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[Commentary:
The reference on this page is to Proposition 16 from Supplementum geometriæ
(Viète .
Proposition XVI.
Si duo triangula fuerint aequicrura singula, & ipsa alterum alteri cruribus aequalia, angulus autem qui est ad basin secundi sit triplus anguli qui est ad basin primi: cubus ex base primi, minus triplo solido sub base primi & cruris communis quadrato, aequalis est solido sub base secundi & ejusdem cruris
If two triangles are each isosceles, the legs of one equal to the legs of the other, and moreover the angle at the base of the second is three times the angle at the base of the first, then the cube of the first base, minus three times the product of the base of the first and the square of the common side, is equal to the product of the second base and the square of the same side.
For Harriot's statement of Proposition 16, and a geometric version of the proof, see Add MS f. . Here he works the proposition algebraically. ]
Proposition XVI.
Si duo triangula fuerint aequicrura singula, & ipsa alterum alteri cruribus aequalia, angulus autem qui est ad basin secundi sit triplus anguli qui est ad basin primi: cubus ex base primi, minus triplo solido sub base primi & cruris communis quadrato, aequalis est solido sub base secundi & ejusdem cruris
If two triangles are each isosceles, the legs of one equal to the legs of the other, and moreover the angle at the base of the second is three times the angle at the base of the first, then the cube of the first base, minus three times the product of the base of the first and the square of the common side, is equal to the product of the second base and the square of the same side.
For Harriot's statement of Proposition 16, and a geometric version of the proof, see Add MS f. . Here he works the proposition algebraically. ]
prop. 16.
[Translation: Proposition 16 from the ]
[Translation: Proposition 16 from the ]
duplicature
cubus
[Translation: the cube is ]
cubus
[Translation: the cube is ]