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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