3 Oblongs made of the whole line given, and of the segments, are equall to the quadrate of the whole 2 p ij.
This is also a Consectary out of the [7. e xj].
As let the line ae, 6. be cut into ai, 2. io. 2. and oe, 2. The Oblongs as, 12. ir, 12. and oy, 12. made of the whole ae, and of those segments, are equall to ay, the quadrates of the whole.
Here the segments are more than two, and yet notwithstanding from the first the rest may be taken for one, seeing that the particular rectangle in like manner is equall to them. This proposition is used in the demonstration of the [9. e xviij].
Thirdly,
4 Two Oblongs made of the whole line given, and of the one segment, with the third quadrate of the other segment, are equall to the quadrates of the whole, and of the said segment. 7 p ij.
As for example, let the right line ae, 8. be cut into ai, 6. and ie, 2. The oblongs ao, and iu, of the whole, and 2. the segments, are 32. The quadrate of 6. the other segment 36. And the whole 68. Now the quadrate, of the whole ae. 8. is 64. And the quadrate of the said segment 2, is 4. And the summe of these is 68.