104 BRAHMASPHUTASIDDHANTA'S KHANDAKHADYAKA Brabmagupta corrects Dimensions of the Epicycle of Apsis Brahmagupta corrects the dimensions of the epicycles of apsis of the Sun and Moon by-1/42 nd part and 1/48th parts respectively. The reference may be made to the following verse in the Uttara Khandakhadyaka: The Sun's equations are to be made less by dvikytām- sonam (1/42nd) and the Moon's equations, increased by vasuvedabhagayutam (1/48th). Multiply the Sun's equa- tion a planet's daily motion in minutes and divide by the number of minutes of a whole circle and this is called Bhujantara correction and applied in the same way to the planet the equation is applied to the Sun. The Sun's epicycle of apsis has the dimension 14" in the Khandakhadyaka proper. With the correction introduced here, the value becomes 14° 1- =13° 40¹. 42 The correction to the Moon's equations would make the 31°38'45". epicycle's dimension changed from 31° to 31° ¹° {1+1] 48 Prthudaka's commentary further corrects it to 31°(1+3)-31°35′ Brahmagupta 's correction to Saturn's epicycle of apsis is1/5th part and that to the Sighra epicycle of Mercury 1/16th part as seen in the verse: Of Mars the apogee (the aphelion point) is to be increased by 17, that of Jupiter by 10°: from the Sighra of Venus 74' are to be subtracted: Saturn's equation of apsis should be decreased by its one-fifth and the Saghra equation of Mercury should be increased by one-sixteenth. In the Khandakhadyaka proper (IL.6), we have been given the longitudes of the apogee of planets: Mars 11°, Mercury 22", Jupiter 160°, Venus 80° and Saturn 240°. Now with these correc- tions introduced in the Uttara Khandakhadyaka in the above 1. द्विकृतांशोनं रविफलमिन्दोसुवेदभागयुतम् । अर्कफलभुक्तिघाताद् भगय कलाप्तं भुजान्तरं रविवत् || 2- सप्तदशांशैरधिकं भौमस्यो रोई शरिशैः । सितशीघ्रात कृतमुनयो लिप्ताः शोभ्याः शनैः फलं मान्यम् | पक्वांशोनं शैष्र्यं षोडशभा नाभिकं बुधस्य फलम् ।। UKK. IX. 9 UKK.IX.11
