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Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.
Archimedes
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Thou shalt likewise know that according to Law, the nature of this universe is in all things a like.
Pythagoras
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If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.
Diophantus
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We are now in a position to prove the following propositions : —
1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon.
2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon.
3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one fifteenth part of a sign of the zodiac.
Aristarchus of Samos
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Bees... by virtue of a certain geometrical forethought... know that the hexagon is greater than the square and the triangle, and will hold more honey for the same expenditure of material.
Pappus of Alexandria
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The laws of nature are but the mathematical thoughts of God.
Euclid
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Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves.
Nicomachus
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