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

22
belated by the duration of time that the arc of the ecliptic
covered by the Sun's today's motion takes to rise. This
duration of time is variable on two counts; first by the
variable motion of the Sun and second by the obliquity of
the ecliptic on account of which even equal arcs of the
ecliptic will not rise in equal times. In other words the
duration of time between two consecutive Sun-rises will
not be the same. This duration of a particular day can
roughly be calculated by the rule of three as follows. Let
the Sun be in a particular Rasi, the rising time T of which
could be computed; let the Sun cover an arc of x° in that
Rasi on that day. Then the time taken by that arc to rise
is xT / 30, where a Rasi consists of 30°. This time computed
in Sidereal measure added to 60 Sideral ghatis is equal to
the length of the day. During the course of an year ie the
time taken by the Sun to move round the ecliptic starting
from the Zero-point of the zodiac and again returning to
the same point, the Sun will have made one revolution less
than the stars. Thus if ‘ R ’ the number of diurnal revolu-
tions of the Sun (where R will be not an integer) during an
year or what is the same the number of Sāvana or civil
days during an year, they are equal to R + 1 sideral days.
Hence the number of sideral days in a kalpa will be equal
to the number of civil days in a kalpa together with the
number 4320000.000 which is the number of revolutions
made by the Sun relative to the stars.
In this context we are to know the number of civil
days in a kalpa. The proof given by Bhaskara in Gaṇita-
dhyāya under verses 1-6 in Bhagaṇopapatthi is as follows.
Draw a circle on a horizontal plane and place a vertical
pole called gnomon at the centre of the circle. Observe the
point of intersection of the gnomon's shadow with the
circumference of the circle at Sun-rise on a day in the
Uttarāyaṇa ie during the course of the Sun’s north-word
journey, just at the time when his rising point is very near
the east point and also to the south thereof. Then from