ch is brought for the
explication of this laste theoreme, by whiche you may without
any teachinge easyly perceaue both the meanyng and also the
truth of this proposition.

_The Liiij. Theoreme._

If a point be set forthe in a circle, and from that pointe
vnto the circumference many lines drawen, of which more then
two are equal togither, then is that point the centre of
that circle.

_Example._

[Illustration]

The circle is A.B.C, and within it I haue sette fourth for an
example three prickes, which are D.E. and F, from euery one of
them I haue drawen (at the leaste) iiij. lines vnto the
circumference of the circle but frome D, I haue drawen more, yet
maye it appear readily vnto your eye, that of all the lines
whiche be drawen from E. and F, vnto the circumference, there
are but twoo equall, and more can not bee, for G.E. nor E.H.
hath none other equal to theim, nor canne not haue any beinge
drawen from the same point E. No more can L.F, or F.K, haue anye
line equall to either of theim, beinge drawen from the same
pointe F. And yet from either of those two poinctes are there
drawen twoo lines equall togither, as A.E, is equall to E.B, and
B.F, is equall to F.C, but there can no third line be drawen
equall to either of these two couples, and that is by reason
that they be drawen from a pointe distaunte from the centre of
the circle. But from D, althoughe there be seuen lines drawen,
to the circumference, yet all bee equall, bicause it is the
centre of the circle. And therefore if you drawe neuer so mannye
more from it vnto the circumference, all shall be equal, so that
this is the priuilege (as it were of the centre) and therfore no
other point can haue aboue two equal lines drawen from it vnto
the circumference. And from all pointes you maye drawe ij.
equall lines to the circumference of the circle, whether that
pointe be within the circle or without it.

_The lv. Theoreme._

No circle canne cut an other circle in more pointes then
two.

_Example._

[Illustration]

The first circle is A.B.F.E, the second circle is B.C.D.E, and
they crosse one an other in B. and in E, and in no more pointes.
Nother is it possible that they should, but other figures ther
be, which maye cutte a circle in foure partes, as you se in this
example. Where I haue set forthe one tunne forme, and one eye
forme, and eche of them cutteth euery of their two circles into
foure partes. But as they be irregulare f