hyperbola of Apollonius

ralphiep

Simple question. Is what we now call a 'rectangular hyperbola' what was once called the hyperbola of Apollonius? Thanks

Infinitum

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.

tiny-tim

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=q...onius%22&hl=en