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

308
If the zenith-distance and the declination are of the
same direction, their difference, otherwise their sum will
be the latitude.
[Fig. 58] Comm. Suppose the zenith-
distance is north and decli-
nation also north, then
clearly from fig. 58, in this
position S₁ of the Sun QS₁ —
ZS₁ = ϕ = δ — Z (1) Again
in the position S₃ of the Sun,
zenith-distance is south and
declination is also south ; so,
here also difference gives ϕ
ie. ZS₃ — QS₃ = Z — δ = ϕ.
(3) In the position S₂, how-
ever, Z is south and δ is north, so that their sum is
equal to ϕ. It will be noted that the Hindu convention
of signs does not contemplate negative declination and
also it uses the word 'difference' to signify the positive
difference, as for example, in the first two cases δ ~ Z is
taken as ϕ. The modern formula Z + δ = ϕ applies
universally with the convention that δ is +ve if north,
ϕ is +ve if south.
Verses 72, 73. To obtain the Bhuja from the shadow.
Karṇa Vrittāgrā = (A × K) / R where A = Agrā and K
the Chāyākarṇa. This Karnāgrā is to be taken as
belonging to the opposite hemisphere to the Sun. Calling
this Karnāgra as a and the equinoctial shadow as s, a ⨦ s
according as δ is south or north gives the Chāyābhuja b.
Thus a ⨦ s = b. If the extremity of the shadow be on the
north and δ be north, then b + a = s ; if δ be south
b ~ a = s. If b be north, b ~ s = A, otherwise ie. if
south b + s = a. (R × a) / K = Agrā and
(Agrā × Koṭi of latitudinal triangle) / (Karṇa of the latitudinal triangle) = H sin δ.