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

66 Rule. If the Ahargaṇa be x days then the Śīghra will be 4x° + (4x × 3') / 130 + Dhruvaka. Proof. For x days, the mean motion is x × 4° + x × (0-5′-32″-18‴-28⁗). The second part is taken to be 4x × 3° / 130 ie x × 12° / 130 = x × 6/65° for 6/65 of a degree = 0-5′-32″-18‴-"28"". The fraction 6/65 can be seen to be a convergent of the remainder for 5′-32″- 18‴-28⁗ = 299077° / 3240000 = 1/(10 +) 1/(1 +) 1/(4 +) 1/(1 +) 1/9968 of which the penultimate convergent is 6/65. Verse 19. The Ahargaṇa divided by 12 and by 71 gives respectively the positive degrees and negative minutes to be added to the Dhruvaka of Jupiter. Comm. If x be the Ahargaṇa x° / 12 − x' / 71 + Dhruvaka = Guru. The mean daily motion of Jupiter is 0-4-59-9.9 = 0-5′ minus 0-0-0-50-51. Evidently 0-5′ × x = x° / 12. The remainder 0-0-0-50-51 = 61′ / 4320 of which the continued fraction is 1/(70 +) 1/(1 +) 1/4. A very approximate convergent is 1/71 as given. Verse 19 contd. To obtain the position of the Śīghra of venus. The Ahargaṇa multiplied by 10 and divided by 6 and 155 respectively gives degrees positive and negative to be added to the Dhruvaka of Venus to give his position. Comm. The formula is 10 x / 6 − 10 x / 155. The mean daily motion of the Śīghra of Venus is 1°-36′-7″-44‴-35⁗ =