53
[Commentary:
This page refers to Proposition 21 from Book I of Apollonius, as edited by Commandino Conicorum libri quattuor
(Apollonius .
I.21 If in a hyperbola or ellipse or circumference of a circle straight lines are dropped as ordinates to the diameter, the square on them will be to the areas contained by the straight lines cut off by them beginning from the ends of the transverse side of the figure, as the upright side of the figure is to the transverse, and to each other as the areas contained by the straight lines cut off, as we have ]
I.21 If in a hyperbola or ellipse or circumference of a circle straight lines are dropped as ordinates to the diameter, the square on them will be to the areas contained by the straight lines cut off by them beginning from the ends of the transverse side of the figure, as the upright side of the figure is to the transverse, and to each other as the areas contained by the straight lines cut off, as we have ]
Ergo:
per: 21, p.
1. lib.
[Translation: Therefore, by Proposition 21 of Book I of ]
per: 21, p.
1. lib.
[Translation: Therefore, by Proposition 21 of Book I of ]
cum sit parallela lineæ
est ordinatim applicata
ad diametrum ; et punctum
est in elipsi.
Quod demonstrare
[Translation: , since it is parallel to the line is an ordinate to the diameter ; and the point is on the ellipse.
Which was to be ]
est ordinatim applicata
ad diametrum ; et punctum
est in elipsi.
Quod demonstrare
[Translation: , since it is parallel to the line is an ordinate to the diameter ; and the point is on the ellipse.
Which was to be ]