are made of A.B,
and A.D, A.B. beyng the line or syde on which the perpendicular
line falleth, and A.D. beeyng that portion of the same line
whiche doth lye betwene the perpendicular line, and the sayd
sharpe angle limitted, whiche angle is by A.

For declaration of the figures, the square marked with E. is the
square of B.C, whiche is the syde that lieth agaynst the sharpe
angle, the square marked with G. is the square of A.B, and the
square marked with F. is the square of A.C, and the two longe
squares marked with H.K, are made of the hole line A.B, and one
of his portions A.D. And truthe it is that the square E. is
lesser than the other two squares C. and F. by the quantitee of
those two long squares H. and K. Wherby you may consyder agayn,
an other proportion of equalitee, that is to saye, that the
square E. with the twoo longsquares H.K, are iuste equall to the
other twoo squares C. and F. And so maye you make, as it were an
other theoreme. _That in al sharpe cornered triangles, where a
perpendicular line is drawen frome one angle to the side that
lyeth againste it, the square of anye one side, with the ij.
longesquares made at that hole line, whereon the perpendicular
line doth lighte, and of that portion of it, which ioyneth to
that side whose square is all ready taken, those thre figures,
I say, are equall to the ij. squares, of the other ij. sides of
the triangle._ In whiche you muste vnderstand, that the side on
which the perpendiculare falleth, is thrise vsed, yet is his
square but ones mencioned, for twise he is taken for one side of
the two long squares. And as I haue thus made as it were an
other theoreme out of this fourty and sixe theoreme, so mighte I
out of it, and the other that goeth nexte before, make as manny
as woulde suffice for a whole booke, so that when they shall bee
applyed to practise, and consequently to expresse their
benefite, no manne that hathe not well wayde their wonderfull
commoditee, would credite the possibilitie of their wonderfull
vse, and large ayde in knowledge. But all this wyll I remitte to
a place conuenient.

_The xlvij. Theoreme._

If ij. points be marked in the circumference of a circle, and
a right line drawen frome the one to the other, that line
must needes fal within the circle.

_Example._

[Illustration]

The circle is A.B.C.D, the ij. poinctes are A.B, the righte line
that is drawenne frome the one to the other, is the line A.B,
which as you