at is to say, into .ij. equall
triangles) those be counted _to stande aboute one bias line_,
and the other squares, whiche touche that bias line, with one of
their corners onely, those doo I call _Fyll squares_, [Sidenote:
_Fyll squares._] accordyng to the greke name, which is
_anapleromata_, [Sidenote: #anaple:ro:mata#] and called in latin
_supplementa_, bycause that they make one generall square,
includyng and enclosyng the other diuers squares, as in this
example H.C.E.N. is one square likeiamme, and L.M.G.C. is an
other, whiche bothe are made aboute one bias line, that is N.M,
than K.L.H.C. and C.E.F.G. are .ij. fyll squares, for they doo
fyll vp the sydes of the .ij. fyrste square lykeiammes, in suche
sorte, that all them foure is made one greate generall square
K.M.F.N.

Nowe to the sentence of the theoreme, I say, that the .ij. fill
squares, H.K.L.C. and C.E.F.G. are both equall togither, (as it
shall bee declared in the booke of proofes) bicause they are the
fill squares of two likeiammes made aboute one bias line, as the
exaumple sheweth. Conferre the twelfthe conclusion with this
theoreme.

_The xxxiij. Theoreme._

In all right anguled triangles, the square of that side
whiche lieth against the right angle, is equall to the .ij.
squares of both the other sides.

_Example._

[Illustration]

A.B.C. is a triangle, hauing a ryght angle in B. Wherfore it
foloweth, that the square of A.C, (whiche is the side that lyeth
agaynst the right angle) shall be as muche as the two squares of
A.B. and B.C. which are the other .ij. sides.

[Sec.] By the square of any lyne, you muste vnderstande a figure made
iuste square, hauyng all his iiij. sydes equall to that line,
whereof it is the square, so is A.C.F, the square of A.C.
Lykewais A.B.D. is the square of A.B. And B.C.E. is the square
of B.C. Now by the numbre of the diuisions in eche of these
squares, may you perceaue not onely what the square of any line
is called, but also that the theoreme is true, and expressed
playnly bothe by lines and numbre. For as you see, the greatter
square (that is A.C.F.) hath fiue diuisions on eche syde, all
equall togyther, and those in the whole square are twenty and
fiue. Nowe in the left square, whiche is A.B.D. there are but
.iij. of those diuisions in one syde, and that yeldeth nyne in
the whole. So lykeways you see in the meane square A.C.E. in
euery syde .iiij. partes, whiche in the whole amount vnto
sixtene. N