705353
[Translation: ]
[Commentary:
On this page Harriot investigates Propositions 12, 13, and 14 from Supplementum geometriæ
(Viète 1593c, Props 12, 13, .
Proposition XII.
Si fuerint tres lineæ rectæ proportionales: cubus compositæ e duabus extremis, minus solido quod fit sub eadem composita & adgregato quadratorum a tribus, æqualis est solido sub eadem composita & quadrato
If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the
Proposition XIII.
Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregato quadratorum a tribus, minus cubo e prima, æquale est solido sub eadem prima & adgregato quadratorum secundæ &
If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.
Proposition XIV.
Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregatum quadratorum a tribus, minus cubo e tertia, æquale est solido sub eadem tertia & adgregato quadratorum primæ &
If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.
The 'Consectarium' appears verbally in Viete's proposition; Harriot has re-written it in symbolic ]
Proposition XII.
Si fuerint tres lineæ rectæ proportionales: cubus compositæ e duabus extremis, minus solido quod fit sub eadem composita & adgregato quadratorum a tribus, æqualis est solido sub eadem composita & quadrato
If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the
Proposition XIII.
Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregato quadratorum a tribus, minus cubo e prima, æquale est solido sub eadem prima & adgregato quadratorum secundæ &
If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.
Proposition XIV.
Si fuerint tres lineæ rectæ proportionales: solidum sub prima & adgregatum quadratorum a tribus, minus cubo e tertia, æquale est solido sub eadem tertia & adgregato quadratorum primæ &
If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.
The 'Consectarium' appears verbally in Viete's proposition; Harriot has re-written it in symbolic ]
prop. 12.
[Translation: Proposition 12 from the ]
[Translation: Proposition 12 from the ]
Si fuerint tres lineæ rectæ proportionales: cubus compositæ e duabus extremis,
minus solido quod fit sub eadem composita et adgregato quadratorum a tribus:
æqualis est solido sub eadem composita et quadrato
[Translation: If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the ]
Sint 3 continue proportionales
utrinque addatur
[…]
Fiant solida ab extremis et etiam a medijs, et inde:
[Translation: let there be three continued proportionals
add to each side
There may be made solids from the extremes and also form the means, and hence the ]
minus solido quod fit sub eadem composita et adgregato quadratorum a tribus:
æqualis est solido sub eadem composita et quadrato
[Translation: If there are three proportional lines, the cube of the sum of the two extremes, minus the product of that sum and the sum of squares of all three, is equal to the product of the sum and the square of the ]
Sint 3 continue proportionales
utrinque addatur
[…]
Fiant solida ab extremis et etiam a medijs, et inde:
[Translation: let there be three continued proportionals
add to each side
There may be made solids from the extremes and also form the means, and hence the ]
Prop. 13. Si fuerint tres lineæ rectæ proportionales: solidum sub prima et adgregato
quadratorum tribus, minus cubo e prima: æquale est solido sub eadem
prima et adgregato quadratorum secundæ et
[Translation: Proposition 13. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.
Sint tres continue proportionales
[…]
Resoluatur Analogia et erit:
[Translation: Let there be three continued proportionals
The ratio is resolved, and hence the ]
quadratorum tribus, minus cubo e prima: æquale est solido sub eadem
prima et adgregato quadratorum secundæ et
[Translation: Proposition 13. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the first, is equal to the product of the first and the sum of squares of the second and third.
Sint tres continue proportionales
[…]
Resoluatur Analogia et erit:
[Translation: Let there be three continued proportionals
The ratio is resolved, and hence the ]
Prop. 14. Si fuerint tres lineæ rectæ proportionales: solidum sub prima et adgregatum quadratorum
a tribus minus cubo e tertia: æquale est solido sub eadem tertia et adgregato
quadratorum primæ et
[Translation: Proposition 14. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.
Sint tres continue proportionales
[…]
Resoluatur Analogia et erit:
[Translation: Let there be three continued proportionals
The ratio is resolved, and hence the ]
a tribus minus cubo e tertia: æquale est solido sub eadem tertia et adgregato
quadratorum primæ et
[Translation: Proposition 14. If there are three proportional lines, the product of the first and the sum of squares of all three, minus the cube of the third, is equal to the product of the third and the sum of the first and second.
Sint tres continue proportionales
[…]
Resoluatur Analogia et erit:
[Translation: Let there be three continued proportionals
The ratio is resolved, and hence the ]
[Translation: ]
Quia æquantur æqualibus
ex antecedente
[Translation: Because equals are equated to equals, by the preceding ]
ex antecedente
[Translation: Because equals are equated to equals, by the preceding ]
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