393197
[Commentary:
This question is a slight variation on a question from Girolamo De arithmetica liber X (= Ars magna)
(Cardano , page 143, Chapter 39, Question I:
Quaestio I.
Exemplum. Inuenias tres numeros in continua proportione, quorum quadratum primi fit aequale secundo & & quadratum tertij fit aequale quadratis primi &
Question 1.
Example. Find three numbers in continual proportion, such that the square of the first is equal to the second and third, and the square of the third is equal to the square of the first and ]
Quaestio I.
Exemplum. Inuenias tres numeros in continua proportione, quorum quadratum primi fit aequale secundo & & quadratum tertij fit aequale quadratis primi &
Question 1.
Example. Find three numbers in continual proportion, such that the square of the first is equal to the second and third, and the square of the third is equal to the square of the first and ]
Cardan. Arith, lib. 10. cap. 39. pag.
[Translation: Cardano, De arithmetica liber X, Chapter 39, page 143.
[Translation: Cardano, De arithmetica liber X, Chapter 39, page 143.
Invenire tres numeros
continue proportionales
quorum tertius sit aequalis
primo et secundo, et
quadratum primi sit aequale
aggregato secundi et
[Translation: Find three numbers in continual proportion of which the third is equal to the first and second, and the square of the first is equal to the sum of the second and third.
continue proportionales
quorum tertius sit aequalis
primo et secundo, et
quadratum primi sit aequale
aggregato secundi et
[Translation: Find three numbers in continual proportion of which the third is equal to the first and second, and the square of the first is equal to the sum of the second and third.
Argumentatio
[Translation: First ]
[…]
Ergo prima dispositio terminorum proportionalium ex prima conditione illata
ita se
[Translation: Therefore the arrangement of proportional terms according to the first condition is had ]
[Translation: First ]
[…]
Ergo prima dispositio terminorum proportionalium ex prima conditione illata
ita se
[Translation: Therefore the arrangement of proportional terms according to the first condition is had ]
Argumentatio secunda, seu de secunda
[Translation: Second argument, or from the second ]
[…]
Unde tres proportionales
[Translation: Whence the three proportionals ]
Examen fit in altera
[Translation: To be tested in another ]
[Translation: Second argument, or from the second ]
[…]
Unde tres proportionales
[Translation: Whence the three proportionals ]
Examen fit in altera
[Translation: To be tested in another ]
Aggregatum I + II + III vel duplum
[Translation: The sum of the first, second, and third is , or twice the third.
[Translation: The sum of the first, second, and third is , or twice the third.