Geometric Algebra
Measuring by units leads to many surprising results in geometry. For example, connecting the midpoints of each side of a triangle to the opposing vertex gives the three medians, which meet at the triangle centroid. The centroid to a midpoint gives one length, while the distance to the vertex is exactly twice that length. An angle to a chord from a circle point is half the angle from the circle center. Hero’s formula relates the area of a triangle to the side lengths.
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Euclid Book 2 Proposition 1
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Euclid Book 2 Proposition 2
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Euclid Book 2 Proposition 3
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Euclid Book 2 Proposition 4
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Euclid Book 2 Proposition 5
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Euclid Book 2 Proposition 6
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Euclid Book 2 Proposition 7
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Euclid Book 2 Proposition 8
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Euclid Book 2 Proposition 9
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Euclid Book 2 Proposition 10
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Euclid Book 2 Proposition 11
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Euclid Book 2 Proposition 12
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Euclid Book 2 Proposition 13
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Euclid Book 5 Proposition 1
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Euclid Book 5 Proposition 2
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Euclid Book 5 Proposition 3
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Euclid Book 5 Proposition 4
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Euclid Book 5 Proposition 5
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Euclid Book 5 Proposition 6
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Euclid Book 5 Proposition 7
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Euclid Book 5 Proposition 8
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Euclid Book 5 Proposition 9a
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Euclid Book 5 Proposition 9b
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Euclid Book 5 Proposition 10a
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Euclid Book 5 Proposition 10b
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Euclid Book 5 Proposition 11
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Euclid Book 5 Proposition 12
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Euclid Book 5 Proposition 13
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Euclid Book 5 Proposition 14
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Euclid Book 5 Proposition 15
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Euclid Book 5 Proposition 16
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Euclid Book 5 Proposition 17
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Euclid Book 5 Proposition 18
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Euclid Book 5 Proposition 19
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Euclid Book 5 Proposition 20
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Euclid Book 5 Proposition 21
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Euclid Book 5 Proposition 22
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Euclid Book 5 Proposition 23
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Euclid Book 5 Proposition 24
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Euclid Book 5 Proposition 25
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Euclid Book 6 Proposition 16a
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Euclid Book 6 Proposition 16b
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Euclid Book 6 Proposition 17a
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Euclid Book 6 Proposition 17b
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Euclid Book 13 Proposition 1
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Euclid Book 13 Proposition 2
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Euclid Book 13 Proposition 3
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Euclid Book 13 Proposition 4
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Euclid Book 13 Proposition 5