“Proposition 8. When the sun is totally eclipsed, the sun and the moon are then comprehended by one and the same cone which has its vertex at our eye.”

—  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

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Aristarchus of Samos photo

“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)

Aristarchus of Samos photo

“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.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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

Aristarchus of Samos photo

“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 ancient Greek astronomer and mathematician

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

Aristarchus of Samos photo

“[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)

“Do you see it?
Do you see that sunflower, raising its head
Glaring at the sun?
Its head almost eclipses the sun
Yet even when there is no sun
Its head still glows.”

Mang Ke (1951) Chinese writer

"Sunflower in the Sun" ( trans. Jonathan Stalling and Yibing Huang https://english.chass.ncsu.edu/freeverse/Archives/Winter_2010/prose/PushOpenTheWindow.htm)

Aristarchus of Samos photo

“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)

Aristarchus of Samos photo

“Proposition 13. 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.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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

Archimedes photo

“The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple”

Archimedes book The Method of Mechanical Theorems

of the portion adjacent to the base
Proposition presumed from previous work.
The Method of Mechanical Theorems

A.C. Bhaktivedanta Swami Prabhupada photo

“Although Rahu attempts to attack both the sun and the Moon, they are protected by Lord Visnu. Being very afraid of Lord Visnu’s cakra, Rahu cannot stay in front of the sun or Moon for more than a muhurta (forty-eight minutes). The phenomenon that occurs when Rahu blocks the light of the sun or Moon is called an eclipse. The attempt of the scientists of this earth to go to the Moon is as demoniac as Rahu’s attack. Of course, their attempts will be failures because no one can enter the Moon or sun so easily. Like the attack of Rahu, such attempts will certainly be failures.”

A.C. Bhaktivedanta Swami Prabhupada (1896–1977) Indian guru

Srimad Bhagavatam, Bhaktivedanta Book Trust, 1999. Canto 5, Chapter 24, verse 3, purport. Vedabase http://www.vedabase.com/en/sb/5/24/3
Quotes from Books: Loving God, Quotes from Books: Regression of Science

“The sun and moon are my Father's eyes.”

Aaron Weiss

The Sun and the Moon.
Brother, Sister (2006)

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