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 to their whole.
24. The Gnomon is any one of the Diagonall with the two complements.
There is therefore in every Parallelogramme a double Gnomon; as in these two examples. Of all the space of a
parallelogramme about his diameter, any parallelogramme with the two complements, let it be called the Gnomon. Therefore the gnomon is compounded, or made of both the kindes of diagonall and complements.
