e sides in suche a blunt cornered triangle may the
better bee knowen.

[Illustration]

Fyrst therfore I sette foorth the triangle A.B.C, whose corner
by C. is a blunt corner as you maye well iudge, than to make an
other triangle of yt with a ryght angle, I must drawe forth the
side B.C. vnto D, and from the sharp corner by A. I brynge a
plumbe lyne or perpendicular on D. And so is there nowe a newe
triangle A.B.D. whose angle by D. is a right angle. Nowe
accordyng to the meanyng of the Theoreme, I saie, that in the
first triangle A.B.C, because it hath a blunt corner at C, the
square of the line A.B. whiche lieth against the said blunte
corner, is more then the square of the line A.C, and also of the
lyne B.C, (whiche inclose the blunte corner) by as muche as will
amount twise of the line B.C, and that portion D.C. whiche lieth
betwene the blunt angle by C, and the perpendicular line A.D.

The square of the line A.B, is the great square marked with E.
The square of A.C, is the meane square marked with F. The square
of B.C, is the least square marked with G. And the long square
marked with K, is sette in steede of two squares made of B.C,
and C.D. For as the shorter side is the iuste lengthe of C.D, so
the other longer side is iust twise so longe as B.C, Wherfore I
saie now accordyng to the Theoreme, that the greatte square E,
is more then the other two squares F. and G, by the quantitee of
the longe square K, wherof I reserue the profe to a more
conuenient place, where I will also teache the reason howe to
fynde the lengthe of all suche perpendicular lynes, and also of
the line that is drawen betweene the blunte angle and the
perpendicular line, with sundrie other very pleasant
conclusions.

_The .xlvi. Theoreme._

In sharpe cornered triangles, the square of anie side that
lieth against a sharpe corner, is lesser then the two
squares of the other two sides, by as muche as is comprised
twise in the long square of that side, on whiche the
perpendicular line falleth, and the portion of that same
line, liyng betweene the perpendicular, and the foresaid
sharpe corner.

_Example._

[Illustration]

Fyrst I sette foorth the triangle A.B.C, and in yt I draw a
plumbe line from the angle C. vnto the line A.B, and it lighteth
in D. Nowe by the theoreme the square of B.C. is not so muche as
the square of the other two sydes, that of B.A. and of A.C. by
as muche as is twise conteyned in the long squ