aies, and maketh the ij. ouer corners towarde one
hande equall togither, then ar those .ij. lines paralleles.
And in like maner if two inner corners toward one hande, be
equall to .ii. right angles.

_Example._

As the Theoreme dothe speake of .ij. ouer angles, so muste you
vnderstande also of .ij. nether angles, for the iudgement is
lyke in bothe. Take for example the figure of the last theoreme,
where A.B, and C.D, be called paralleles also, bicause E. and K,
(whiche are .ij. ouer corners) are equall, and lykewaies L.
and M. And so are in lyke maner the nether corners N. and H, and
G. and F. Nowe to the seconde parte of the theoreme, those .ij.
lynes A.B. and C.D, shall be called paralleles, because the ij.
inner corners. As for example those two that bee toward the
right hande (that is G. and L.) are equall (by the fyrst parte
of this nyntenth theoreme) therfore muste G. and L. be equall to
two ryght angles.

_The xx. Theoreme._

When a right line is drawen crosse ouer .ij. right gemow
lines, it maketh .ij. matche corners of the one line, equall
to two matche corners of the other line, and also bothe ouer
corners of one hande equall togither, and bothe nether
corners like waies, and more ouer two inner corners, and two
vtter corners also towarde one hande, equall to two right
angles.

_Example._

Bycause A.B. and C.D, (in the laste figure) are paralleles,
therefore the two matche corners of the one lyne, as E.G. be
equall vnto the .ij. matche corners of the other line, that is
K.F, and lykewaies M.N, equall to H.L. And also E. and K. bothe
ouer corners of the lefte hande equall togyther, and so are M.
and L, the two ouer corners on the ryghte hande, in lyke maner
N. and H, the two nether corners on the lefte hande, equall eche
to other, and G. and F. the two nether angles on the right hande
equall togither.

[Sec.] Farthermore yet G. and L. the .ij. inner angles on the right
hande bee equall to two right angles, and so are M. and F. the
.ij. vtter angles on the same hande, in lyke manner shall you
say of N. and K. the two inner corners on the left hand. and of
E. and H. the two vtter corners on the same hande. And thus you
see the agreable sentence of these .iii. theoremes to tende to
this purpose, to declare by the angles how to iudge paralleles,
and contrary waies howe you may by paralleles iudge the
proportion of the angles.

_The xxi. Theoreme._

What so euer lines be pa