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
A B
F
LET A B, Fig. 84, 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.^
* If either of the sides of the greater square is parallel to the plane
E F
D H G
35
of the picture, as D G in Fig. 35, D G of course must be equal to A c,
and D H equal to and the construction is as in Fig 35.
285
TO DRAW A SQUARE, GIVEN IN MAGNITUDE, WITHIN A
LARGER SQUARE, GIVEN IN POSITION AND MAGNITUDE;
THE SIDES OF THE TWO SQUARES BEING PARALLEL
A B
F
LET A B, Fig. 84, 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.^
* If either of the sides of the greater square is parallel to the plane
E F
D H G
35
of the picture, as D G in Fig. 35, D G of course must be equal to A c,
and D H equal to and the construction is as in Fig 35.
285