The Elements of Perspective

PROBLEM XIII.

Reading edition

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.

Fig. 34.

Let A B, Fig. 34., be the sight-magnitude of the side of the smaller square, and A C that of the side of the larger square.

Draw the larger square. Let D E F G be the square so drawn.

Join E G and D F.

On either D E or D G set off, in perspective ratio, D H equal to one half of B C. Through H draw H K to the vanishing-point of D E, cutting D F in I and E G in K. Through I and K draw I M, K L, to vanishing-point of D G, cutting D F in L and E G in M. Join L M.

COROLLARY.

Fig. 36.

If, instead of one square within another, it be required to draw one circle within another, the dimensions of both being given, inclose each circle in a square. Draw the squares first, and then the circles within, as in Fig. 36.

Fig. 35.

Notes in this chapter

Note 1 · : If either of the sides of the greater square is parallel to the plane of the picture, as D G in Fig. 35., D G of course must be equal to A Note 2 · Then I K L M is the smaller square, inscribed as required.[Footnote 23]