Eudoxus of Cnidos
Exercises

Suppose x is a
number whose cube is equal to its negative:
Show that
x
= 0 by employing a double reductio ad absurdum proof. That
is, show that x can't be positive, or negative.

An arbelos (Greek
for "cobbler's knife") is a figure bounded by circular arcs, like a lune.
Given a semicircle with diameter AB, choose a point D on
the diameter and draw semicircles on diameters AD and DB.
The arbelos is the region inside the original semicircle that is outside
the smaller semicircles:
Use Eudoxus' result on
the areas of circles to show that the arbelos has the same area as the
circle drawn on diameter CD where C is the point where the
perpendicular to AB at D strikes the large circle.
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last modified 8/30/02
Copyright (c) 2000.
Daniel E. Otero