सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

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above correction leads to an error of a day. So, it is
that we pronounced that out of the years 2000, 2100,
2200, 2300 A.D., the year 2000 A.D. alone is a leap year
and not the remaining, the convention being that the
number of the century, here 20, must be also a multiple
of four. On this back-ground, suppose we prepare a
manual called a Karaṇa grantha taking the length of the
year to be 365·25 days. It works alright for some time
but in the course of 400 years the error will have reached
to as much as one day. Thus a manual like the above
works only for a short time and the approximation made
gradually brings in a divergence on account of which such
a manual grows obsolete. That is why one Narasimha who
happened to prepare a manual in 1333 Saka year (1411AD)
opens his work with the words “तिथिचक्रं यत्प्रणीतं मल्लिका-
र्जुनसूरिणा, कालेन महता तस्मिन् खिलीभूते तदादरात्, नौपुरीसिङ्गयार्यस्य
नरसिंहेनसूनुना एतदेव स्फुटतरं क्रियते सौरसम्मतम्” i.e. “In as much
as a manual named Tithi-Cakra prepared by one Mallikār-
juna Sūri long ago, based upon the Sūryasiddhānta has now
diverged far from the Sūryasiddhānta (on account of the
approximations made transcending the limits of negligibi-
lity) I, the son of one Singaya belonging to a place named
Nau-puri (probably Vada-palle of the East Godavary Dt.)
am rectifying it and bringing it to accord with the Sūrya
Siddhānta again.”
This kind of obsoleteness arising out of inevitable ap-
proximations that have to be made in the preparation of
manuals is permissible. But Suppose the premise of the
manuals itself is incorrect, then the rectification of the
manuals is no good so long as the data given in the pre-
mise are not corrected. There are two fundamental
defects in the ancient works according to a modern analysis
namely (1) The Supposition that all the planets were in
conjunction at the Zero-point of the Zodiac in the beginn-
ing of a Mahāyuga (2) Small variations in the constants
like the daily motion of the planets and the like. Accord-
ing to the modern interpreters of Hindu Astronomy the