th him
but in one point, that is to say in A, so lykewaies the third
circle L.M, is drawen without the firste circle and toucheth
hym, as you maie see, but in one place. And now as for the
.iiij. circle, it is drawen to declare the diuersitie betwene
touchyng and cuttyng, or crossyng. For one circle maie crosse
and cutte a great many other circles, yet can be not cutte any
one in more places then two, as the fiue and fiftie Theoreme
affirmeth.

_The .lix. Theoreme._

In euerie circle those lines are to be counted equall,
whiche are in lyke distaunce from the centre, And contrarie
waies they are in lyke distance from the centre, whiche be
equall.

_Example._

[Illustration]

In this figure you see firste the circle drawen, whiche is
A.B.C.D, and his centre is E. In this circle also there are
drawen two lines equally distaunt from the centre, for the line
A.B, and the line D.C, are iuste of one distaunce from the
centre, whiche is E, and therfore are they of one length. Again
thei are of one lengthe (as shall be proued in the boke of
profes) and therefore their distaunce from the centre is all
one.

_The lx. Theoreme._

In euerie circle the longest line is the diameter, and of
all the other lines, thei are still longest that be nexte
vnto the centre, and they be the shortest, that be farthest
distaunt from it.

_Example._

[Illustration]

In this circle A.B.C.D, I haue drawen first the diameter, whiche
is A.D, whiche passeth (as it must) by the centre E, Then haue I
drawen ij. other lines as M.N, whiche is neerer the centre, and
F.G, that is farther from the centre. The fourth line also on
the other side of the diameter, that is B.C, is neerer to the
centre then the line F.G, for it is of lyke distance as is the
lyne M.N. Nowe saie I, that A.D, beyng the diameter, is the
longest of all those lynes, and also of any other that maie be
drawen within that circle, And the other line M.N, is longer
then F.G. Also the line F.G, is shorter then the line B.C, for
because it is farther from the centre then is the lyne B.C. And
thus maie you iudge of al lines drawen in any circle, how to
know the proportion of their length, by the proportion of their
distance, and contrary waies, howe to discerne the proportion of
their distance by their lengthes, if you knowe the proportion of
their length. And to speake of it by the waie, it is a
maruaylouse thyng to consider, that a man maie knowe an ex