848425
[Translation: ]
[Commentary:
The reference towards the end of this page is to Giambattista Diversarum speculationum mathematicarum et physicarum liber
(Benedetti 1585, , though the theorem on page 26 is actually Theorem 41, not Theorem 45.
There is also a reference to Proposition 13 from Effectionum geometricarum canonica recensio (Viète 1593b, Prop , which explains how to find two quantities from their geometric mean and their sum. ]
There is also a reference to Proposition 13 from Effectionum geometricarum canonica recensio (Viète 1593b, Prop , which explains how to find two quantities from their geometric mean and their sum. ]
[Translation: ]
Data in partibus
[Translation: Given in parts of the ]
[Translation: Given in parts of the ]
Ex Methodo
Adde [???]
vel illa æqualium
qui in centro
sed in
[Translation: By the method: add or its equal which in the centre is but in the beginning .
[Translation: ]
Adde [???]
vel illa æqualium
qui in centro
sed in
[Translation: By the method: add or its equal which in the centre is but in the beginning .
[Translation: ]
tum quæritur et inde . per Theor. 45. pag. 26. Joh. Baptistæ
de
[Translation: then there is sought and hence , by Theorem 45, page 26, Johan Baptista de Benedictis
de
[Translation: then there is sought and hence , by Theorem 45, page 26, Johan Baptista de Benedictis
Vel per
[Translation: Or by ]
Sit . tum erit . hoc multiplicatum per faciet .
quod æquale erit rectangulo et , hoc est 78,545,532.
Forma æquationis ita erit .
Et duplis erit responsum,
[Translation: Let . then will be . This multiplied by makes .
which is equal to the rectangle of and , that is 78,545,532.
Thus the form of the equation will be .
And it will be twice the answer, ]
Habetur alias per 13 prop. Geom. Effect.
[Translation: can be had otherwise by Proposition 13 of Viète, Effectionum geometricarum.
[Translation: Or by ]
Sit . tum erit . hoc multiplicatum per faciet .
quod æquale erit rectangulo et , hoc est 78,545,532.
Forma æquationis ita erit .
Et duplis erit responsum,
[Translation: Let . then will be . This multiplied by makes .
which is equal to the rectangle of and , that is 78,545,532.
Thus the form of the equation will be .
And it will be twice the answer, ]
Habetur alias per 13 prop. Geom. Effect.
[Translation: can be had otherwise by Proposition 13 of Viète, Effectionum geometricarum.