Aristarque de Samos citations (16 citations)

“Proposition 18. 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.”

Help us translate this quote

Aristarchus of Samos

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variante: Proposition 17. 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.

“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.”

Help us translate this quote

Aristarchus of Samos

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“[Hypotheses]
1. That the Moon receives its light from the sun.
2. That the earth is in the relation of a point and centre to the sphere in which the moon moves.
3. That, when the moon appears to us halved, the great circle which divides the dark and the bright portions of the moon is in the direction of our eye.
4. That, when the moon appears to us halved, its distance from the sun is then less than a quadrant by one-thirtieth of a quadrant.
5. That the breadth of the (earth's) shadow is (that) of two moons.
6. That the moon subtends one fifteenth part of a sign of the zodiac.”

Help us translate this quote

Aristarchus of Samos

Note "is less than a quadrant..." is less than 90° by l/30th of 90° or 3°, and is therefore equal to 87°.
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“Proposition 9. The diameter of the sun is greater than 18 times, but less than 20 times, the diameter of the moon.”

Help us translate this quote

Aristarchus of Samos

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variante: Proposition 7. 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.

“Proposition 1. Two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or of the cone, touches the spheres.”

Help us translate this quote

Aristarchus of Samos

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“Proposition 15. 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.”

Help us translate this quote

Aristarchus of Samos

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variante: Proposition 10. 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.