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

145
Again expanding (E₁M₁ + M₁N₂)², (E₁M₁ + M₁N₂)²

• M₂N₂² = E₁M₂² we have the third formula; similarly
  expanding (E₁Q₁ + Q₁Q₂)², (E₁Q₁ + Q₁Q₂)² + M₂Q₂² =
  E₁M₂² we have the fourth formula.
  Since the S'ighraphala has been defined to be equal to
  r/K H Sin m, we have had the necessity of knowing the
  value of K. The convention of signs mentioned in the
  formulation in the words 'योगो मृगादावथ कर्कटादौ केन्द्रेऽन्तरम्'
  is due to the fact that cosine is positive in the fourth and
  first Quadrants and that the Kotiphala becomes negative
  in the 2nd and 3rd Quadrants as could be seen by draw-
  ing the figure in those Quadrants.
  Now we shall prove what is most important, namely
  that postulating an entirely different geocentric motion
  how the Hindu Astronomers could formulate the S'ighra-
  phala which accords exactly with the heliocentric theory,
  assuming of course coplanar circular orbits. Let figures
  11 and 12 pertain to the modern heliocentric geometry,
  Fig. 11 Fig. 12
  the former with respect to the Inferior planets Mercury
  and Venus signified by V, and the latter to the superior
  planets Mars, Jupiter and Saturn signified by J. Let fig. 13
  pertain to the Hindu geocentric geometry dealing with
  both the Inferior and Superior planets as well. In the
  heliocentric figures let S = Sun, E = Earth, SA = directon to
  Aswini, the Zero-point of the Zodiac from the Sun, EA' =
  19