/sci/ - Science & Math

Ancient Greek geometry.

Planar geometry was mentioned above. Essentially very similar.

Post beautiful propositions by mathematicians

Prop I.45 of On Conics by Apollonius.

He spent the preceding 5 propositions or so introducing parallel properties for hyperbolas and circles/ellipses and then just combines both lines of reasoning and thought and finishes the proposition that applies to both!

Apollonius prop. 38

Trying to prove rect. FG,GH = sq. GC

Since
rect. FG, GH = square GC = rect. CG, GD
for
CG=GD,
therefore
rect. FG,GH = rect. CG,GD;
therefore
FG:GD :: CG:GH
and convertendo
GF:FD :: GC:CH
and let the doubles of the antecedents be taken; but
2GF= CF+FD
because
CG=GD

I shouldn't have to draw it out, G is the midpoint of both the regular diameter and the second diameter(CD) of the hyperbola. Everything else is just playing with ratios.

Now my question is how the FUCK isn't CF added to FD the same as CD???

>goat mathematician
>not pic related

Has anyone read On Conics? What a dense work this is. The definition of a hyperbola is complex indeed.