The Five Astronomical Canons

The mean motions of the planets (apart from the sun and moon) are provided in chapter XVI. The following statement shows the numbers of complete revolutions during one mahâyugaA "great age" in Hindu cosmology, representing a cycle of 4,320,000 years. according to the old and modern Sûrya SiddhântasThe "Sun Treatise," one of the most significant historical texts of Indian astronomy..

The two Siddhântas thus agree concerning Jupiter only, and disagree therein from ÂryabhaṭaA famous 5th-century Indian mathematician and astronomer., according to whom Jupiter's revolutions amount to 364,224 in one mahâyuga. The old Sûrya Siddhânta agrees with Âryabhaṭa and the Pauliśa Siddhânta (according to the commentator Bhaṭṭotpala), as far as Venus, Mars, and Saturn are concerned, while it agrees with the Pauliśa Siddhânta only concerning Mercury and Jupiter.

The positions of the apogeesThe point in an orbit farthest from the Earth. and the dimensions of the epicyclesSmall circles whose centers move around the circumference of larger circles, used in ancient astronomy to explain planetary paths. of the apsisThe point of greatest or least distance of a body from its center of attraction. and the conjunction are given in XVII, 1—3. It will be observed that, as regards the numbers indicating the size of the epicycles of the apsis of Venus and Saturn, the translation diverges from the corrected text given by us. The manifestly corrupt text was at first emended on the basis of the dimensions stated in the modern Sûrya Siddhânta, the hypothesis of the agreement of the two Siddhântas in this detail being resorted to in the absence of evidence decidedly favouring any other assumption. But I afterwards discovered that such evidence exists. The statements which Brahmagupta in his KhaṇḍakhādyakakaraṇaAn astronomical treatise written by Brahmagupta in 665 CE. makes about the places of the apogees and the dimensions of the epicycles agree with those made in the sixteenth chapter of the PañchasiddhāntikāThe "Five Astronomical Treatises" compiled by Varāhamihira., in all those details in which the text of the latter work needs no emendation, and it therefore may be presumed that the agreement extended also to the epicycles of Venus and Saturn. And examining the traditional text of the Pañchasiddhāntikā from this point of view, we find that instead of the Surâsoriginal: "Surâs" (gods) of stanza 1 we have to read not śarâsoriginal: "śarâs" (arrows, representing the number 5) but svarâsoriginal: "svarâs" (musical notes, representing the number 7) and that the triṃśāḥoriginal: "triṃśāḥ" (thirty) is correct without any further addition. It is true that thus the ÂryâA specific meter used in Sanskrit verse. remains defective; but the word, or words, missing were most probably expletive rather than essential to the sense. Brahmagupta maintains his karaṇaA concise astronomical handbook used for practical calculations. to be founded on Âryabhaṭa, or at any rate to give re-