For 55 years, one man in Kerala kept checking the astronomy books of his time against the actual sky. The books lost.
This is the story of a man stating the circumradius formula for a cyclic quadrilateral about 350 years before Lhuilier (1782)…
In 1393, Vatasseri Paramesvara, a Rigvedi Nambudiri of the Bhrigu (bhargava) gotra living in Alattur village on the northern bank of the Nila (Bharathappuzha), started recording every eclipse he saw, with the place.
- Navakshetra, 1422.
- Gokarna, 1425.
- Gokarna again, 1430.
His last recorded observation is from 1445, when he was an old man.
The problem he faced was real. The standard planetary tables, descended from Aryabhata’s Parahita system, no longer matched the sky.
Eclipses were arriving early / late. His student Nilakantha Somayaji writes:
परमेश्वराचार्येण ग्रहणग्रहयोगादिकं यन्त्रैः पञ्चपञ्चाशद्वर्षकालं सम्यक् परीक्षितम्
Acharya Paramesvara carefully examined eclipses and planetary conjunctions, with instruments, for fifty-five years.
So Paramesvara rebuilt the system from observation. In 1431 he brought out his corrected astronomy and named it simply Drgganita, “computed as seen”:
दृग्गणितं नाम गणितं क्रियते मया
(I compose this work called Drgganita).
He also wrote a manual devoted only to eclipses, the Grahanamandana (c. 1410).
And he was honest about his own results. His computations, he wrote, will agree with the sky only “prayah” - approximately.
The small remaining differences come from factors not yet known, and future observers will find the corrections. On a riverbank in 15th century Malabar, that is the scientific method in one shloka.
The same Paramesvara stated the circumradius formula for a cyclic quadrilateral, the one textbooks credit to Lhuilier in 1782, about 350 years earlier.
His Siddhantadipika carries an iterative scheme that is essentially the modern secant method. His son Damodara went on to teach the great Nilakantha Somayaji.
Everyone knows Aryabhata and Bhaskara. The man who taught Indian astronomy to check itself against the sky lives in a handful of research papers. 🙏🙏
P.S. Drgganita = drk (seen) + ganita (computed). The name is the method.
Sources: K.V. Sarma (ed.), Grahanamandana, Hoshiarpur 1965, Introduction; Nilakantha Somayaji, Aryabhatiya-bhashya, Golapada, Trivandrum Sanskrit Series 185, pp. 154-155; D. Pingree, JAOS 87 (1967) 337-339; K.V. Sarma (ed.), Drgganita, Hoshiarpur 1963; Kuppanna Sastri (ed.), Mahabhaskariya with Siddhantadipika, Madras 1957; R.C. Gupta, Historia Mathematica 4 (1977) 67-74; K. Plofker, Historia Mathematica 23 (1996) 246-256.
Photo 1: The key image. Nilakantha’s Aryabhatiya-bhashya, Golapada 48: Paramesvara examined eclipses and conjunctions with instruments for 55 years (left, top). Right page: the Drgganita verse and his own eclipse verses naming Gokarna and Navakshetra.
Photo 2: Sarma’s introduction p. xii: Rigvedi Brahmin of the Bhrgu gotra, Alattur village, house Vatasseri on the northern bank of the Nila. Top highlight: Drgganita II.46, his “prayah” (more or less) statement.
Photo 3: Same introduction p. xiii: teachers Rudra, Narayana, Madhava. Drgganita composed in Saka 1353 (1431 CE).
Photo 4: Same introduction p. xiv: the last observation in Kali 4536 (1445 CE), and the 55 years of observation.