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[Commentary:
On this page Harriot investigates Proposition 18 from Supplementum geometriæ
(Viète 1593c, Prop .
Proposition XVIII.
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: triplum solidum sub quadrato cruris communis & dimidia base primi multata continuatave longitudine ejus cujus quadratum æquale est triplo quadrato altitudinis primi, cum multabitur ejusdem dimidiæ basis multatæ continuatve cubo, æquale est solido sub base secundi & ejusdem cruris
If two triangles are each isosceles, equal to one another in their legs, and moreover the angle at the base of the second is three times the angle at the base of the first, then three times the product of the square of the common leg and half the base of the first decreased or increased by a length whose square is equal to three times the square of the altitude of the first, when reduced by the cube of the same half base thus decreased or increased, is equal to the product of the second base and the square of the common leg.
For Harriot's statement of Propostion 18, and a geometric version of the proof, see Add MS f. . Here he works the proposition algebraically.
This page also refers to Proposition 17 from the Supplementum, (see MS 6784 f. ). ]
Proposition XVIII.
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: triplum solidum sub quadrato cruris communis & dimidia base primi multata continuatave longitudine ejus cujus quadratum æquale est triplo quadrato altitudinis primi, cum multabitur ejusdem dimidiæ basis multatæ continuatve cubo, æquale est solido sub base secundi & ejusdem cruris
If two triangles are each isosceles, equal to one another in their legs, and moreover the angle at the base of the second is three times the angle at the base of the first, then three times the product of the square of the common leg and half the base of the first decreased or increased by a length whose square is equal to three times the square of the altitude of the first, when reduced by the cube of the same half base thus decreased or increased, is equal to the product of the second base and the square of the common leg.
For Harriot's statement of Propostion 18, and a geometric version of the proof, see Add MS f. . Here he works the proposition algebraically.
This page also refers to Proposition 17 from the Supplementum, (see MS 6784 f. ). ]
prop. 18.
[Translation: Proposition 18 from the ]
[Translation: Proposition 18 from the ]