Timeline
1400 to 1637: Kerala, print, and the algebraic turn
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| c. 1400 | Madhava of Sangamagrama obtains infinite series for pi, sine, cosine and arctangent, with end-correction (antya-samskara) terms Disputed: Madhava's own works are lost; attribution rests on quotations by Nilakantha and Sankara Variyar | Madhava of Sangamagrama | Sangamagrama, Kerala | Source 50, Ramasubramanian; Source 55, O'Connor |
| c. 1502 | Nilakantha's Aryabhatiya-bhasya argues that the circumference and diameter of a circle cannot both be integers in any unit - an argument for incommensurability | Nilakantha Somayaji | Kerala | Source 50, Ramasubramanian; Source 56, O'Connor |
| c. 1530 | Jyeshthadeva's Yuktibhasa sets out, in Malayalam prose, demonstrations of the Kerala series including the derivation of the error terms Disputed: S050 gives c. 1530; MacTutor gives c. 1550 | Jyeshthadeva | Kerala | Source 50, Ramasubramanian; Source 55, O'Connor |
| c. 1530 | The Tantrasangraha-vyakhya states the sine and cosine power series in Sanskrit verse; the Yuktibhasa, in Malayalam, gives the derivation and credits the series to Madhava. The derivation uses ibn al-Haytham's summation identity for the case k = 1, without naming him | - | Kerala | Source 61, Katz |
| 1578 | Matteo Ricci arrives in Goa with instructions to investigate Indian science - the opportunity in the Kerala transmission argument | Matteo Ricci | Goa, India | Source 51, Almeida |
| 1599 | Galileo attempts the quadrature of the cycloid by weighing it: he cuts an arch and a generating circle from the same material, balances them, finds the arch about three times the circle, and abandons the result believing the ratio incommensurable. The true ratio is exactly 3 | - | Padua / Florence | Source 64, Whitman |
| 1609 | Kepler's Astronomia Nova gives the ellipse law and the area law; time in orbit is identified with area swept out | Johannes Kepler | Prague | Source 152, Davis; Source 154, O'Connor |
| 1613 | At his second wedding in Linz Kepler watches a wine merchant gauge a barrel with a rod through the bung-hole and objects to the method Disputed: MacTutor (S154) and Cardil (S134) tie the incident to the 1613 wedding; the 1911 Britannica (S151) frames it around the abundant vintage of 1612 | Johannes Kepler | Linz, Austria | Source 134, Cardil; Source 154, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] |
| 1615 | Kepler's Nova stereometria doliorum vinariorum, printed at Linz by Johannes Plancus; volumes of some ninety solids of revolution by summing infinitely thin slices | Johannes Kepler | Linz, Austria | Source 134, Cardil; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED]; Source 159, Kepler |
| 15 December 1621 | Cavalieri first puts the problem of ratios between infinite collections to Galileo | Bonaventura Cavalieri | Bologna/Florence | Source 156, Andersen |
| 1624 | Edmund Gunter introduces the abbreviation 'sin' | - | England | Source 60 |
| 2 October 1634 | Cavalieri writes to Galileo: 'I absolutely do not declare to compose the continuum by indivisibles' | Bonaventura Cavalieri | Bologna | Source 156, Andersen |
| c. 1634 | Roberval effects the quadrature of the cycloid using a companion curve and Cavalieri's theorem; he does not publish, and the proof appears only in the Traite des Indivisibles of 1693 | - | Paris | Source 64, Whitman |
| 1635 | Cavalieri's Geometria indivisibilibus continuorum nova quadam ratione promota published at Bologna, about 700 pages, eight years after the manuscript was finished | Bonaventura Cavalieri | Bologna | Source 135, O'Connor; Source 156, Andersen |
| 1636 | Fermat's Methodus ad disquirendam maximam et minimam begins circulating in Paris through Mersenne | Pierre de Fermat | Toulouse/Paris | Source 144, O'Connor; Source 130, Katz |