Therefore
21. If one of the Complements be made equall to a triangle given, in a right-lined angle given, the other made upon a right line given shall be in like manner equall to the same triangle. 44 p j.
As if thou shouldest desire to have a parallelogramme upon a right line given, and in a right lined angle given, to be made equall to a triangle given, this proposition shall give satisfaction.
Let aei be the Triangle given: The Angle be o: And the right line given be iu: And the Parallelogramme ay is equall to aei, triangle given in the angle assigned, by the [13 e]. Then let the side ay, bee continued to r, equally to iu, the line given: And let ru be knit by a right line: And from r drawne out a diagony untill it doe meete with as, infinitely continued; which shall meete with it, by the [19 e v], in l. And the sides yi, and ru, let them be continued equally to sl. in m and n. And knit ln together with a right line. This complement mu, is equall to the complement ys, which is equall to the Triangle assigned, by the former, and that in a right lined angle given.
And
22 If parallelogrammes be continually made equall to all the triangles of an assigned triangulate, in a right lined angle given, the whole parallelogramme shall in like manner be equall to the whole triangulate. 45 p j.
This is a corollary of the former, of the Reason or rate of a Parallelogramme with a Triangulate; and it needeth no
farther demonstration; but a ready and steddy hand in describing and working of it.
