The same argument shall serve in a Triangulate.
6. If two right lines do right anglewise cut into two equall parts two sides of an assigned rectilineall, the circle of the ray from their meeting unto the angle, shall be circumscribed unto the assigned rectilineall. 5 p iiij.
As in former figures. The demonstration is the same with the former. For the three rayes, by the [2 e vij], are equall: And the meeting of them, by the [17 e x], is the center.
And thus is the common adscription of a circle: The adscription of a rectilineall followeth, and first of a Triangle.
7. If two inscripts, from the touch point of a right line and a periphery, doe make two angles on each side equall to two angles of the triangle assigned be knit together, they shall inscribe a triangle into the circle given, equiangular to the triangle given è 2 p iiij.
Let the Triangle aei be given: And the circle, o, into which a Triangle equiangular to the triangle given, is to be inscribed. Therefore let the right line uys, touch the periphery yrl: And from the touch y, let the inscripts yr, and yl, make with the tangent two angles uyr, and syl, equall to the assigned angles aei, and aie: And let them be knit together with the right line rl: They shall by the [27 e xvj], make the angle of the alterne segments equall to the angles uyr, and syl. Therefore by the [4 e vij] seeing that two are equall, the other must needs be equall to the remainder.
The circumscription here is also speciall.