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

408
body which lies between the position of the eclipsing body
at the moment of first contact and the point of intersection
with the path of the eclipsing body of the circle drawn
with the centre of the eclipsed body as centre and radius
equal to the difference of p+r -g where g is the magni-
tude of the eclipse (grāsa) at the moment, or similarly the
time taken by the centre of the eclipsing body to move
through a similar and equal segment of the path of the
eclipsing body on the other side, gives the time elapsed
after the moment of first contact or the time before the
moment of last contact.
Comm. This is the converse of the above problem.
The method is clear being based on rule of three as above.
Both the problems could be algebraically expressed as
follows. Let T, t, l, g, and k, stand respectively for the
Sthiti-Khanda ie. the time between the moment of first
contact to the middle of the eclipse or the time between
the middle moment to the moment of last contact ; (2).
the time elapsed after the moment of first contact or the
time before the moment of last contact, as the case may
be ; (3) the length of the Pragrahamārga or Mokṣamārga ;
(4) the grāsa which is defined as p+r-k ; (5) the Karṇa
whose expression is √(B²+β²), B being the Bhuja defined
and β the latitude of the Moon.
Then the following working is stipulated (a) If in
time T, a path of length l is traced, what will be traced in
t? The result is lt/T (b) Then B = l - lt/T (c) B² + β² = K²
(d) p+r-k=g. Thus combining all the steps
{l (T-t) / T}² + β² = (p+r-g)² ie.
l² (T-t)² + β² T² = T² (p+r-g)² I
given t, this equation gives g and given g it gives t.