879440
[Translation: ]
[Commentary:
This sheet contains Harriot's exploration of Proposition 2, Lemma 4, from the Sphaerica Menelai of Menelaus, as translated by Maurolico (1558). The text includes a supplement by Thabit ibn Qurra (see Add MS 6787
f.
f.
f. ).
For Harriot's copy of Propositions 1 and 2 see Add MS f. f. . The pages relevant to Proposition 2, Lemma 4, are f. , f. , and f. . ]
For Harriot's copy of Propositions 1 and 2 see Add MS f. f. . The pages relevant to Proposition 2, Lemma 4, are f. , f. , and f. . ]
Si fuerint sex quantitates, quorum ratio primæ ad secundum: componatur ex rationibus,
tertia ad quartam, et quintæ ad sextam. Tum solidum sub prima quarta et sexta
contentum, æquale erit solido sub secundo tertia et quinta
[Translation: If there are six quantities, where the ratio of the first to the second is composed of the ratio of the third to the fourth and of the fifth to the sixth, then the solid content of the first, fourth, and sixth will be equal to the solid composed of the second, third, and fifth.
tertia ad quartam, et quintæ ad sextam. Tum solidum sub prima quarta et sexta
contentum, æquale erit solido sub secundo tertia et quinta
[Translation: If there are six quantities, where the ratio of the first to the second is composed of the ratio of the third to the fourth and of the fifth to the sixth, then the solid content of the first, fourth, and sixth will be equal to the solid composed of the second, third, and fifth.
Sex
[Translation: The six ]
[Translation: The six ]
Ergo solidum
[Translation: Therefore the solid .
[Translation: Therefore the solid .
Varia transpositio utrinque solilidi solidi
[Translation: Various transpositions of the terms of both ]
[Translation: Various transpositions of the terms of both ]
Habitudines æqualium solidorum.
[Translation: Forms of equal ]
[Translation: Forms of equal ]
Thebit ben Corat.
et Mau
[Translation: Thabit ibn Qurra and ]
et Mau
[Translation: Thabit ibn Qurra and ]
[Translation: ]
componentes rationes
[Translation: components of the transposed ]
[Translation: components of the transposed ]
Si consequentes fiant antecedentes
et antecedentes consequentes; sunt alia
36
[Translation: If the consequents become antecedents and antecedents consequents, there are another 36 ]
et antecedentes consequentes; sunt alia
36
[Translation: If the consequents become antecedents and antecedents consequents, there are another 36 ]