ng squares (as is before mencioned) and
one full square. which is the intent of the Theoreme.

_The xliij. Theoreme._

If a right line be deuided into ij. equal partes first, and
one of those parts again into other ij. parts, as chaunce
hapeneth, the square that is made of the last part of the
line so diuided, and the square of the residue of that whole
line, are double to the square of halfe that line, and to
the square of the middle portion of the same line.

_Example._

[Illustration]

The line to be deuided is A.B, and is parted in C. into two
equall partes, and then C.B, is deuided againe into two partes
in D, so that the meaninge of the Theoreme, is that the square
of D.B. which is the latter parte of the line, and the square of
A.D, which is the residue of the whole line. Those two squares,
I say, ar double to the square of one halfe of the line, and to
the square of C.D, which is the middle portion of those thre
diuisions. Which thing that you maye more easilye perceaue,
I haue drawen foure squares, whereof the greatest being marked
with E. is the square of A.D. The next, which is marked with G,
is the square of halfe the line, that is, of A.C, And the other
two little squares marked with F. and H, be both of one bignes,
by reason that I did diuide C.B. into two equall partes, so that
you amy take the square F, for the square of D.B, and the square
H, for the square of C.D. Now I thinke you doubt not, but that
the square E. and the square F, ar double so much as the square
G. and the square H, which thing the easyer is to be
vnderstande, bicause that the greate square hath in his side
iij. quarters of the firste line, which multiplied by itselfe
maketh nyne quarters, and the square F. containeth but one
quarter, so that bothe doo make tenne quarters.

Then G. contayneth iiij. quarters, seynge his side containeth
twoo, and H. containeth but one quarter, whiche both make
but fiue quarters, and that is but halfe of tenne.
Whereby you may easylye coniecture,
that the meanynge of the theoreme
is verified in the
figures of this
example.

_The xliiij. Theoreme._

If a right line be deuided into ij. partes equally, and an
other portion of a righte lyne annexed to that firste line,
the square of this whole line so compounded, and the square
of the portion that is annexed, ar doule as much as the
square of the halfe of the firste line, and the square of
the ot