1. The Persian mathematician Al Kwarizmi (780 – c
The Persian mathematician Al Kwarizmi (780 – c. 850) gives the general recipes for solving “algebraic” problems
In prose…
no Equations

8. Muḥammad ibn Mūsā al-Khwārizmī
Persian c. 780 – c. 850)
A 12th century Latin translation of his study of Indian Numerals introduced the decimal system to the Europe.

9. Muḥammad ibn Mūsā al-Khwārizmī
Persian c. 780 – c. 850)
A 12th century Latin translation of his study of Indian Numerals introduced the decimal system to the Europe.
Although the basic methods for solving linear and quadratic equations were known to the Indian and Greek mathematicians in his second book “A Compendium on Calculation by Completion and Balancing” he presented a general recipe and formalised the rules.

10. Muḥammad ibn Mūsā al-Khwārizmī
Persian c. 780 – c. 850)
A 12th century Latin translation of his study of Indian Numerals introduced the decimal system to the Europe.
Although the basic methods for solving linear and quadratic equations were known to the Indian and Greek mathematicians in his second book “A Compendium on Calculation by Completion and Balancing” he presented a general recipe and formalised the rules.
"Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations and Algorithm from his name
Wikipedia,

12. Muḥammad ibn Mūsā al-Khwārizmī
From Wikipedia, the free encyclopedia
"al-Khwārizmī" redirects here. For other uses, see al-Khwārizmī (disambiguation).
Muḥammad ibn Mūsā al-Khwārizmī A stamp issued September 6, 1983 in the Soviet Union, commemorating al-Khwārizmī's (approximate) 1200th birthday. Born c. 780 Died c. 850 Ethnicity Persian[1][2][3] Known for Treatises on algebra and Indian numerals Influenced Abu Kamil Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī[note 1] (c. 780, Khwārizm[2][4][5] – c. 850) was a Persian[1][2][3] mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world.[5] His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources.[6] He revised Ptolemy's Geography and wrote on astronomy and astrology.
Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name.[7] His name is also the origin of (Spanish) guarismo[8] and of (Portuguese) algarismo, both meaning digit.

13. Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabalaالكتاب المختصر في حساب الجبر والمقابلة).
On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm".
Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.
Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.
He also wrote on mechanical devices like the astrolabe and sundial.
He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.[13]
When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.[14]

14. Algebra
Main article: The Compendious Book on Calculation by Completion and Balancing
A page from al-Khwārizmī's Algebra
Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة‎, 'The Compendious Book on Calculation by Completion and Balancing') is a mathematical book written approximately 830 CE. The book was written with the encouragement of the Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance.[15] The term algebra is derived from the name of one of the basic operations with equations (al-jabr, meaning completion, or, subtracting a number from both sides of the equation) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.[16

15. It provided an exhaustive account of solving polynomial equations up to the second degree,[17] and discussed the fundamental methods of "reduction" and "balancing", referring to 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.[18]
Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)
squares equal roots (ax2 = bx)
squares equal number (ax2 = c)
roots equal number (bx = c)
squares and roots equal number (ax2 + bx = c)
squares and number equal roots (ax2 + c = bx)
roots and number equal squares (bx + c = ax2)