the circle, that is to saye, E.A.B, is lesser then
any sharpe angle that can be made of right lines also. For as it
was before rehersed, there canne no right line be drawen to the
angle, betwene the circumference and the right line E.A. Then
must it needes folow, that there can be made no lesser angle of
righte lines. And againe, if ther canne be no lesser then the
one, then doth it sone appear, that there canne be no greater
then the other, for they twoo doo make the whole right angle, so
that if anye corner coulde be made greater then the one parte,
then shoulde the residue bee lesser then the other parte, so
that other bothe partes muste be false, or els bothe graunted to
be true.

_The lxij. Theoreme._

If a right line doo touche a circle, and an other right line
drawen frome the centre of the circle to the pointe where
they touche, that line whiche is drawenne frome the centre,
shall be a perpendicular line to the touch line.

_Example._

[Illustration]

The circle is A.B.C, and his centre is F. The touche line is
D.E, and the point wher they touch is C. Now by reason that a
right line is drawen frome the centre F. vnto C, which is the
point of the touche, therefore saith the theoreme, that the
sayde line F.C, muste needes bee a perpendicular line vnto the
touche line D.E.

_The lxiij. Theoreme._

If a righte line doo touche a circle, and an other right
line be drawen from the pointe of their touchinge, so that
it doo make righte corners with the touche line, then shal
the centre of the circle bee in that same line, so drawen.

_Example._

[Illustration]

The circle is A.B.C, and the centre of it is G. The touche line
is D.C.E, and the pointe where it toucheth, is C. Nowe it
appeareth manifest, that if a righte line be drawen from the
pointe where the touch line doth ioine with the circle, and that
the said lyne doo make righte corners with the touche line, then
muste it needes go by the centre of the circle, and then
consequently it must haue the sayde centre in him. For if the
saide line shoulde go beside the centre, as F.C. doth, then
dothe it not make righte angles with the touche line, which in
the theoreme is supposed.

_The lxiiij. Theoreme._

If an angle be made on the centre of a circle, and an other
angle made on the circumference of the same circle, and
their grounde line be one common portion of the
circumference, then is the angle on the centre tw