# „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.“

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

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##### Aristarchos von Samos
griechischer Astronom, Vertreter des heliozentrischen Weltb…

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### „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)

### „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)
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.

### „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)
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 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 ancient Greek astronomer and mathematician

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

### „Proposition 11. The diameter of the moon is less than 2/45ths, but greater than 1/30th of the distance of the centre of the moon from 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 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.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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.

### „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 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)

### „[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)

### „Proposition 14. 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.“

—  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 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)

### „The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.“

—  Archimedes, buch The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

### „Proposition 2. If a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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

### „Every one is a moon, and has a dark side which he never shows to anybody.“

—  Mark Twain, buch Following the Equator

Pudd'nhead Wilson's New Calendar, Ch. LXVI
Following the Equator (1897)

### „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 ancient Greek astronomer and mathematician

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

### „Before bed, the bright moon was shining.Now, I think the ground has a frost covering.I raise my head … to view the bright moon,Then I lower my head … and I think of home.“

—  Li Bai, Quiet Night Thought

"Thoughts on a Still Night" (静夜思); in Jean Ward's Li T'ai-po: Remembered (2008), p. 99
Variant translation:
Before my bed the moonlight glitters
Like frost upon the ground.
I look up to the mountain moon,
Look down and think of home.
"Quiet Night Thought", in Classical Chinese Literature: An Anthology of Translations (2000), p. 723
Original: (zh_Hant) 床前明月光，疑是地上霜。

### „She's Prim's size in diameter.“

—  Suzanne Collins, The Hunger Games

Quelle: The Hunger Games

### „Heaven's ebon vault,Studded with stars unutterably bright,Through which the moon's unclouded grandeur rolls,Seems like a canopy which love has spreadTo curtain her sleeping world.“

—  Percy Bysshe Shelley, Königin Mab

Canto IV
Queen Mab (1813)

### „I was on par with the Creator of the Universe there in the dark in the cocktail lounge. I shrunk the Universe to a ball exactly one light-year in diameter.“

—  Kurt Vonnegut, buch Breakfast of Champions

Breakfast of Champions (1973)
Kontext: I was on par with the Creator of the Universe there in the dark in the cocktail lounge. I shrunk the Universe to a ball exactly one light-year in diameter. I had it explode. I had it disperse itself again.
Ask me a question, any question. How old is the Universe? It is one half-second old, but the half-second has lasted one quintillion years so far. Who created it? Nobody created it. It has always been here.
What is time? It is a serpent which eats its tail, like this:
This is the snake which uncoiled itself long enough to offer Eve the apple, which looked like this:
What was the apple which Eve and Adam ate? It was the Creator of the Universe.
And so on.
Symbols can be so beautiful, sometimes.