Aristarchus of Samos

“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.”

“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 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.”

“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.”

“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.”

“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.”

“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.”

“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.”

“[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.”