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16 Cards in this Set

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Doubling the Cube
given a cube construct another cube with twice the volume
Theory of Proportions

Method of Exhaustion
Eudoxus
Trisecting the General Angle
Given an angle, divide it into three equal parts
Trigonometry
Hipparchus, Mentalaus, Ptolemy
The orbits of the planets
Aristarchus, Hipparchus, Ptolemy
The volumes of cones, cylinders, and hemispheres
Archimedes
The theory of proportions
Eudoxus
The size of the Earth
Arosthothenes
Parallel Postulate

5th Postulate
Much more complicated less intuitive thus people tried to replace or get rid of it.

Greeks had difficulty because there tools were not accurate.
Poles and polars
Apollonius
The parallel postulate
Euclid
Conic Sections
Apollonius
Objects floating or immersed in water
Archimedes
3 Major Accomplishments of Archimedes
Pi--He narrowed it down between 223/71 and 22/7

The Sand Reckoner--how many grains of sand it would take to completely fill the Earth.
Squaring the circle
Given a circle, construct a square with the same area
Problems with integer or rational solutions
Diaphantus