Or thus: If the base of a right angled triangle be cut in double proportion, by a perpendicular comming from the right angle, it is in power sesquialter to the greater foote; and treble to the lesser: But if the base be cut in quadruple proportion, it is sesquiarta to the greater side, and quintuple to the lesser.
As in aei, let the base ae, be so cut that the segment ao, be double to the segment oe, to wit, as 2 is to 1. The whole ae, shall be unto ao sesquialtera, that is, as 2 is to 3. And therefore by the [10 e viij], and [25 e iiij], the square of ae, shall be sesquialterum unto the square of ai.
And by the same argument it shall be treble unto the quadrate or square of ei.
The other, of the fourefold or quadruple section, are manifest in the figure following, by the like argument.
14 If a right line be cut into how many parts so ever, the power of it is manifold unto the power of segment, denominated of the square of the number of the section.
Or thus: if a right line be cut into how many parts soever it is in power the multiplex of the segment, the square of the number of the section, being denominated thereof: H.
So if it be cut into two equall parts, the power of it shall be foure times so much, as is the power of the halfe, taking demonstration from 4, which is the square of 2, according to which the division was made: If it be cut into three equall parts, the power of it shall be nine fold the power of the third part. If into foure equall parts, it shall be 16 times so much as is the power of the quarter: As here thou seest in these examples.