19 If the base of a triangle doe subtend an obtuse angle, the power of it is more than the power of the shankes, by a double right angle of the one, and of the continuation from the said obtusangle unto the perpendicular of the toppe. 12. p ij.
Or thus: If the base of a triangle doe subtend an obtuse angle, it is in power more than the feete, by the right angled figure twise taken, which is contained under one of the feete and the line continued from the said foote unto the perpendicular drawne from the toppe of the triangle. H.
There is a comparison of a quadrate with two in like manner triangles, and as many quadrates, but of unequality.
As in the triangle aei, the quadrate of the base ai, is greater in power, than the quadrates of the shankes ae, and ei, by double of the rectangle ar, which is made of ae, one of the shankes, and of eo, the continuation of the same ae, unto o, the perpendicular of the toppe i.
For by [9. e], the quadrate of ai, is equall to the quadrates of ao, and oi, that is, to three quadrates, of io, oe, ea, and the double rectangle aforesaid. But the quadrates of the shankes ae, ei, are equall to those three quadrates, to wit, of ai, his owne quadrate, and of ei, two, the first io, the second oe, by the [9. e.] Therefore the excesse remaineth of a double rectangle.
Of Geometry, the thirteenth Booke, Of an Oblong.
