called equall, that be
of one bygnesse, so that the one is nother greater nother lesser
then the other. And in this kinde of comparison, they must so
agree, that if the one be layed on the other, they shall exactly
agree in all their boundes, so that nother shall excede other.

[Illustration]

Nowe for the example of the Theoreme, I haue set forthe diuers
varieties of cantles of circles, amongest which the first and
seconde are made vpon equall lines, and ar also both equall and
like. The third couple ar ioyned in one, and be nother equall,
nother like, but expressyng an absurde deformitee, whiche would
folowe if this Theoreme wer not true. And so in the fourth
couple you maie see, that because they are not equall cantles,
therfore can not they be like cantles, for necessarily it goeth
together, that all cantles of circles made vpon equall right
lines, if they be like they must be equall also.

_The lxix. Theoreme._

In equall circles, suche angles as be equall are made vpon
equall arch lines of the circumference, whether the angle
light on the circumference, or on the centre.

_Example._

[Illustration]

Firste I haue sette for an exaumple twoo equall circles, that is
A.B.C.D, whose centre is K, and the second circle E.F.G.H, and
his centre L, and in eche of them is there made two angles, one
on the circumference, and the other on the centre of eche
circle, and they be all made on two equall arche lines, that is
B.C.D. the one, and F.G.H. the other. Now saieth the Theoreme,
that if the angle B.A.D, be equall to the angle F.E.H, then are
they made in equall circles, and on equall arch lines of their
circumference. Also if the angle B.K.D, be equal to the angle
F.L.H, then be they made on the centres of equall circles, and
on equall arche lines, so that you muste compare those angles
together, whiche are made both on the centres, or both on the
circumference, and maie not conferre those angles, wherof one is
drawen on the circumference, and the other on the centre. For
euermore the angle on the centre in suche sorte shall be double
to the angle on the circumference, as is declared in the three
score and foure Theoreme.

_The .lxx. Theoreme._

In equall circles, those angles whiche bee made on equall
arche lynes, are euer equall together, whether they be made
on the centre, or on the circumference.

_Example._

This Theoreme doth but conuert the sentence of the last Theoreme
before,