gooeth by the centre, and that is shortest, that
is farthest distant from it, wherefore I saie, that G.B, is
longer then G.C, and therfore muche more longer then G.D, sith
G.C, also is longer then G.D, and by this maie you soone
perceiue, that it is not possible to drawe .ij. lynes on any one
side of the diameter, whiche might be equall in lengthe
together, but on the one side of the diameter maie you easylie
make one lyne equall to an other, on the other side of the same
diameter, as you see in this example G.H, to bee equall to G.D,
betweene whiche the lyne G.E, (as the shortest in all the
circle) doothe stande euen distaunte from eche of them, and it
is the precise knoweledge of their equalitee, if they be equally
distaunt from one halfe of the diameter. Where as contrary waies
if the one be neerer to any one halfe of the diameter then the
other is, it is not possible that they two may be equall in
lengthe, namely if they dooe ende bothe in the circumference of
the circle, and be bothe drawen from one poynte in the diameter,
so that the saide poynte be (as the Theoreme doeth suppose)
somewhat distaunt from the centre of the said circle. For if
they be drawen from the centre, then must they of necessitee be
all equall, howe many so euer they bee, as the definition of a
circle dooeth importe, withoute any regarde how neere so euer
they be to the diameter, or how distante from it. And here is to
be noted, that in this Theoreme, by neerenesse and distaunce is
vnderstand the nereness and distaunce of the extreeme partes of
those lynes where they touche the circumference. For at the
other end they do all meete and touche.

_The .liij. Theoreme._

If a pointe bee marked without a circle, and from it diuerse
lines drawen crosse the circle, to the circumference on the
other side, so that one of them passe by the centre, then
that line whiche passeth by the centre shall be the loongest
of them all that crosse the circle. And of the other lines
those are longest, that be nexte vnto it that passeth by the
centre. And those ar shortest, that be farthest distant from
it. But among those partes of those lines, whiche ende in
the outewarde circumference, that is most shortest, whiche
is parte of the line that passeth by the centre, and
amongeste the othere eche, of them, the nerer they are vnto
it, the shorter they are, and the farther from it, the
longer they be. And amongest them all there can not