ralphiep
- 2
- 0
Simple question. Is what we now call a 'rectangular hyperbola' what was once called the hyperbola of Apollonius? Thanks
What is the Hyperbola of Apollonius?
- Level: Undergrad
- Thread starter ralphiep
- Start date
-
- Tags
- Hyperbola
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
2 replies · 3K views
Discussion
Infinitum
- 880
- 40
Hi ralphiep. 
As far as I know Apollonius was the one who named the conics, i.e parabola, ellipse, and hyperbola. He related them to the well known analogy of slicing an oblique cone. That obviously includes the regular(non rectangular) hyperbolas.
As far as I know Apollonius was the one who named the conics, i.e parabola, ellipse, and hyperbola. He related them to the well known analogy of slicing an oblique cone. That obviously includes the regular(non rectangular) hyperbolas.
Science Advisor
Homework Helper
- 25,837
- 258
hi ralphiep!
all hyperbolas of Apollonius are rectangular hyperbolas
but "hyperbola of Apollonius" on its own (i think) has no meaning …
a particular point has a hyperbola of Apollonius relative to a particular conic (and it is rectangular),
see theorem 26 (p.150) of http://books.google.co.uk/books?id=qIFzkgBikEUC&pg=PA151&dq="hyperbola+of+apollonius"&hl=en
all hyperbolas of Apollonius are rectangular hyperbolas
but "hyperbola of Apollonius" on its own (i think) has no meaning …
a particular point has a hyperbola of Apollonius relative to a particular conic (and it is rectangular),
see theorem 26 (p.150) of http://books.google.co.uk/books?id=qIFzkgBikEUC&pg=PA151&dq="hyperbola+of+apollonius"&hl=en