Such is the Adscription of a triangle: The adscription of an ordinate triangulate is now to be taught. And first the common adscription, and yet out of the former adscription, after this manner.
1. If right lines doe touch a periphery in the angles of the inscript ordinate triangulate, they shall onto a circle cirumscribe a triangulate homogeneall to the inscribed triangulate.
The examples shall be laid downe according as the species or severall kindes doe come in order. The speciall inscription therefore shall first be taught, and that by one side, which reiterated, as oft as need shall require, may fill up the whole periphery. For that Euclide did in the quindecangle
one of the kindes, we will doe it in all the rest.
2. If the diameters doe cut one another right-angle-wise, a right line subtended or drawne against the right angle, shall be the side of the quadrate. è 6 p iiij.
As here. For the shankes of the angle are the raies whose diameters knit together shall make foure rectangled triangles, equall in shankes: And by the [2 e vij], equall in bases. Therefore they they shall inscribe a quadrate.
Therefore
3. A quadrate inscribed is the halfe of that which is circumscribed.
Because the side of the circumscribed (which here is equall to the diameter of the circle) is of power double, to the side of the inscript, by the [9 e xij].