15. If a right line be cut into two segments, the quadrate of the whole is equall to the quadrats of the segments, and a double rectanguled figure, made of them both. 4 p ij.
The third rate of a quadrate is hereafter with two rectangles, and two quadrates, and first of equality.
This is a consectary out of the [22 e x]: Because a parallelogramme is equall to his two diagonals and complements. If the right ae, be cut in i, it maketh the quadrate aeuo, greater than eyi, and yus, the quadrates of the segments, by the two rectangles ay and yo. This is the rate of a quadrate with a rectangle and a quadrate. But the side of a quadrate proposed in a number is oft times sought. Therefore by the
next precedent element and his consectaries, the analysis or finding of the side of a quadrate is made and taught.
Therefore
16. The side of the first diagonall, is the side of one of the complements; And being doubled, it is the side of them both together: Now the other side of the same complements both together, is the side of the other diagonall.
The side of a quadrate given is many times in numbers sought. Therefore by the former element and his consectaries the resolution of a quadrates side is framed and performed.
Let therefore the side now of the quadrate number given be sought: And first let the Genesis or making be considered, such as you see here by the multiplication of numbers in the numbers themselves:
| 10 2 | 10 2 | The number or |
| 10 2 | 10 2 | side divided. |
| ——— | ——— | |
| 2 4 | 4 | The lesser diagonall. |
| 2 0 | Or thus 2 0 | One Complement. |
| 1 0 0 | 2 0 | Th'other Complement |
| ——— | 1 0 0 | The greater diagonall. |
| 1 4 4 | ——— | |
| 1 4 4 | The quadrate. |