heoreme._

In euery triangle, the greattest side lieth against the
greattest angle.

_Example._

[Illustration]

As in this triangle A.B.C, the greattest angle is C. And A.B.
(whiche is the side that lieth against it) is the greatest and
longest side. And contrary waies, as A.C. is the shortest side,
so B. (whiche is the angle liyng against it) is the smallest and
sharpest angle, for this doth folow also, that is the longest
side lyeth against the greatest angle, so it that foloweth

_The twelft Theoreme._

In euery triangle the greattest angle lieth against the
longest side.

For these ij. theoremes are one in truthe.

_The thirtenth theoreme._

In euerie triangle anie ij. sides togither how so euer you
take them, are longer then the thirde.

[Illustration]

For example you shal take this triangle A.B.C. which hath a very
blunt corner, and therfore one of his sides greater a good deale
then any of the other, and yet the ij. lesser sides togither ar
greater then it. And if it bee so in a blunte angeled triangle,
it must nedes be true in all other, for there is no other kinde
of triangles that hathe the one side so greate aboue the other
sids, as thei y^t haue blunt corners.

_The fourtenth theoreme._

If there be drawen from the endes of anie side of a triangle
.ij. lines metinge within the triangle, those two lines
shall be lesse then the other twoo sides of the triangle,
but yet the corner that thei make, shall bee greater then
that corner of the triangle, whiche standeth ouer it.

_Example._

[Illustration]

A.B.C. is a triangle. on whose ground line A.B. there is drawen
ij. lines, from the ij. endes of it, I say from A. and B, and
they meete within the triangle in the pointe D, wherfore I say,
that as those two lynes A.D. and B.D, are lesser then A.C. and
B.C, so the angle D, is greatter then the angle C, which is the
angle against it.

_The fiftenth Theoreme._

If a triangle haue two sides equall to the two sides of an
other triangle, but yet the angle that is contained betwene
those sides, greater then the like angle in the other
triangle, then is his grounde line greater then the grounde
line of the other triangle.

[Illustration]

_Example._

A.B.C. is a triangle, whose sides A.C. and B.C, are equall to
E.D. and D.F, the two sides of the triangle D.E.F, but bicause
the angle in D, is greatter then the angle C. (whiche are the
ij.