The Five Astronomical Canons

check neither by means of the originals nor with the assistance of modern recasts. There also we must hold Varāha Mihira A 6th-century Indian astronomer and polymath, author of the Pañcasiddhāntikā to have closely followed the elements and methods of the authors of the Siddhāntas term: Siddhānta (Sanskrit: "established tenet"); refers to the five foundational astronomical treatises summarized in this work, and to have permitted himself only minor changes, such as facilitate calculation without affecting the fundamental character of the rules. General principles, enabling us to judge with certainty how far those changes may extend, can however not be laid down; we rather must judge each given case on its own merits. When we for instance find that the yuga term: yuga; a vast cycle of time in Indian cosmology of the Romaka Siddhānta The "Roman" or "Greek" astronomical treatise comprised, according to Varāha Mihira, only 2850 years, we may raise the question whether this yuga is the true yuga of the Romaka, or only represents a subdivision of the true yuga, analogous to the 180,000 years of the Sūrya Siddhānta The "Sun Treatise," the most significant of the five which, as we have seen above, must be considered as the smallest fraction of the mahāyuga term: mahāyuga; a "great age" consisting of 4,320,000 years with which the calculation of the ahargaṇa term: ahargaṇa; the "heap of days," or the number of days elapsed from a fixed epoch to a given date can be effected. But we shall without much hesitation decide in favour of the former alternative, in the first place because the yuga of the Romaka Siddhānta is expressly called a yuga of the sun and moon, for the formation of which a comparatively small number of years was sufficient, and in the second place because Brahmagupta A famous 7th-century mathematician and astronomer, in a passage to be quoted later on, testifies that the Romaka Siddhānta did not conform to the traditional views concerning the large periods of time. If, again, we find that according to the Pañchasiddhāntikā the Pauliśa Siddhānta The treatise attributed to "Pauliśa," often identified by scholars with the Greek astrologer Paulus Alexandrinus made no use of yugas of any kind to the end of calculating the ahargaṇa and the mean positions of the planets, but employed for those purposes a peculiar system of its own, we certainly must conclude that system to have been actually taught in the original Pauliśa Siddhānta, and not constructed, as indeed it might have been, by Varāha Mihira on the elements of the Pauliśa Siddhānta. For why, we must ask ourselves, should he have transformed in that way the elements of the Pauliśa Siddhānta rather than those of the other Siddhāntas which without any difficulty might have been thrown into the same form? And, to single out one further point, if we find that the Pañchasiddhāntikā gives a rule how to calculate, according to the Sūrya Siddhānta, the equation of the centre of sun and moon for any given anomaly, while it represents the Pauliśa and Romaka Siddhāntas as merely stating the amount of those equations for a certain series of anomalies, without teaching us how to calculate the equations for the intervening anomalies; we must again suppose that Varāha Mihira faithfully renders characteristic features of the original Siddhāntas as he found them; for if he had held the opinion (which as the writer of a karaṇa term: karaṇa; a concise astronomical handbook used for practical calculations he indeed might have held) that the practical astronomer knows enough, if he can assign the equations of the centre for, let us say, each fifteen degrees of anomaly, he would no doubt not have given the general rule from the Sūrya