“Proposition 4. The circle which divides the dark and the bright portions in the moon is not perceptibly different from a great circle in the moon.”

— 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

“Proposition 5. When the moon appears to us halved, the great circle parallel to the circle which divides the dark and the bright portions in the moon is then in the direction of our eye; that is to say, the great circle parallel to the dividing circle and our eye are in one plane.”

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 3. The circle in the moon which divides the dark and the bright portions is least when the cone comprehending both the sun and the moon has its vertex at our eye.”

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 12. 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.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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.”

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)