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 thẽ 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 ãgle 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. angles contayned betwene the equal lynes) therfore muste the ground line E.F. nedes bee greatter thenne the grounde line A.B, as you se plainely. [Illustration] _The xvi. Theoreme._ If a triangle haue twoo sides equalle to the two sides of an other triangle, but yet hathe a longer ground line thẽ that other triangle, then is his angle that lieth betwene the equall sides, greater thẽ the like corner in the other triangle. _Example._ This Theoreme is nothing els, but the sentence of the last Theoreme turned backward, and therfore nedeth none other profe nother declaration, then the other example. _The seuententh Theoreme._