line be deuided by chaunce, as it maye happen,
the square that is made of the whole line, and one of the
partes of it which soeuer it be, shal be equall to that
square that is made of the ij. partes ioyned togither, and
to an other square made of that part, which was before
ioyned with the whole line.

_Example._

[Illustration]

The line A.B. is deuided in C. into twoo partes, though not
equally, of which two partes for an example I take the first,
that is A.C, and of it I make one side of a square, as for
example D.G. accomptinge those two lines to be equall, the other
side of the square is D.E, whiche is equall to the whole line
A.B.

Now may it appeare, to your eye, that the great square made of
the whole line A.B, and of one of his partes that is A.C, (which
is equall with D.G.) is equal to two partiall squares, whereof
the one is made of the saide greatter portion A.C, in as muche
as not only D.G, beynge one of his sides, but also D.H. beinge
the other side, are eche of them equall to A.C. The second
square is H.E.F.K, in which the one side H.E, is equal to C.B,
being the lesser parte of the line, A.B, and E.F. is equall to
A.C. which is the greater parte of the same line. So that those
two squares D.H.K.G and H.E.F.K, bee bothe of them no more then
the greate square D.E.F.G, accordinge to the wordes of the
Theoreme afore saide.

_The xxxviij. Theoreme._

If a righte line be deuided by chaunce, into partes, the
square that is made of that whole line, is equall to both
the squares that ar made of eche parte of the line, and
moreouer to two squares made of the one portion of the
diuided line ioyned with the other in square.

[Illustration]

_Example._

Lette the diuided line bee A.B, and parted in C, into twoo
partes: Nowe saithe the Theoreme, that the square of the whole
lyne A.B, is as mouche iuste as the square of A.C, and the
square of C.B, eche by it selfe, and more ouer by as muche
twise, as A.C. and C.B. ioyned in one square will make. For as
you se, the great square D.E.F.G, conteyneth in hym foure lesser
squares, of whiche the first and the greatest is N.M.F.K, and is
equall to the square of the lyne A.C. The second square is the
lest of them all, that is D.H.L.N, and it is equall to the
square of the line C.B. Then are there two other longe squares
both of one bygnes, that is H.E.N.M. and L.N.G.K, eche of them
both hauyng .ij. sides equall to A.C, the longer parte