ith the fyrst lyne, two right
angles, other suche as be equall to two right angles, and
that towarde one hande, than those two lines doo make one
streyght lyne.

_Example._

[Illustration]

A.B. is a streyght lyne, on which there doth lyght two other
lines one frome D, and the other frome C, but considerynge that
they meete in one pricke E, and that the angles on one hand be
equal to two right corners (as the laste theoreme dothe declare)
therfore maye D.E. and E.C. be counted for one ryght lyne.

_The eight Theoreme._

When two lines do cut one an other crosseways they do make
their matche angles equall.

[Illustration]

_Example._

What matche angles are, I haue tolde you in the definitions of
the termes. And here A, and B. are matche corners in this
example, as are also C. and D, so that the corner A, is equall
to B, and the angle C, is equall to D.

_The nynth Theoreme._

Whan so euer in any triangle the line of one side is drawen
forthe in lengthe, that vtter angle is greater than any of
the two inner corners, that ioyne not with it.

_Example._

[Illustration]

The triangle A.D.C hathe hys grounde lyne A.C. drawen forthe in
lengthe vnto B, so that the vtter corner that it maketh at C, is
greater then any of the two inner corners that lye againste it,
and ioyne not wyth it, whyche are A. and D, for they both are
lesser then a ryght angle, and be sharpe angles, but C. is a
blonte angle, and therfore greater then a ryght angle.

_The tenth Theoreme._

In euery triangle any .ij. corners, how so euer you take
them, ar lesse then ij. right corners.

_Example._

[Illustration]

In the firste triangle E, whiche is a threlyke, and therfore
hath all his angles sharpe, take anie twoo corners that you
will, and you shall perceiue that they be lesser then ij. right
corners, for in euery triangle that hath all sharpe corners (as
you see it to be in this example) euery corner is lesse then a
right corner. And therfore also euery two corners must nedes be
lesse then two right corners. Furthermore in that other triangle
marked with M, whiche hath .ij. sharpe corners and one right,
any .ij. of them also are lesse then two right angles. For
though you take the right corner for one, yet the other whiche
is a sharpe corner, is lesse then a right corner. And so it is
true in all kindes of triangles, as you maie perceiue more
plainly by the .xxij. Theoreme.

_The .xi. T