ise so
great as the other angle on the circumference.

_Example._

[Illustration]

The circle is A.B.C.D, and his centre is E: the angle on the
centre is C.E.D, and the angle on the circumference is C.A.D t
their commen ground line, is C.F.D. Now say I that the angle
C.E.D, whiche is on the centre, is twise so greate as the angle
C.A.D, which is on the circumference.

_The lxv. Theoreme._

Those angles whiche be made in one cantle of a circle, must
needes be equal togither.

_Example._

Before I declare this theoreme by example, it shall bee
needefull to declare, what is it to be vnderstande by the wordes
in this theoreme. For the sentence canne not be knowen, onles
the uery meaning of the wordes be firste vnderstand. Therefore
when it speaketh of angles made in one cantle of a circle, it is
this to be vnderstand, that the angle muste touch the
circumference: and the lines that doo inclose that angle, muste
be drawen to the extremities of that line, which maketh the
cantle of the circle. So that if any angle do not touch the
circumference, or if the lines that inclose that angle, doo not
ende in the extremities of the corde line, but ende other in
some other part of the said corde, or in the circumference, or
that any one of them do so eande, then is not that angle
accompted to be drawen in the said cantle of the circle. And
this promised, nowe will I cumme to the meaninge of the
theoreme. I sette forthe a circle whiche is A.B.C.D, and his
centre E, in this circle I drawe a line D.C, whereby there ar
made two cantels, a more and a lesser. The lesser is D.E.C, and
the geater is D.A.B.C. In this greater cantle I drawe two
angles, the firste is D.A.C, and the second is D.B.C which two
angles by reason they are made bothe in one cantle of a circle
(that is the cantle D.A.B.C) therefore are they both equall. Now
doth there appere an other triangle, whose angle lighteth on the
centre of the circle, and that triangle is D.E.C, whose angle is
double to the other angles, as is declared in the lxiiij.
Theoreme, whiche maie stande well enough with this Theoreme, for
it is not made in this cantle of the circle, as the other are,
by reason that his angle doth not light in the circumference of
the circle, but on the centre of it.

[Illustration]

_The .lxvi. theoreme._

Euerie figure of foure sides, drawen in a circle, hath his
two contrarie angles equall vnto two right angles.

_Example._

[