and therfore is to be vnderstande by the same examples,
for as that saith, that equall angles occupie equall archelynes,
so this saith, that equal arche lines causeth equal angles,
consideringe all other circumstances, as was taughte in the
laste theoreme before, so that this theoreme dooeth affirming
speake of the equalitie of those angles, of which the laste
theoreme spake conditionally. And where the laste theoreme spake
affirmatiuely of the arche lines, this theoreme speaketh
conditionally of them, as thus: If the arche line B.C.D. be
equall to the other arche line F.G.H, then is that angle B.A.D.
equall to the other angle F.E.H. Or els thus may you declare it
causally: Bicause the arche line B.C.D, is equal to the other
arche line F.G.H, therefore is the angle B.K.D. equall to the
angle F.L.H, consideringe that they are made on the centres of
equall circles. And so of the other angles, bicause those two
arche lines aforesaid ar equal, therfore the angle D.A.B, is
equall to the angle F.E.H, for as muche as they are made on
those equall arche lines, and also on the circumference of
equall circles. And thus these theoremes doo one declare an
other, and one verifie the other.

_The lxxi. Theoreme._

In equal circles, equall right lines beinge drawen, doo
cutte awaye equalle arche lines frome their circumferences,
so that the greater arche line of the one is equall to the
greater arche line of the other, and the lesser to the
lesser.

_Example._

[Illustration]

The circle A.B.C.D, is made equall to the circle E.F.G.H, and
the right line B.D. is equal to the righte line F.H, wherfore it
foloweth, that the ij. arche lines of the circle A.B.D, whiche
are cut from his circumference by the right line B.D, are equall
to two other arche lines of the circle E.F.H, being cutte frome
his circumference, by the right line F.H. that is to saye, that
the arche line B.A.D, beinge the greater arch line of the firste
circle, is equall to the arche line F.E.H, beynge the greater
arche line of the other circle. And so in like manner the lesser
arche line of the firste circle, beynge B.C.D, is equal to the
lesser arche line of the seconde circle, that is F.G.H.

_The lxxij. Theoreme._

In equall circles, vnder equall arche lines the right lines
that bee drawen are equall togither.

_Example._

This Theoreme is none other, but the conuersion of the laste
Theoreme beefore, and therefore needeth none other