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Timeline of algorithms
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==Medieval Period== * 628 β [[Chakravala method]] described by [[Brahmagupta]] * c. 820 β [[Al-Khawarizmi]] described algorithms for solving [[linear equation]]s and [[quadratic equation]]s in his ''[[The Compendious Book on Calculation by Completion and Balancing|Algebra]]''; the word ''algorithm'' comes from his name * 825 β [[Al-Khawarizmi]] described the [[algorism]], algorithms for using the [[HinduβArabic numeral system]], in his treatise ''On the Calculation with Hindu Numerals'', which was [[Latin translations of the 12th century|translated into Latin]] as ''Algoritmi de numero Indorum'', where "Algoritmi", the translator's rendition of the author's name gave rise to the word [[algorithm]] ([[Latin]] ''algorithmus'') with a meaning "calculation method" * c. 850 β [[cryptanalysis]] and [[frequency analysis]] algorithms developed by [[Al-Kindi]] (Alkindus) in ''A Manuscript on Deciphering Cryptographic Messages'', which contains algorithms on breaking [[encryption]]s and [[cipher]]s<ref>[[Simon Singh]], ''[[The Code Book]]'', pp. 14β20</ref> * c. 1025 β [[Ibn al-Haytham]] (Alhazen), was the first mathematician to derive the formula for the sum of the fourth [[Exponentiation|powers]], and in turn, he develops an algorithm for determining the general formula for the sum of any [[integral]] powers<ref name=Katz>Victor J. Katz (1995). "Ideas of Calculus in Islam and India", ''Mathematics Magazine'' '''68''' (3), pp. 163β174.</ref> * c. 1400 β [[Ahmad al-Qalqashandi]] gives a list of [[cipher]]s in his ''Subh al-a'sha'' which include both [[Substitution cipher|substitution]] and [[Transposition cipher|transposition]], and for the first time, a cipher with multiple substitutions for each [[plaintext]] letter; he also gives an exposition on and worked example of [[cryptanalysis]], including the use of tables of [[letter frequencies]] and sets of letters which can not occur together in one word
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