Timeline
500 to 1400: the wider world and the medieval schools
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| c. 500 CE | Aryabhata is the first to write down explicitly the formula for the sum of cubes, according to Katz; the formula for the sum of squares had been stated by Archimedes around 250 BCE | - | India | Source 61, Katz |
| c. 628 CE | Brahmagupta's Brahmasphuta-siddhanta gives a second-order interpolation formula for Rsines and the arithmetic of zero | Brahmagupta | Rajasthan, India | Source 50, Ramasubramanian |
| c. 870 CE | Thabit ibn Qurra computes areas and volumes of parabolas and paraboloids by upper and lower sums, dividing the interval into unequal parts Disputed: Dated from his floruit; specific treatise not identified in the source read | Thabit ibn Qurra | Baghdad | Source 57, O'Connor |
| c. 1000 CE | Ibn al-Haytham sums fourth powers and uses it to find the volume of a paraboloid as 8/15 of the circumscribed cylinder Disputed: Dated to his mature Cairo period; exact year of the treatise not established here | Ibn al-Haytham | Cairo | Source 54, Dennis; Source 58, O'Connor |
| c. 932 CE | Munjala's Laghumanasa gives the first correct formula for true daily planetary motion using the Rcosine as rate of change of the Rsine | Munjala | India | Source 50, Ramasubramanian |
| c. 1000 to 1030 | Ibn al-Haytham derives the sums of integral powers through the fourth and uses them to show that the paraboloid formed by rotating x = ky^2 about x = kb^2 is exactly 8/15 of its circumscribing cylinder, by a Greek-style double reductio argument | - | Cairo | Source 61, Katz |
| c. 1150 CE | Bhaskara II's Siddhanta-siromani distinguishes average from instantaneous velocity (tatkalika gati) and states that the equation of the center is extremal where the velocity correction vanishes | Bhaskara II | India | Source 50, Ramasubramanian |
| c. 1209 | Sharaf al-Din al-Tusi's Treatise on Equations classifies cubics into 25 types and locates the maximum of bx - x^3 at x = sqrt(b/3) Disputed: Whether this involves a derivative is disputed between Rashed and Hogendijk | Sharaf al-Din al-Tusi | Persia | Source 53, O'Connor |
| 14 or 29 April 1229 | The scribe Ioannes Myronas completes the prayer book written over the erased text of Archimedes' Method Disputed: Walters gives 14 April 1229; Smithsonian, reporting the X-ray fluorescence reading of the colophon, gives 29 April 1229 | Ioannes Myronas | Jerusalem | Source 4; Source 6, Miller |
| before 1325 | Kilvington's Sophismata, the earliest calculatory treatment of motion at Oxford | Richard Kilvington | Oxford | Source 102, Jung |
| 1328 | Bradwardine's Tractatus de proportionibus velocitatum in motibus states his rule relating velocity to the force/resistance ratio | Thomas Bradwardine | Merton College, Oxford | Source 103, O'Connor; Source 104, Lovell-Read |
| 1335 | Heytesbury's Regulae solvendi sophismata states the mean speed theorem (ch. VI, De tribus praedicamentis) without proving it | William Heytesbury | Merton College, Oxford | Source 101, Jung |
| c. 1340-1350 | Swineshead's Liber calculationum, sixteen treatises, printed at Venice in 1520 | Richard Swineshead | Oxford | Source 106, Gale |
| 26 August 1349 | Bradwardine dies of plague at Lambeth, about seven weeks after being consecrated Archbishop of Canterbury | Thomas Bradwardine | Lambeth, London | Source 103, O'Connor |
| c. 1350 | Oresme proves the divergence of the harmonic series in Questiones super geometriam Euclidis by grouping terms into blocks each exceeding 1/2 Disputed: Work is dated only loosely by the sources read | Nicole Oresme | Paris | Source 100, Kirschner |
| c. 1350s | Oresme's Tractatus de configurationibus qualitatum et motuum; III.vii proves the mean speed theorem by area under a velocity graph Disputed: No source read gives a firm composition year; SEP (S100) and Caroti (S108) both decline to date it | Nicole Oresme | Paris | Source 100, Kirschner; Source 107, Oresme; Source 108, Caroti |
| 11 July 1382 | Nicole Oresme dies as bishop of Lisieux | Nicole Oresme | Lisieux, Normandy | Source 100, Kirschner |