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 example. For as that did declare the equalitie of the arche lines, by the equalitie of the righte lines, so dothe this Theoreme

declare the equalnes of the right lines to ensue of the equalnes of the arche lines, and therefore declareth that right lyne B.D, to be equal to the other right line F.H, bicause they both are drawen vnder equall arche lines, that is to saye, the one vnder B.A.D, and thother vnder F.E.H, and those two arch lines are estimed equall by the theoreme laste before, and shal be proued in the booke of proofes.

[ The lxxiij. Theoreme.]

In euery circle, the angle that is made in the halfe circle, is a iuste righte angle, and the angle that is made in a cantle greater then the halfe circle, is lesser thanne a righte angle, but that angle that is made in a cantle, lesser then the halfe circle, is greatter then a right angle. And moreouer the angle of the greater cantle is greater then a righte angle and the angle of the lesser cantle is lesser then a right angle.

Example.