nd the righte line B.D, is a iuste righte angle, because
it is made in a semicircle. But the angle made by A, which is
made of the right line A.B, and of the right line A.D, is lesser
then a righte angle, and is named a sharpe angle, for as muche
as it is made in a cantle of a circle, greater then a
semicircle. And contrary waies, the angle by C, beyng made of
the righte line B.C, and of the right line C.D, is greater then
a right angle, and is named a blunte angle, because it is made
in a cantle of a circle, lesser then a semicircle. But now
touchyng the other angles of the cantles, I saie accordyng to
the Theoreme, that the .ij. angles of the greater cantle, which
are by B. and D, as is before declared, are greatter eche of
them then a right angle. And the angles of the lesser cantle,
whiche are by the same letters B, and D, but be on the other
side of the corde, are lesser eche of them then a right angle,
and be therfore sharpe corners.

_The lxxiiij. Theoreme._

If a right line do touche a circle, and from the pointe
where they touche, a righte lyne be drawen crosse the
circle, and deuide it, the angles that the saied lyne dooeth
make with the touche line, are equall to the angles whiche
are made in the cantles of the same circle, on the contrarie
sides of the lyne aforesaid.

_Example._

[Illustration]

The circle is A.B.C.D, and the touche line is E.F. The pointe of
the touchyng is D, from which point I suppose the line D.B, to
be drawen crosse the circle, and to diuide it into .ij. cantles,
wherof the greater is B.A.D, and the lesser is B.C.D, and in ech
of them an angle is drawen, for in the greater cantle the angle
is by A, and is made of the right lines B.A, and A.D, in the
lesser cantle the angle is by C, and is made of y^e right lines
B.C, and C.D. Now saith the Theoreme that the angle B.D.F, is
equall to the angle made in the cantle on the other side of the
said line, that is to saie, in the cantle B.A.D, so that the
angle B.D.F, is equall to the angle B.A.D, because the angle
B.D.F, is on the one side of the line B.D, (whiche is according
to the supposition of the Theoreme drawen crosse the circle) and
the angle B.A.D, is in the cantle on the other side. Likewaies
the angle B.D.E, beyng on the one side of the line B.D, must be
equall to the angle B.C.D, (that is the angle by C,) whiche is
made in the cantle on the other side of the right line B.D. The
profe of all these I do reser