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

144
Comm. As per the formulation.
Bhujaphala = (H sin m × c) / 360 = (H sin m × r) / R
Kotiphala = (H cos m × c) / 360 = (H cos m × r) / R
in the case of Mandaphala or Sīghraphala where c = peri-
phery of the Manda or Sīghra periphery, r=Antyaphalajyā
defined above R = 3438' and m stands for the Manda or
Sīghra anomaly. These Bhujaphala and Kotiphala will
be used in their respective contexts.
Verses 27, 28, 29. Calculation of what is known as
Sīghrakarṇa.
(H Cos m ± r)² + H Sin² m = K² (1)
(R ± Kotiphala)² + Bhujaphala² = K² (2)
R² + r² ± 2 R × Kotiphala = K² (3)
R² + r² ± 2 r × H Cos m = K² (4)
The arc of the H Sine of the equation of centre is
called the Mandaphala.
Comm. Ref. fig. 9. From triangle E₁M₁M₂ (E₁M₁ +
M₁N₂)² + M₂N₂² = E₁M₂² = K². But M₁N₂ = Kotiphala
and M₂N₂ = Bhujaphala defined previously so that we have
the second formula for K enunciated above. From the
similarity of the triangles E₁M₁Q₁ and M₁M₂N₂ we have
M₂N₂ / M₁Q₁ = M₁M₂ / E₁M₁ so that M₂N₂ = r / R × M₁Q₁ ; Since M₁Q₁ is
called the Bhuja, the corresponding M₂N₂ in the Antya-
phalajyā triangle is called the Bhujaphala. Similarly
M₁N₂ is called the Kotiphala.
Again (E₁Q₁ + Q₁Q₂)² + M₂Q₂² = E₁M₂² where E₁Q₁ =
H Cos m, Q₁Q₂ = M₁N₂ = r and M₂Q₂ = M₁Q₁ = H Sin m.
From this we have the first formula enunciated.