PROBLEM XXXI.

To reduce a triangle A B C to a rectangle.

1. Bisect the altitude C G in D, through D' draw E F pa rallel to A B.

2. From B draw B F perpendicular to A B, through A draw A F parallel to BF, then A BFE will be the rectangle required.

PROBLEM XXXII.

To make a rectangle, having a side equal to a given line A B, and equal to a given rectangle CDEF.

1. Produce the sides of the rectangle C F, D E, F E, and C D.

2. Make E G equal to A B, through G draw L H parallel to F E, cutting C F produced at L.

3. Draw the diagonal LE, and produce it till it cut CD at K.

4. Draw K H parallel to E G, then will EIHG be the rectangle required.

PROBLEM. XXXIII.

To make a square equal to a given rectangle ABCD.

1. Produce the side A B, make B E equal to B C.

2. Bisect A E in I, on I, as a centre with the radius I E or I A, describe the semicircle A H E.

3. Produce the side of C B to cut the circle in H, on BH describe the square BH G F, it will be the square required.

VOL. I.

D

PROBLEM