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

THE ADHYĀYA KNOWN AS PRATYABDA
S'UDDHI IN MADHYĀDHIKĀRA
Verse 1. The number of years which have elapsed from
the beginning of the Kalpa, respectively multiplied by 2, 4
and 3 and divided by 8, gives what is called Dinādya in
days, ghatis and Vighatis respectively. If this be added to
the number of years and divided by seven, the remainder
gives the Abdapa or the lord of the year, (under whose name
the week-day of the commencement of the year stands).
Comm. One mean solar year consists of 365 days, 15
ghatis, 30 palas, and 22½ Vipalas where the units are all
mean solar and one mean solar day is equal to 60 mean solar
ghatis, one mean solar ghati is equal to 60 mean solar palas,
one mean solar pala is equal to 60 mean solar Vipalas and
so on in sexagesimal sub-division. The fraction of the day
over and above 365 days, namely 0-15-30-22-30 multiplied
by 8 gives 2 days, 4 ghatis and 3 palas so that by the rule
of three i.e. ‘If in 8 mean solar years, the fraction accrues
to 2 days, 4 ghatis and 3 palas, what will it accrue to in x
elapsed mean solar years from the beginning of the Kalpa ?
we have the answer (x × 2)/8 days, (x × 4)/8 ghatis and (x × 3)/8
palas. If this is added to the number of the elapsed years,
and the result divided by seven, the remainder gives the
week-day of the commencement of the concerned year, be-
cause the remainder got by dividing 365 by 7 is one, and
the week day advances at the rate of one per year. Also
the Kalpa began on Sun-day.
Verse 2. Alternate method.
Half the number of elapsed years added to 1/60 of itself,
then divided by 60 and added to 1/4 of the elapsed years,
gives the Dinādya.