Bhāskara-Kṛti: Siddhānta Śiromaṇi - The Crown Jewel

Bhāskara's 1150 CE masterwork, and his rule that every number in the sky must come with its proof

In 1150 CE, at thirty-six, Bhāskarācārya finished a book of rules for the sky and then wrote a second book to prove them. Learn how the Siddhānta Śiromaṇi was built, how its author hid his own birth year in a verse, how the Golādhyāya taught upapatti (demonstration) with a model sphere and a sine-of-a-sum rule, and how the book lived on in schools, commentaries and even a satellite's name.

The Fruit in the Palm

In the Śaka year 1072, which is 1150 CE, an astronomer named Bhāskara was thirty-six years old. He had just finished a long book of rules for the sky. It told a reader how to place the Sun, the Moon and the five planets on any day, how to time an eclipse, and how to read the hour from a shadow. The rules worked. But Bhāskara knew what happened to a man who only had rules.

He set the problem down in a verse. Picture the hall he describes: a gathering of learned men, and a gaṇaka (a professional calculator of the sky) standing before them with his numbers. Someone asks the simplest question in science: why? The calculator who cannot answer, Bhāskara says, wins no respect in that hall. Worse, he is not free of doubt himself.

So Bhāskara made a promise. He would write a second book that showed the reason behind every rule, as clearly as a small green āmalaka (the Indian gooseberry) held in an open palm. Could a sky full of moving circles really be made that plain? The two books together became the Siddhānta Śiromaṇi, "the crown jewel of the treatises." This lesson is about why the crown fit.

मध्याद्यं द्युसदां यदत्र गणितं तस्योपपत्तिं विना प्रौढिं प्रौढसभासु नैति गणको निःसंशयो न स्वयम्। गोले सा विमला करामलकवत् प्रत्यक्षतो दृश्यते तस्मादस्म्युपपत्तिबोधविधये गोलप्रबन्धोद्यतः॥

madhyādyaṃ dyusadāṃ yad atra gaṇitaṃ tasyopapattiṃ vinā prauḍhiṃ prauḍhasabhāsu naiti gaṇako niḥsaṃśayo na svayam gole sā vimalā karāmalakavat pratyakṣato dṛśyate tasmād asmy upapatti-bodha-vidhaye gola-prabandhodyataḥ

Without the proof of the planet-reckoning, from mean motion on, the calculator wins no standing among the learned, and is not free of doubt himself. On the sphere that proof is seen plainly, like an āmalaka in the palm. So I take up this treatise on the sphere, to teach the proofs.

Siddhānta Śiromaṇi, Golādhyāya, Golapraśaṃsā 2