# Did Apollonius invent co-ordinate geometry?

When I read descriptions of Apollonius' treatise on conics, some of them say that he invented co-ordinate geometry, some say that he kind of did and others are silent on the matter. Or is it the case that there is no simple answer?

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What do you want to know that isn't covered by the Wikipedia article and accompanying references? en.wikipedia.org/wiki/Analytic_geometry#History – Jonas Meyer Mar 22 '10 at 1:19
I'm not a historian of mathematics, but a reasonable-seeming starting point would be to see what Morris Kline has to say in librarything.com/work/3953044 and then to go from there to see if new readings/findings have emerged. (Questions of invention are tricky in history of ideas/science, since it may not be the case that the "inventors" think along the same lines we do. E.g. who "invented" integration?) – Yemon Choi Mar 22 '10 at 1:41
I think questions of history can be extremely appropriate for this site. This question, however, could be improved. For example, you could have included a short bibliography: which descriptions of Apollonius have you read? – Theo Johnson-Freyd Mar 22 '10 at 2:42
Conc. "descriptions of Apollonius' treatise on conics" : Why not the treatise itself? Only that can give an appropriate impression. As far as I remember my one's: He used problem specific coordinates, but had not sized the idea down to the general concept. Successors and popularizators of Appolonius would have IMO arrived at the general use of coordinates, but apparently Apollonius was the endpoint of antique geometry. Even his treatise looks unfinished. – Thomas Riepe Mar 22 '10 at 8:57
A further point may be that ancient geometry teaching worked by personal instruction, books were probably guides for the teachers and not for the students. This would have blocked the normal way of publishing simplyfied popularizations, where a general and systematical use of coordinates could have emerged. – Thomas Riepe Mar 22 '10 at 8:58

Let V be the vertex of a parabola, F its focus, X a point on its symmetry axis, and A a point on the parabola such that AX is orthogonal to VX. It was well within the power of the Greeks to prove relations such as $VX:XA = XA:4VF$. If you introduce coordinate axes, set $x = VX$, $y = XA$ and $p = VF$, you get $y^2 = 4px$, the modern form of the equation of a parabola.