EMS = 180° - (SEA + ESM).
We have then
MS : ES = sin SEA : sin EMS.
Substituting the values of the sines, and reducing the ratio to its lowest terms, we have
MS : ES = 1.524 : 1.
Thus we find that the relative distances of Mars and the earth from the sun are 1.524 and 1. By the simple observation of its greatest elongation, we are able to determine the relative distances of an inferior planet and the earth from the sun; and, by the equally simple observation of the daily retrogression of a superior planet, we can find the relative distances of such a planet and the earth from the sun.
IV. THE SUN.
I. MAGNITUDE AND DISTANCE OF THE SUN.
