate Perspective Law; the modes of construction in common use being various, and, for some problems, insufficient. It would have been desirable to draw up such a code in popular language, so as to do away with the most repulsive difficulties of the subject; but finding this popularization would be impossible, without elaborate figures and long explanations, such as I had no leisure to prepare, I have arranged the necessary rules in a short mathematical form, which any schoolboy may read through in a few days, after he has mastered the first three and the sixth books of Euclid.
Some awkward compromises have been admitted between the first-attempted popular explanation, and the severer arrangement, involving irregular lettering and redundant phraseology; but I cannot for the present do more, and leave the book therefore to its trial, hoping that, if it be found by masters of schools to answer its purpose, I may hereafter bring it into better form.[Footnote 1] ]
An account of practical methods, sufficient for general purposes of sketching, might indeed have been set down in [px] ]much less space: but if the student reads the following pages carefully, he will not only find himself able, on occasion, to solve perspective problems of a complexity greater than the ordinary rules will reach, but obtain a clue to many important laws of pictorial effect, no less than of outline. The subject thus examined becomes, at least to my mind, very curious and interesting; but, for students who are unable or unwilling to take it up in this abstract form, I believe good help will be soon furnished, in a series of illustrations of practical perspective now in preparation by Mr. Le Vengeur. I have not seen this essay in an advanced state, but the illustrations shown to me were very clear and good; and, as the author has devoted much thought to their arrangement, I hope that his work will be precisely what is wanted by the general learner.