[p 45 ] 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 .

[Geometric diagram]
Fig.34.

Let AB, Fig.34., be the sight-magnitude of the side of the smaller square, and AC that of the side of the larger square.

Draw the larger square. Let DEFG be the square so drawn.

Join EG and DF.

On either DE or DG set off, in perspective ratio, DH equal to one half of BC. Through H draw HK to the vanishing-point of DE, cutting DF in I and EG in K. Through I and K draw IM, KL, to vanishing-point of DG, cutting DF in L and EG in M. Join LM.

Then IKLM is the smaller square, inscribed as required.[Footnote 23]

[p46] COROLLARY.

[Geometric diagram]
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.