For my History of Maths class I received the following challenge:

Provegeometricallythat 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 need’s to be done geometrically; something to do with ratio’s.

Of course the area of a rectangle formed by op*pp’ (let p’ be 1/p) equals oq*qq’ and opq*pq(pq)’

But I’m not getting any further staring at my hyperbola...