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This timeline of science and engineering in the Islamic world covers the time period from the eighth century AD to the introduction of European science to the Islamic world in the nineteenth century. All year dates are given according to the Gregorian calendar except where noted.
721 – 815 Chemistry, glass: Jabir ibn Hayyan (Latinized name, Geber,). First chemist known to produce sulfuric acid, as well as many other chemicals and instruments. Wrote on adding color to glass by adding small quantities of metallic oxides to the glass, such as manganese dioxide. This was a new advance in glass industry unknown in antiquity. His works include The Elaboration of the Grand Elixir; The Chest of Wisdom in which he writes on nitric acid; Kitab al-istitmam (translated to Latin later as Summa Perfectionis); and others.
780 – 850 – Mathematics: al-Khwarizmi Developed the "calculus of resolution and juxtaposition" (hisab al-jabr w'al-muqabala), more briefly referred to as al-jabr, or algebra.
801 – 873 Chemistry: Al-Kindi writes on the distillation of wine as that of rose water and gives 107 recipes for perfumes, in his book Kitab Kimia al-`otoor wa al-tas`eedat (book of the chemistry of perfumes and distillations.)
810 – 887 Abbas ibn Firnas. Planetarium, artificial crystals. According to one account written seven centuries after his death, Ibn Firnas was injured during an elevated winged trial flight.
854 – 930 Chemistry, medicine: Al-Razi wrote on Naft (naphta or petroleum) and its distillates in his book "Kitab sirr al-asrar" (book of the secret of secrets.) When choosing a site to build Baghdad's hospital, he hung pieces of fresh meat in different parts of the city. The location where the meat took the longest to rot was the one he chose for building the hospital. Advocated that patients not be told their real condition so that fear or despair do not affect the healing process. Wrote on alkali, caustic soda, soap and glycerine. Gave descriptions of equipment processes and methods in his book Kitab al-Asrar (book of secrets) in 925.
By this century, three systems of counting are used in the Arab world. Finger-reckoning arithmetic, with numerals written entirely in words, used by the business community; the sexagesimal system, a remnant originating with the Babylonians, with numerals denoted by letters of the arabic alphabet and used by Arab mathematicians in astronomical work; and the Indian numeral system, which was used with various sets of symbols. Its arithmetic at first required the use of a dust board (a sort of handheld blackboard) because "the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded."
920 Mathematics: al-Uqlidisi. Modified arithmetic methods for the Indian numeral system to make it possible for pen and paper use. Hitherto, doing calculations with the Indian numerals necessitated the use of a dust board as noted earlier.
940 Mathematics: Born Abu'l-Wafa al-Buzjani. Wrote several treatises using the finger-counting system of arithmetic, and was also an expert on the Indian numerals system. About the Indian system he wrote: "[it] did not find application in business circles and among the population of the Eastern Caliphate for a long time."  Using the Indian numeral system, abu'l Wafa was able to extract roots.
980 Mathematics: al-Baghdadi Studied a slight variant of Thabit ibn Qurra's theorem on amicable numbers. Al-Baghdadi also wrote about and compared the three systems of counting and arithmetic used in the region during this period.
1048 – 1131 Mathematics: Omar Khayyam. Persian mathematician and poet. "Gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections.". Extracted roots using the decimal system (the Indian numeral system).
1100–1165 Cartography: Muhammad al-Idrisi, aka Idris al-Saqalli aka al-sharif al-idrissi of Andalusia and Sicily. Known for having drawn some of the most advanced ancient world maps.
1130–1180 Mathematics: Al-Samawal. An important member of al-Karaji's school of algebra. Gave this definition of algebra: "[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known." 
Mechanical engineering: Ismail al-Jazari described 100 mechanical devices, some 80 of which are trick vessels of various kinds, along with instructions on how to construct them
Medicine; Scientific method: Ibn Al-Nafis (1213-1288) Damascene physician and anatomist. Discovered the lesser circulatory system (the cycle involving the ventricles of the heart and the lungs), and described the mechanism of breathing and its relation to the blood and how it nourishes on air in the lungs. Followed a "constructivist" path of the smaller circulatory system: "blood is purified in the lungs for the continuance of life and providing the body with the ability to work". During his time, the common view was that blood originates in the liver then travels to the right ventricle, then on to the organs of the body; another contemporary view was that blood is filtered through the diaphragm where it mixes with the air coming from the lungs. Ibn al-Nafis discredited all these views including ones by Galen and Avicenna (ibn Sina). At least an illustration of his manuscript is still extant. William Harvey explained the circulatory system without reference to ibn al-Nafis in 1628. Ibn al-Nafis extolled the study of comparative anatomy in his "Explaining the dissection of [Avicenna's] Al-Qanoon" which includes a prefaces, and citations of sources. Emphasized the rigours of verification by measurement, observation and experiment. Subjected conventional wisdom of his time to a critical review and verified it with experiment and observation, discarding errors.
Chemistry: Al-Jawbari describes the preparation of rose water in the work "Book of Selected Disclosure of Secrets" (Kitab kashf al-Asrar).
Chemistry; materials; glassmaking: Arabic manuscript on the manufacture of false gemstones and diamonds. Also describes spirits of alum, spirits of saltpetre and spirits of salts (hydrochloric acid).
1380-1429 Mathematics: al-Kashi. According to, "contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as pi. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner."
Mathematics: Ibn al-Banna and al-Qalasadi used symbols for mathematics "and, although we do not know exactly when their use began, we know that symbols were used at least a century before this." 
Astronomy and mathematics: Ibn Masoud (Ghayyathuddin Jamshid ibn Mohamed ibn mas`oud, d. 1424 or 1436.) Wrote on the decimal system. Computed and observed the solar eclipses of 809AH, 810AH and 811AH, after being invited by Ulugh Beg, based in Samarqand to pursue his study of mathematics, astronomy and physics. His works include "The Key of arithmetics"; "Discoveries in mathematics"; "The Decimal point"; "the benefits of the zero". The contents of the Benefits of the Zero are an introduction followed by five essays: On whole number arithmetic; On fractional arithmetic; on astrology; on areas; on finding the unknowns [unknown variables]. He also wrote a "Thesis on the sine and the chord"; "thesis on the circumference" in which he found the ratio of the circumference to the radius of a circle to sixteen decimal places; "The garden of gardens" or "promenade of the gardens" describing an instrument he devised and used at the Samarqand observatory to compile an ephemeris, and for computing solar and lunar eclipses; The ephemeris "Zayj Al-Khaqani" which also includes mathematical tables and corrections of the ephemeresis by Al-Tusi; "Thesis on finding the first degree sine".
^Wilkins, John. Mathematicall Magick or the Wonders that may be performed by Mechanicall Geometry. In two books. Concerning Mechanicall Powers and Motions, London 1648, 204; also see a reprint of the same book in The Mathematical and Philosophical Works of John Wilkins to which is prefixed the author's life and an account of his works, 1802, vol. II, 201