English: How Aristarchus might have calculated the size of the Moon if he knew the Sun is extremely far away. To the left we see a full moon, and to the right we see two adjacent Moons that represent a statement attributed to Aristarchus to the effect that the Earth's umbra is twice as large as the Moon at one lunar distance from the Sun. At two lunar distances the base of the triangle is one lunar diameter, and the apex of the Earth's umbra is situated three lunar distances from Earth (seen at extreme right of figure). All triangles are similar if the Sun and Moon have the same angular size. Hence, Aristarchus might have calculated that Earth is 3 times as large as the Moon (the actual ratio is closer to 3.67). The bottom figure was created by compressing the top one in the vertical direction by a factor of 3. These figures are not too scale in that they assume that the angular diameter of the Sun and Moon are 6.7 degrees (instead of 0.5 degrees.) Hence the Moon is represented as being over 10 times closer to Earth than it really is.