481241
[Commentary:
There is a reference on this page to Proposition II.12 from Conicorum libri quattuor
(Apollonius . ]
De
[Translation: On ]
[Translation: On ]
Sit datus angulus. .
et punctum. .
oportet ducere lineam
ut sit
.
[Translation: Let there be a given angle and a point .
It is required to draw a line so that , a given line.
et punctum. .
oportet ducere lineam
ut sit
.
[Translation: Let there be a given angle and a point .
It is required to draw a line so that , a given line.
fiat: .
producta, in .
fiat: .
per punctum , ad angulum
fiat hyperbola: .
Inscribatur .
fiat
agatur , quæ secabit , in .
Dico quod: ,
[Translation: Make , meeting with extended at .
Make .
Through the point , at angle , make the hyperbola .
Inscribe .
Make
Construct , which will cut at .
I say that , the given line.
producta, in .
fiat: .
per punctum , ad angulum
fiat hyperbola: .
Inscribatur .
fiat
agatur , quæ secabit , in .
Dico quod: ,
[Translation: Make , meeting with extended at .
Make .
Through the point , at angle , make the hyperbola .
Inscribe .
Make
Construct , which will cut at .
I say that , the given line.
per. 12,2i
[Translation: by II.12 of the ]
[Translation: by II.12 of the ]
Aliter.
Et continuetur ad utrasque partes.
usque ad , .
fiat: , quæ secabit in .
Dico quod:
[Translation: Another way.
And continuing on both sides, as far as and , make , which will cut at .
I say that .
Et continuetur ad utrasque partes.
usque ad , .
fiat: , quæ secabit in .
Dico quod:
[Translation: Another way.
And continuing on both sides, as far as and , make , which will cut at .
I say that .
Quoniam,
erit: . propter asymptotes
sed: . ob parallelismum, ,
Ergo:
[Translation: Since , therefore on account of the asymptotes.
But because and are parallel.
Therefore .
erit: . propter asymptotes
sed: . ob parallelismum, ,
Ergo:
[Translation: Since , therefore on account of the asymptotes.
But because and are parallel.
Therefore .