The fourth part followeth of the third.
The fifth let it be thus: sr, making the angle asr, equall to the angle asu, the bases au, and ar, shall be equall by the [2 e vij]. To these if the third be supposed to be equall, as al, it would follow by the [1 e vij]. that the whole angle sa, should be equall to rsa, the particular angle, which is impossible. And out of this fifth part issueth this Consectary.
Therefore
17 If a point in a circle be the bound of three equall right lines determined in the periphery, it is the center of the circle. 9 p iij.
Let the point a, in a circle be the common bound of three right lines, ending in the periphery and equall betweene themselves, be ae, ai, au. I say this point is the center of the Circle.
Otherwise from a point of the diameter which is not the center, not onely two right lines on each side should be equall. For by any point whatsoever the diameter may be drawne. Such was before observed in a quinquangle; If three angles be equall, all are equall; so in a Circle: If three right lines falling from the same point unto the perephery be equall, all are equall.
18 Of right lines drawne from a point assigned without the periphery, unto the concavity or hollow of the same, that which is by the center is the greatest; And that next to the greatest, is greater than that which is farther off: But of those which fall upon the convexitie of the circumference, the segment of the greatest is least. And that which is next unto the least is lesser than that is farther off: And two on each side of the greatest or least are onely equall. 8 p iij.