.E.F.G, is the square of the
whole line, D.H.K.M. is the square of the lesser portion (whyche
I take for an example) and therfore must bee twise reckened.
Nowe I saye that those ij. squares are equall to two longe
squares of the whole line A.B, and his sayd portion A.C, and
also to the square of the other portion of the sayd first line,
whiche portion is C.B, and his square K.N.F.L. In this theoreme
there is no difficultie, if you consyder that the litle square
D.H.K.M. is .iiij. tymes reckened, that is to say, fyrst of all
as a parte of the greatest square, whiche is D.E.F.G. Secondly
he is rekned by him selfe. Thirdely he is accompted as parcell
of the long square D.E.N.M, And fourthly he is taken as a part
of the other long square D.H.L.G, so that in as muche as he is
twise reckened in one part of the comparison of equalitee, and
twise also in the second parte, there can rise none occasion of
errour or doubtfulnes therby.

_The xlij. Theoreme._

If a right line be deuided as chance happeneth the iiij.
long squares, that may be made of that whole line and one of
his partes with the square of the other part, shall be
equall to the square that is made of the whole line and the
saide first portion ioyned to him in lengthe as one whole
line.

_Example._

[Illustration]

The firste line is A.B, and is deuided by C. into two vnequall
partes as happeneth. The long square of yt, and his lesser
portion A.C, is foure times drawen, the first is E.G.M.K, the
seconde is K.M.Q.O, the third is H.K.R.S, and the fourthe is
K.L.S.T. And where as it appeareth that one of the little
squares (I meane K.L.P.O) is reckened twise, ones as parcell of
the second long square and agayne as parte of the thirde long
square, to auoide ambiguite, you may place one insteede of it,
an other square of equalitee, with it. that is to saye, D.E.K.H,
which was at no tyme accompting as parcell of any one of them,
and then haue you iiij. long squares distinctly made of the
whole line A.B, and his lesser portion A.C. And within them is
there a greate full square P.Q.T.V. whiche is the iust square of
B.C, beynge the greatter portion of the line A.B. And that those
fiue squares doo make iuste as muche as the whole square of that
longer line D.G, (whiche is as longe as A.B, and A.C. ioyned
togither) it may be iudged easyly by the eye, sith that one
greate square doth comprehend in it all the other fiue squares,
that is to say, foure lo