0 b distances of two given points (a and b) from the base line, which distances being carried to the base line, as indicated, and repeated thereon, by arcs, or measurement, give two points (a and b ) equivalent to the diagonal points of squares equal to the distances of a and b from the base line. Hence the lines connecting the points (candd) marking the distances of a and b to the base line, with d, the point of sight—and the connexion of the diagonal points (a and b) with c, the point of distance of the picture, give in the intersection e the perspective position of a , and in f that of b — under the circumstances of cdc, the line of the horizon—d, the point of sight—d r, the distance of the picture, and a c, b a, the distances of a and b from the base line of the picture.

73. To place a Line in Perspective—having once secured its extreme points, as above.

will certainly present no difficulty, no matter in what direction that line may be in reference to the base line of the picture. That done, it will be as easy to place three points in perspective as two, and four as three ; therefore—

74. To place a triangle or irregular figure in perspective, by merely connecting such points thus attained, is a process equally as plain, without regard to the distinction between parallel or oblique perspective (48). All that is required to be known is the actual position in which it is desired to place such figures on the perspective plane in reference to the base line. In this example there is not a single line of the figures either at right angles or parallel with the base line; hence, not one in their perspective representation seeking a vanishing point in the point of sight, or running parallel with the base line and line of the horizon, as in the numerous instances of the square lying parallel to the picture, to which we have so often referred, and which must be sufficiently familiar to the student to render a repetition unnecessary; nor would it appear more requisite to renew our example.

75. To place a perpendicular line or figure in perspective, except to preserve progression in our operations, and recall to mind those of a similar character which have been previously considered more at length. — Here, as in the case of all before us, we have no square or its diagonal expressed, but »we have its governing principles throughout, working in as perfect harmony as to results. With a little careful practice and proper understanding of the princi-pies involved in the few cases which will now be added, in connexion with what has been previously said and exemplified, the student may be safely considered in the possession of the ele-

J ments of the art, and he should learn to look to himself for the

perfection of the knowledge he may require, rather than to desire that all should be prepared for his hand. In the field of art, he that would reap must toil, however light may be made that toil if entered upon with a right spirit. He toils most painfully

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