]

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
then 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 triangles haue there ij. sides equal one to an other,
and their ground 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 ground 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._

If .ij. lines be drawen to any one pricke in an other lyne,
and those .ij. lines do make w