To make a square quadrate equall to any right lined figure
appoincted.
First make a likeiamme equall to that right lined figure, with a
right angle, accordyng to the .xi. conclusion, then consider the
likeiamme, whether it haue all his sides equall, or not: for yf
they be all equall, then haue you doone your conclusion. but and
if the sides be not all equall, then shall you make one right
line iuste as long as two of those vnequall sides, that line
shall you deuide in the middle, and on that pricke drawe half a
circle, then cutte from that diameter of the halfe circle a
certayne portion equall to the one side of the likeiamme, and
from that pointe of diuision shall you erecte a perpendicular,
which shall touche the edge of the circle. And that
perpendicular shall be the iuste side of the square quadrate,
equall both to the lykeiamme, and also to the right lined figure
appointed, as the conclusion willed.
_Example._
[Illustration]
K, is the right lined figure appointed, and B.C.D.E, is the
likeiamme, with right angles equall vnto K, but because that this
likeiamme is not a square quadrate, I must turne it into such
one after this sort, I shall make one right line, as long as
.ij. vnequall sides of the likeiamme, that line here is F.G,
whiche is equall to B.C, and C.E. Then part I that line in the
middle in the pricke M, and on that pricke I make halfe a
circle, accordyng to the length of the diameter F.G. Afterward I
cut awaie a peece from F.G, equall to C.E, markyng that point
with H. And on that pricke I erecte a perpendicular H.K, whiche
is the iust side to the square quadrate that I seke for,
therfore accordyng to the doctrine of the .x. conclusion, of the
lyne I doe make a square quadrate, and so haue I attained the
practise of this conclusion.