ralleles to any other line, those
same be paralleles togither.

_Example._

[Illustration]

A.B. is a gemow line, or a parallele vnto C.D. And E.F,
lykewaies is a parallele vnto C.D. Wherfore it foloweth, that
A.B. must nedes bee a parallele vnto E.F.

_The .xxij. theoreme._

In euery triangle, when any side is drawen forth in length,
the vtter angle is equall to the ij. inner angles that lie
againste it. And all iij. inner angles of any triangle are
equall to ij. right angles.

[Illustration]

_Example._

The triangle beeyng A.D.E. and the syde A.E. drawen foorthe vnto
B, there is made an vtter corner, whiche is C, and this vtter
corner C, is equall to bother the inner corners that lye agaynst
it, whyche are A. and D. And all thre inner corners, that is to
say, A.D. and E, are equall to two ryght corners, whereof it
foloweth, _that all the three corners of any one triangle are
equall to all the three corners of euerye other triangle_. For
what so euer thynges are equalle to anny one thyrde thynge,
those same are equalle togitther, by the fyrste common sentence,
so that bycause all the .iij. angles of euery triangle are
equall to two ryghte angles, and all ryghte angles bee equall
togyther (by the fourth request) therfore must it nedes folow,
that all the thre corners of euery triangle (accomptyng them
togyther) are equall to iij. corners of any triangle, taken all
togyther.

_The .xxiii. theoreme._

When any ij. right lines doth touche and couple .ij. other
righte lines, whiche are equall in length and paralleles,
and if those .ij. lines bee drawen towarde one hande, then
are thei also equall together, and paralleles.

_Example._

[Illustration]

A.B. and C.D. are ij. ryght lynes and paralleles and equall in
length, and they ar touched and ioyned togither by ij. other
lynes A.C. and B.D, this beyng so, and A.C. and B.D. beyng
drawen towarde one syde (that is to saye, bothe towarde the
lefte hande) therefore are A.C. and B.D. bothe equall and also
paralleles.

_The .xxiiij. theoreme._

In any likeiamme the two contrary sides ar equall togither,
and so are eche .ij. contrary angles, and the bias line that
is drawen in it, dothe diuide it into two equall portions.

_Example._

[Illustration]

Here ar two likeiammes ioyned togither, the one is a longe
square A.B.E, and the other is a losengelike D.C.E.F. which ij.
likeiammes ar proued equall togither, byc