ormes, that is to saye,
suche formes as haue no precise measure nother proportion in
their draughte, so can there scarcely be made any certaine
theorem of them. But circles are regulare formes, that is to
say, such formes as haue in their protracture a iuste and
certaine proportion, so that certain and determinate truths may
be affirmed of them, sith they ar vniforme and vnchaungable.

_The lvi. Theoreme._

If two circles be so drawen, that the one be within the
other, and that they touche one an other: If a line bee
drawen by bothe their centres, and so forthe in lengthe,
that line shall runne to that pointe, where the circles do
touche.

_Example._

[Illustration]

The one circle, which is the greattest and vttermost is A.B.C,
the other circle that is y^e lesser, and is drawen within the
firste, is A.D.E. The centre of the greater circle is F, and the
centre of the lesser circle is G, the pointe where they touche
is A. And now you may see the truthe of the theoreme so
plainely, that it needeth no farther declaracion. For you maye
see, that drawinge a line from F. to G, and so forth in lengthe,
vntill it come to the circumference, it wyll lighte in the very
poincte A, where the circles touche one an other.

_The Lvij. Theoreme._

If two circles bee drawen so one withoute an other, that
their edges doo touche and a right line bee drawnenne frome
the centre of the one to the centre of the other, that line
shall passe by the place of their touching.

_Example._

[Illustration]

The firste circle is A.B.E, and his centre is K, The second
circle is D.B.C, and his centre is H, the point wher they do
touch is B. Nowe doo you se that the line K.H, whiche is drawen
from K, that is centre of the firste circle, vnto H, beyng
centre of the second circle, doth passe (as it must nedes by the
pointe B,) whiche is the verye poynte wher they do to touche
together.

_The .lviij. theoreme._

One circle can not touche an other in more pointes then one,
whether they touche within or without.

_Example._

[Illustration]

For the declaration of this Theoreme, I haue drawen iiij.
circles, the first is A.B.C, and his centre H. the second is
A.D.G, and his centre F. the third is L.M, and his centre K. the
.iiij. is D.G.L.M, and his centre E. Nowe as you perceiue the
second circle A.D.G, toucheth the first in the inner side, in so
much as it is drawen within the other, and yet it touche