ration]

This theoreme seemeth of it selfe so manifest, that it neadeth
nother demonstration nother declaracion. Yet for the plaine
vnderstanding of it, I haue sette forthe a figure here, where
ij. circles be drawen, so that one of them doth crosse the other
(as you see) in the pointes B. and G, and their centres appear
at the firste sighte to bee diuers. For the centre of the one is
F, and the centre of the other is E, which diffre as farre
asondre as the edges of the circles, where they bee most
distaunte in sonder.

_The Li. Theoreme._

If two circles be so drawen, that one of them do touche the
other, then haue they not one centre.

_Example._

[Illustration]

There are two circles made, as you see, the one is A.B.C, and
hath his centre by G, the other is B.D.E, and his centre is by
F, so that it is easy enough to perceaue that their centres doe
dyffer as muche a sonder, as the halfe diameter of the greater
circle is longer then the half diameter of the lesser circle. And
so must it needes be thought and said of all other circles in
lyke kinde.

_The .lij. theoreme._

If a certaine pointe be assigned in the diameter of a
circle, distant from the centre of the said circle, and from
that pointe diuerse lynes drawen to the edge and
circumference of the same circle, the longest line is that
whiche passeth by the centre, and the shortest is the
residew of the same line. And of al the other lines that is
euer the greatest, that is nighest to the line, which
passeth by the centre. And contrary waies, that is the
shortest, that is farthest from it. And amongest them all
there can be but onely .ij. equall together, and they must
nedes be so placed, that the shortest line shall be in the
iust middle betwixte them.

_Example._

[Illustration]

The circle is A.B.C.D.E.H, and his centre is F, the diameter is
A.E, in whiche diameter I haue taken a certain point distaunt
from the centre, and that pointe is G, from which I haue drawen
.iiij. lines to the circumference, beside the two partes of the
diameter, whiche maketh vp vi. lynes in all. Nowe for the
diuersitee in quantitie of these lynes, I saie accordyng to the
Theoreme, that the line whiche goeth by the centre is the
longest line, that is to saie, A.G, and the residewe of the same
diameter beeyng G.E, is the shortest lyne. And of all the other
that lyne is longest, that is neerest vnto that parte of the
diameter whiche