29 If the angle of the secant and touch line be equall to an assigned rectilineall angle, the angle in the opposite section shall likewise be equall to the same. 34. p iij.
As in this figure underneath. And from hence one may from a circle given cut off a section, in which there is an
angle equall to the assigned. As let the angle given be a: And the circle eio. Thou must make at the point e, of the secant eo, and the tangent yu, an angle equall to the assigned, by the [11 e iij]. such as here is oeu: Then the section oei, shall containe an angle equall to the assigned.
Of Geometry the seventeenth Booke, Of the Adscription of a Circle and Triangle.
Hitherto we have spoken of the Geometry of Rectilineall plaines, and of a circle: Now followeth the Adscription of both: This was generally defined in the first book [12 e]. Now the periphery of a circle is the bound therof. Therefore a rectilineall is inscribed into a circle, when the periphery doth touch the angles of it 3 d iiij. It is circumscribed when it is touched of every side by the periphery; 4 d iij.
1. If rectilineall ascribed unto a circle be an equilater, it is equiangle.
Of the inscript it is manifest; And that of a Triangle by it selfe: Because if it be equilater, it is equiangle, by the [19 e vj]. But in a Triangulate the matter is to be prooved by demonstration. As here, if the inscripts ou, and sy, be equall, then doe they subtend equall peripheries, by the 32