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The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. . Calculations of volumes and areas, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (c. 1820 BC), but the formulas are only given for concrete numbers, some are only approximately true, and they are not ...
Ancient Greece. Greek Dark Ages (1100 BC–750 BC) Archaic Greece (800 BC–480 BC) ... 1684 - Leibniz publishes his first paper on calculus, 1686 ...
1856: Icosian calculus discovered by William Rowan Hamilton. [28] 1857: Modern isoseismal map invented by Robert Mallet. [29] 1859: Proof of the greenhouse effect discovered by John Tyndall. [30] 1864: Capnography invented by John Tyndall. [31] 1865: The first Transatlantic telegraph cable pioneered by William Thomson on Valentia Island. [32]
[147] [148] It has been argued that certain ideas of calculus like infinite series and taylor series of some trigonometry functions, were transmitted to Europe in the 16th century [6] via Jesuit missionaries and traders who were active around the ancient port of Muziris at the time and, as a result, directly influenced later European ...
He was "the first who introduced the theory of algebraic calculus". [12] c. 1000 – Abu Mansur al-Baghdadi studied a slight variant of Thābit ibn Qurra's theorem on amicable numbers, and he also made improvements on the decimal system. 1020 – Abu al-Wafa' al-Buzjani gave the formula: sin (α + β) = sin α cos β + sin β cos α.
Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (independently of each other, first publishing around the same time) but elements of it first appeared in ancient Egypt and later Greece, then in China and the Middle East, and still later again in medieval Europe and India.
The historian of mathematics F. Woepcke, in Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle. [12] 895
1843 – William Hamilton discovers the calculus of quaternions and deduces that they are non-commutative, 1854 – Bernhard Riemann introduces Riemannian geometry, 1854 – Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space, 1858 – August Ferdinand Möbius invents the Möbius strip,