Illustration]

The circle is A.B.C.D, and the figure of foure sides in it, is
made of the sides B.C, and C.D, and D.A, and A.B. Now if you
take any two angles that be contrary, as the angle by A, and the
angle by C, I saie that those .ij. be equall to .ij. right
angles. Also if you take the angle by B, and the angle by D,
whiche two are also contray, those two angles are like waies
equall to two right angles. But if any man will take the angle
by A, with the angle by B, or D, they can not be accompted
contrary, no more is not the angle by C. estemed contray to the
angle by B, or yet to the angle by D, for they onely be
accompted _contrary angles_, whiche haue no one line common to
them bothe. Suche is the angle by A, in respect of the angle by
C, for there both lynes be distinct, where as the angle by A,
and the angle by D, haue one common line A.D, and therfore can
not be accompted contrary angles, So the angle by D, and the
angle by C, haue D.C, as a common line, and therefore be not
contrary angles. And this maie you iudge of the residewe, by
like reason.

_The lxvij. Theoreme._

Vpon one right lyne there can not be made two cantles of
circles, like and vnequall, and drawen towarde one parte.

_Example._

[Illustration]

Cantles of circles be then called like, when the angles that are
made in them be equall. But now for the Theoreme, let the right
line be A.E.C, on whiche I draw a cantle of a circle, whiche is
A.B.C. Now saieth the Theoreme, that it is not possible to draw
an other cantle of a circle, whiche shall be vnequall vnto this
first cantle, that is to say, other greatter or lesser then it,
and yet be lyke it also, that is to say, that the angle in the
one shall be equall to the angle in the other. For as in this
example you see a lesser cantle drawen also, that is A.D.C, so
if an angle were made in it, that angle would be greatter then
the angle made in the cantle A.B.C, and therfore can not they be
called lyke cantels, but and if any other cantle were made
greater then the first, then would the angle in it be lesser
then that in the firste, and so nother a lesser nother a greater
cantle can be made vpon one line with an other, but it will be
vnlike to it also.

_The .lxviij. Theoreme._

Lyke cantelles of circles made on equal righte lynes, are
equall together.

_Example._

What is ment by like cantles you haue heard before. and it is
easie to vnderstand, that suche figures a