d to declare that particularly, Fyrst I make an other
line G.K, equall to the line .C.D, and the line G.H. to be equal
to the line A.B, and to bee diuided into iij. like partes, so
that G.M. is equall to A.E, and M.N. equal to E.F, and then
muste N.H. nedes remaine equall to F.B. Then of those ij. lines
G.K, vndeuided, and G.H. which is deuided, I make a square, that
is G.H.K.L, In which square if I drawe crosse lines frome one
side to the other, according to the diuisions of the line G.H,
then will it appear plaine, that the theoreme doth affirme. For
the first square G.M.O.K, must needes be equal to the square of
the line C.D, and the first portion of the diuided line, which is
A.E, for bicause their sides are equall. And so the seconde
square that is M.N.P.O, shall be equall to the square of C.D,
and the second part of A.B, that is E.F. Also the third square
which is N.H.L.P, must of necessitee be equal to the square of
C.D, and F.B, bicause those lines be so coupeled that euery
couple are equall in the seuerall figures. And so shal you not
only in this example, but in all other finde it true, that if
one line be deuided into sondry partes, and an other line whole
and vndeuided, matched with him in a square, that square which
is made of these two whole lines, is as muche iuste and equally,
as all the seuerall squares, whiche bee made of the whole line
vndiuided, and euery part seuerally of the diuided line.

_The xxxvi. Theoreme._

If a right line be parted into ij. partes, as chaunce may
happe, the square that is made of the whole line, is equall
to bothe the squares that are made of the same line, and the
twoo partes of it seuerally.

_Example._

[Illustration]

The line propounded beyng A.B. and deuided, as chaunce
happeneth, in C. into ij. vnequall partes, I say that the square
made of the hole line A.B, is equal to the two squares made of
the same line with the twoo partes of itselfe, as with A.C, and
with C.B, for the square D.E.F.G. is equal to the two other
partial squares of D.H.K.G and H.E.F.K, but that the greater
square is equall to the square of the whole line A.B, and the
partiall squares equall to the squares of the second partes of
the same line ioyned with the whole line, your eye may iudg
without muche declaracion, so that I shall not neede to make
more exposition therof, but that you may examine it, as you did
in the laste Theoreme.

_The xxxvij. Theoreme._

If a right