The Way To Geometry

Excerpt: ... 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 146 farther demonstration; but a ready and steddy hand in describing and working of it. Take therefore an infinite right line; upon the continue the particular parallelogrammes, As if the Triangulate aeiou, were given to be brought into a parallelogramme: Let it be resolved into three triangles, aei, aio, and aou: And let the Angle be y: First in the assigned Angle, upon the Infinite right line, make by the former the Parallelogramme ae, in the angle assigned, equall to aei, the first triangle. Then the second triangle, thou shalt so make upon the said Infinite line, that one of the shankes may fall upon the side of the equall complement; The other be cast on forward, and so forth in more, if neede be. Here thou hast 3 complements continued, and continuing the Parallelogramme: But it is best in making and working of them, to put out the former, and one of the sides of the inferiour or latter Diagonall, least the confusion of lines doe hinder or trouble thee. Therefore 23. A Parallelogramme is equall to his diagonals and complements. For a Parallelogramme doth consist of two diagonals, and as many complements: Wherefore a Parallelogramme is equall to his parts: And againe the parts are equall...