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16 Cards in this Set
 Front
 Back
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

PiHe narrowed it down between 223/71 and 22/7
The Sand Reckonerhow 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
