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 then that
other triangle, then is his angle that lieth betwene the
equall sides, greater then 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._

If two triangles be such sort, that two angles of the one be
equal to ij. angles of the other, and that one side of the
one be equal to on side of the other, whether that side do
adioyne to one of the equall corners, or els lye againste
one of them, then shall the other twoo sides of those
triangles bee equalle togither, and the thirde corner also
shall be equall in those two triangles.

_Example._

[Illustration]

Bicause that A.B.C, the one triangle hath two corners A. and B,
equal to D.E, that are twoo corners of the other triangle.
D.E.F. and that they haue one side in theym bothe equall, that
is A.B, which is equall to D.E, therefore shall both the other
ij. sides be equall one to an other, as A.C. and B.C. equall to
D.F. and E.F, and also the thirde angle in them both shal be
equall, that is, the angle C. shal be equall to the angle F.

_The eightenth Theoreme._

When on ij. right lines ther is drawen a third right line
crosse waies, and maketh .ij. matche corners of the one line
equall to the like twoo matche corners of the other line,
then ar those two lines gemmow lines, or paralleles.

_Example._

[Illustration]

The .ij. fyrst lynes are A.B. and C.D, the thyrd lyne that
crosseth them is E.F. And bycause that E.F. maketh ij. matche
angles with A.B, equall to .ij. other lyke matche angles on C.D,
(that is to say E.G, equall to K.F, and M.N. equall also to
H.L.) therfore are those ij. lynes A.B. and C.D. gemow lynes,
vnderstand here by _lyke matche corners_, those that go one way
as doth E.G, and K.F, lyke ways N.M, and H.L, for as E.G. and
H.L, other N.M. and K.F. go not one waie, so be not they lyke
match corners.

_The nyntenth Theoreme._

When on two right lines there is drawen a thirde right line
crossew