2513
[Translation: ]
[Commentary:
This page refers to Propositions I.21 and III.52 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
III.52 If in an ellipse a rectangle equal to the fourth part of the figure is applied from both sides to the major axis and deficient by a square figure, and from the points resulting from the application straight lines are deflected to the line of the section, then they will be equal to the axis.]
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
III.52 If in an ellipse a rectangle equal to the fourth part of the figure is applied from both sides to the major axis and deficient by a square figure, and from the points resulting from the application straight lines are deflected to the line of the section, then they will be equal to the axis.]
per 21, p.
1. lib.
[Translation: by Proposition 21 of Book I of ]
1. lib.
[Translation: by Proposition 21 of Book I of ]
[Translation: ]
figura
vel
[Translation: figure
or of the figure
vel
[Translation: figure
or of the figure
fiat […] vel figura
ut sequitur
ponatur: dari
[…] centro igitur , intervallo ad
periferia agatur secabit in
Ergo est centroides per 52. p. 3.
[Translation: Let or of the figure, as follows.
Put to be given
Therefore the centre is , the interval taken to the periphery will therefore cut in .
Therefore is the centroid by Proposition 52 of Book 3 of Apollonius.
ut sequitur
ponatur: dari
[…] centro igitur , intervallo ad
periferia agatur secabit in
Ergo est centroides per 52. p. 3.
[Translation: Let or of the figure, as follows.
Put to be given
Therefore the centre is , the interval taken to the periphery will therefore cut in .
Therefore is the centroid by Proposition 52 of Book 3 of Apollonius.