Aristarchus of Samos - Ratio Quotes

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The sun has to the earth a ratio greater than that which 6859 has to 27, but less than that which 79507 has to 216.
Proposition 16

Aristarchus of Samos
The straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the moon move is less than double of the diameter of the moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the sun, but has to it a ratio greater than that which 22 has to 225. But it has to the straight line drawn from the centre of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10125.
Proposition 13

Aristarchus of Samos
The diameter of the circle which divides the dark and the bright portions in the moon is less than the diameter of the moon, but has to it a ratio greater than that which 89 has to 90.
Proposition 12

Aristarchus of Samos
The diameter of the earth is to the diameter of the moon in a ratio greater than that which 108 has to 43, but less than that which 60 has to 19.
Proposition 17

Aristarchus of Samos
The earth is to the moon in a ratio greater than that which 1259712 has to 79507, but less than that which 216000 has to 6859.
Proposition 18

Aristarchus of Samos
The sun has to the moon a ratio greater than that which 5832 has to 1, but less than that which 8000 has to 1.
Proposition 10

Aristarchus of Samos
The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.
Proposition 14

Aristarchus of Samos
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