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

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unable to adduce a proof he declares (2) 'उपलब्धिरेव
वासना' meaning thereby (1) 'In this branch of science, we
reckon only such an authority which has a proof behind
it ie. which could be substantiated' and (2) 'There is no
proof in this but accordance with observations alone
has to be taken as a proof'.
Though in the case of formulating the equation of
centre Karṇānupāta was not stipulated to simplify matters,
as there was not much difference, the Equation of centre
being generally small. It is to answer such contexts as
this that Bhāskara said in the Golādhyāya 'स्वल्पान्तरत्वात्,
अबहूपयोगात्, प्रसिद्धभावाच्च बहुप्रयासात्, ग्रन्थस्य तद्वैर्गुरुताभयेन
यत्त्यज्यतेऽर्थो न स दूषणाय" ie. 'If we in some particular
context do not mention certain things it should not be
condemned because in such contexts, (1) there is not
much difference or (2) no useful purpose is served to
a good extent or (3) it is too clear as does not require
to be mentioned (4) the procedure implies a lot of
cumbrous calculations and the result is after all negli-
gible and (5) Mention will make the work on hand
too unwieldy and brevity which is the soul of wit is
to be sacrificed. In the present context this procedure
of 'rectification of the Karṇa' is sought to improve
matters. Bhāskara's words 'यदा ग्रहस्य कर्ण उत्पन्नः तदा कर्णो
व्यासार्धं ग्रहकक्षायाः' seem really to imply that in the formula
r/R H sin m for the equation of centre in the place of R,
we are called upon to substitute really K. Though we had
been in default for not doing so in the context of the
Equation of centre, there is no reason why we should not
make up the deficiency in this context. So, therefore,
this rectification of Karṇa is stipulated here.