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🔗 Biography 🔗 Mathematics 🔗 Environment 🔗 Iran 🔗 Biography/science and academia 🔗 Astronomy 🔗 Geography 🔗 History of Science 🔗 Astrology 🔗 Middle Ages 🔗 Islam 🔗 Middle Ages/History 🔗 Central Asia 🔗 Maps 🔗 Iraq 🔗 Biography/Core biographies 🔗 Islam/Muslim scholars

Muḥammad ibn Mūsā al-Khwārizmī (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی‎; c. 780 – c. 850), Arabized as al-Khwarizmi with al- and formerly Latinized as Algorithmi, was a Persian polymath who produced works in mathematics, astronomy, and geography. Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.

Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.

In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.

🔗 History 🔗 Lists 🔗 Geography 🔗 Israel 🔗 Palestine

The population of the region of Palestine, which approximately corresponds to modern Israel, the Palestinian territories and Jordan, has varied in both size and ethnic composition throughout its history.

The following table shows the total population and that of the main ethno-religious groups living in the area from the First Century CE up until the last full calendar year of the British Mandate, 1947.

Note: Figures prior to the 1500s are all only estimates by researchers. For some periods, there are multiple researchers who have made differing estimates. None should be taken as exact numbers, and further context and detail is available by following links to the full description on Wikipedia as well as links to the original information sources.

^†including what is today the Kingdom of Jordan