- ...(incommensurables)
- Incommensurables had only been recently discovered, reportedly by Hippasus of Metapontum
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...made
- at the expense of algebra. All mathematicians were driven to geometry. The consequence persists. Even today, we still speak of and as
*x squared*and*x cubed*.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...given
- Note the assumption that is superfluous in the language of the time as there were only positive numbers.
So, the assumption is implicit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...cube
- This is a modern word; the original word as given by Archimedes is
*triple*.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...famous
- Try to prove either of these without calculus!! Yet, the Egyptians seems to have been aware of the formulas. Levels of understanding progress.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mon Feb 10 08:03:17 CST 1997