There are methods to add two lines of arbitrary lengths or multiply them together known since Greek times; and more advanced methods based on the concepts of bases and units.
But, I have not been able to find a way to exponentiate a number geometrically without using algebra. I would love if someone could somehow illustrate the concept.
Basically I am asking is it possible to draw the graph of a^x geometrically.
On questions raised by Aretino and RickyDemer I want to clarify that: I am talking about Euclidean geometry (so a collapsible compass,straight-edge are allowed); although, Cartesian geometry is fine, too.
Also, is there a book that can teach a basic concept as this? You know, a book on Euclidean geometry that teaches exponentiation, multiplication etc.