List of Popositions:
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 centers 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.
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.
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.
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.
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.
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.
7) The distance of the sun from the earth is greater than 18 times but less than 20 times the distance of the moon from the earth.
8) When the sun is totally eclipsed, the sun and moon are then comprehended by one and the same cone which has its vertex at our eye.
9) The Diameter of the sun is greater than 18 times but less than 20 times the diameter of the moon.
10) The sun has to the moon a ratio greater than 5832 to 1, but less than 8000 to 1.
11) The diameter of the moon is less than 2/45ths, but greater than 1/30th, of the distance of the center of the moon from our eye.
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 89 to 90.
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 of the moon move is less than double the diameter of the moon, but has to it a ratio greater than 22 to 225. But it has to the straight line drawn from the center of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than 979 to 10125.
14) The straight line joined from the center of the earth to the center of the moon has to the straight line cut off from the axis towards the center of the moon by the straight line subtending the circumference within the earth's shadow a ratio greater than 675 to 1.
15) The diameter of the sun has to the diameter of the earth a ratio greater than 19 to 3, but less than 43 to 6.
16) The sun has to the earth a ratio greater than 6859 to 27, but less than 79507 to 216.
17) The diameter of the earth is to the diameter of the moon in a ratio greater than 108 to 43, but less than 60 to 19.
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.
