726364
[Commentary:
The inclusion of a page number confirms that Harriot was using Commandino's edition of Apollonii Pergaei conicorum libri quattuor
(Apollonius . Proposition 39 gives a further property of a tangent to a hyperbola or ellipse or circle (see also Add MS 6787
f.
f. ).
I.39 If a straight line touching a hyperbola or ellipse or circumference of a circle meets the diameter, and if from the point of contact a straight line is dropped as ordinate to the diameter, then whichever of the two straight lines is taken, of which one is the straight line between the [intersection of the] ordinate [with the diameter] and the centre of the section, and the other is between [the intersection of] the ordinate and the tangent [with the diameter], the ordinate will have to it the ratio compounded of the ratio of the other of the two straight lines to the ordinate and of the ratio of the upright side of the figure to the transverse.]
I.39 If a straight line touching a hyperbola or ellipse or circumference of a circle meets the diameter, and if from the point of contact a straight line is dropped as ordinate to the diameter, then whichever of the two straight lines is taken, of which one is the straight line between the [intersection of the] ordinate [with the diameter] and the centre of the section, and the other is between [the intersection of] the ordinate and the tangent [with the diameter], the ordinate will have to it the ratio compounded of the ratio of the other of the two straight lines to the ordinate and of the ratio of the upright side of the figure to the transverse.]
lib. 1.
App. pag. 29.
pro:
[Translation: Book I, Apollonius, page 29, Proposition ]
App. pag. 29.
pro:
[Translation: Book I, Apollonius, page 29, Proposition ]
Nostro modo
[Translation: My method, very ]
[Translation: My method, very ]
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 ]
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