He was, however, very famous as a mathematician, and also as an observer. Ptolemy quotes his determination of the summer solstice of the year b.c. 281, and this tells us the date at which he flourished. He was renowned for a very ingenious method by which he tried to discover how much further from us the sun is than the moon. When the moon is half full the angle sun-moon-earth is a right angle, and if the angle sun-earth-moon be measured, by pointing the astrolabe first to sun and then to moon, the third angle, at the sun, may be computed, and then the ratio sun-earth to moon-earth will be known. The method is perfect theoretically, and if the sun were comparatively near, say about ten times the moon’s distance, it would be practicable; but the distance is really so much greater that the angle at the sun almost vanishes, and a very small error in estimating it causes an error equal to many millions of miles in the result. It is also impossible to determine from looking at the moon the exact time when the division between light and dark is a straight line. Aristarchus made the angle at Earth 87° instead of 89° 50′, and this gave the sun a distance of about 19 times as far as the moon, instead of 400 times, which is the true value. [Illustration: Fig. 20. Method of Aristarchus for finding the distance of the sun.] The foolish fad (as they thought it) about Earth’s motion, held by this otherwise great man, is described quite clearly by the two writers above-mentioned. He suggested that the stars might be immoveable, and Earth be turning on her axis at the same time that she moves in a circle round the sun. Moreover realizing all that this implies with regard to the immense distance of the stars, he said that the circle in which Earth revolves round the sun, compared with the sphere of the stars, is as the centre of a sphere compared with its circumference. That is, not only Earth, but Earth’s whole orbit, shrinks to a point when compared with the infinite distance of the stars.