This triangle A.B.C. hath two corners equal eche to other, that is A. and B, as I do by supposition limite, wherfore it foloweth that the side A.C, is equal to that other side B.C, for the side A.C, lieth againste the angle B, and the side B.C, lieth against the angle A. _The fourth Theoreme._ When two lines are drawen frõ the endes of anie one line, and meet in anie pointe, it is not possible to draw two other lines of like lengthe ech to his match that shal begĩ at the same pointes, and end in anie other pointe then the twoo first did. _Example._ [Illustration] The first line is A.B, on which I haue erected two other lines A.C, and B.C, that meete in the pricke C, wherefore I say, it is not possible to draw ij. other lines from A. and B. which shal mete in one point (as you se A.D. and B.D. mete in D.) but that the match lines shalbe vnequal, I mean by _match lines_, the two lines on one side, that is the ij. on the right hand, or the ij. on the lefte hand, for as you se in this example A.D. is longer thẽ A.C, and B.C. is longer then B.D. And it is not possible, that A.C. and A.D. shall bee of one lengthe, if B.D. and B.C. bee like longe. For if one couple of matche lines be equall (as the same example A.E. is equall to A.C. in length) then must B.E. needes be vnequall to B.C. as you see, it is here shorter. _The fifte Theoreme._ If two triãgles haue there ij. sides equal one to an other, and their groũd lines equal also, then shall their corners, whiche are contained betwene like sides, be equall one to the other. _Example._ [Illustration] Because these two triangles A.B.C, and D.E.F. haue two sides equall one to an other. For A.C. is equall to D.F, and B.C. is equall to E.F, and again their groũd lines A.B. and D.E. are lyke in length, therfore is eche angle of the one triangle equall to ech angle of the other, comparyng together those angles that are contained within lyke sides, so is A. equall to D, B. to E, and C. to F, for they are contayned within like sides, as before is said. _The sixt Theoreme._ When any right line standeth on an other, the ij. angles that thei make, other are both right angles, or els equall to .ij. righte angles. _Example._ [Illustration] A.B. is a right line, and on it there doth light another right line, drawen from C. perpendicularly on it, therefore saie I, that the .ij. angles that thei do make, are .ij. right angles as maie be iudged by the definition of a right angle. But in the second part of the example, where A.B. beyng still the right line, on which D. standeth in slope wayes, the two angles that be made of them are not righte angles, but yet they are equall to two righte angles, for so muche as the one is to greate, more then a righte angle, so muche iuste is the other to little, so that bothe togither are equall to two right angles, as you maye perceiue. _The seuenth Theoreme._