For my History of Maths class I received the following challenge:
Prove geometrically that the area under the hyperbola (y=1/x) from 1 to p, is equal to the area from q to pq. Deduce that the area (as function) has the addition property of logarithms, log(ab)=log(a)+log(b).
The problem (to me!) that it needís to be done geometrically; something to do with ratioís.
Of course the area of a rectangle formed by op*ppí (let pí be 1/p) equals oq*qqí and opq*pq(pq)í
But Iím not getting any further staring at my hyperbola...