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
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.
Then I K L M is the smaller square, inscribed as required.23
Corollary
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.
Notes
23 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 C, and D H equal to B C/2, and the construction is as in Fig. 35.