722362
[Commentary:
The inclusion of a page number confirms that Harriot was using Commandino's edition of Apollonii Pergaei conicorum libri quattuor
(Apollonius . Proposition 38 gives a further property of a tangent to a hyperbola or ellipse or circle (see also Add MS 6787
f. ).
I.38 If a straight line touching a hyperbola or ellipse or circumference of a circle meets the second diameter, and if from the point of contact a straight line is dropped to that same [second] diameter parallel to the other diameter, then the straight line cut off from the centre of the section by the dropped straight line, together with the straight line cut off [on the second diameter] by the tangent from the centre of the section will contain an area equal to the square on the half of the second diameter, and, together with the straight line [on the second diameter] between the dropped straight line and the tangent, will contain an area having a ratio to the square on the dropped straight line which the upright side of the figure has to the transverse.]
I.38 If a straight line touching a hyperbola or ellipse or circumference of a circle meets the second diameter, and if from the point of contact a straight line is dropped to that same [second] diameter parallel to the other diameter, then the straight line cut off from the centre of the section by the dropped straight line, together with the straight line cut off [on the second diameter] by the tangent from the centre of the section will contain an area equal to the square on the half of the second diameter, and, together with the straight line [on the second diameter] between the dropped straight line and the tangent, will contain an area having a ratio to the square on the dropped straight line which the upright side of the figure has to the transverse.]
Appol. pag. 28
pro:
[Translation: Apollonius, page 28, Proposition ]
pro:
[Translation: Apollonius, page 28, Proposition ]
Iisdem
[Translation: Under the same ]
1. casus:
[Translation: Case 1. ]
[Translation: Under the same ]
1. casus:
[Translation: Case 1. ]
Sed:
in elipsi
per
[Translation: But in an ellipse, by proposition ]
in elipsi
per
[Translation: But in an ellipse, by proposition ]
In
[Translation: In an ]
[Translation: In an ]