“Proposition 6. The moon moves (in an orbit) lower than (that of) the sun, and, when it is halved, is distant less than a quadrant from the sun.”

— Aristarchus of Samos

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

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Aristarchus of Samos 16

ancient Greek astronomer and mathematician

Related quotes

“[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.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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)

“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 ancient Greek astronomer and mathematician

p, 125
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.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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

Aristarchus of Samos ancient Greek astronomer and mathematician

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