701351
[Commentary:
On this page Harriot investigates Proposition 16 from Supplementum geometriæ
(Viète 1593c, Prop .
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.
The working contains a reference to Euclid's Elements, Proposition .
If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half that line. ]
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.
The working contains a reference to Euclid's Elements, Proposition .
If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half that line. ]
prop. 16.
[Translation: Proposition 16 from the ]
[Translation: Proposition 16 from the ]
Si duo triangula fuerint aequicrura singula,
et 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
et cruris communis quadrato, aequalis
est solido sub base secundi et ejusdem
cruris
[Translation: 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.
et 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
et cruris communis quadrato, aequalis
est solido sub base secundi et ejusdem
cruris
[Translation: 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.
per 5,2 el.
[…]
Quia parallogramma æquialta
et sunt ut bases. . .
[…]
vel per notas
simplices
Resoluatur analogia et erit:
[Translation: by Elements II.5
Because the parallelograms are of equal height and are as the bases , .
or in simple notation
The ratio is resolved, and hence the ]
[…]
Quia parallogramma æquialta
et sunt ut bases. . .
[…]
vel per notas
simplices
Resoluatur analogia et erit:
[Translation: by Elements II.5
Because the parallelograms are of equal height and are as the bases , .
or in simple notation
The ratio is resolved, and hence the ]
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