178 That is, the diameter of the shadow where length of Earth's shadow { length of Earth's shadow - Moon's distance} S ECLIPSES length of Earth's shadow This result is approximate and is the same as that given by Aryabhaṭa I. It is usually derived by the following method (called "the lamp and shadow method"): Therefore Sun's distance X Earth's diameter Sun's diameter - - Earth's diameter Consider Fig. 19. S is the centre of the Sun and E that of the Earth. SA and EB are drawn perpendicular to SE and denote the semi-diameters of the Sun and the Earth respectively. BL is parallel to ES. O is the point where SE and AB produced meet each other. E Fig. 19 Hindu astronomers compare SA with a lamp-post, EB with a gno- mon, and EO with the length of the shadow cast by the gnomon due to the light of the lamp. Consequently, they call EO "the length of the shadow". EO x Earth's diameter The triangles BEO and ALB are similar, therefore EO BL BE LA = B i.e., length of Earth's shadow= SE SA-EB SEX BE SEX 2BE = SA EB 2SA 2EB Sun's distance x Earth's diameter Sun's diameter - Earth's diameter = ¹ See A, iv. 39-40. This rule is found also in BrSpSi, xxiii. 8-9; and ŚiDV, I, iv. 6 (ii)-7.
