711356
[Commentary:
On this page Harriot examines a particular case arising from Proposition VII of Supplementum geometriæ
(Viète 1593c, Prop , when the fourth proportional is twice the first. ]
prop. 7. Supplementi de
[Translation: Proposition 7 of the Supplement, on a ]
[Translation: Proposition 7 of the Supplement, on a ]
Sint 4or proportionales
in specie.
Si quarta sit dupla ad prima, erit:
[…]
Ergo quatuor proportionales
quarum extremæ sunt in
ratione dupla
[Translation: Let there be 4 proportionals in general form.
If the fourth is twice the firs, then:
Therefore the four proportionals whose extremes are in double ratio will ]
in specie.
Si quarta sit dupla ad prima, erit:
[…]
Ergo quatuor proportionales
quarum extremæ sunt in
ratione dupla
[Translation: Let there be 4 proportionals in general form.
If the fourth is twice the firs, then:
Therefore the four proportionals whose extremes are in double ratio will ]
Tunc fac […] et nota quadratorum differentiam.
[Translation: Then make [the square of the first and second and the square of the third and fourth], and note the difference of the
[Translation: Then make [the square of the first and second and the square of the third and fourth], and note the difference of the
Differentia quadratorum
Hoc est triplum quadratum primæ
[Translation: The difference of the squares is .
This is three times the square of the first ]
Hoc est triplum quadratum primæ
[Translation: The difference of the squares is .
This is three times the square of the first ]