Biographical fact from the life of al-Khwarizmi. Muhammad ibn Musa al-Khwarizmi and his contribution to the history of science
« He influenced mathematical thinking more than any other medieval writer.».
Philip Hitty, famous American scientist, professor at Princeton University (1886-1978)
In 832, the Abbasid caliph Al-Ma'mun founded a research and educational center in the capital of his state, Baghdad, modeled on the ancient Museum in Alexandria, which became known as the House of Wisdom. In essence, the House of Wisdom was the Academy of Sciences. Many scientists from various regions of Central Asia and the Arab East worked there, they had at their disposal a rich library of old manuscripts, as well as a large specially built astronomical observatory. The House of Wisdom became a center for the study of mathematics, astronomy, medicine and chemistry. For a significant period of his life, the library of the "House of Wisdom" was headed by Abu Abdullah Muhammad ibn Musa Al-Khwarizmi, nicknamed the "father of algebra". It was thanks to Al-Khwarizmi that Europe learned what decimal counting and numbers are. It was he who first proposed dividing the globe into meridians and parallels. So every point on earth had clear coordinates, latitude and longitude. It was Al-Khwarizmi who created the first reliable model of the earth, the prototype of the modern globe, and this was 700 years before the famous Italian scientist Galileo Galilei.
Largely thanks to this Muslim scholar, today the world is what it is.
Al-Khwarizmi's contribution to mathematics
The modern word "algorithm" comes from the name of Al-Khwarizmi, and it is associated with the title of his book " Al-kitab al-mukhtasar fi hisab al-jabr wa-al-muqabala ". This book was translated into Latin twice in the 12th century and played an extremely important role in the development of mathematics in Europe. In translation, the title means "A Brief Book of Complementing and Contrasting." The word "algebra" comes from the title of this book. "Al-jabr" means the operation of moving negative terms from one side of an equation to the other to get positive terms on both sides. " Al muqabala” means “opposition”, that is, the reduction of similar terms in both parts of the equation. This labor Al-Khwarizmi became the first written work on algebra.
Thanks to Latin translations, he gained fame in Europe and had a huge impact on the development of Western science. His book on algebra introduced Europeans to a hitherto unknown discipline and for several centuries served as a classic mathematical text for students of European universities. Al-Khwarizmi was the first to present algebra as an independent science of general methods for solving linear and quadratic equations, and gave a classification of these equations. Also Al-Khwarizmi separated algebra from geometry in 834.
Al-Khwarizmi's contribution to astronomy
The leading place among the exact sciences in the medieval East was occupied by astronomy as one of the most necessary sciences in practice, without which it was impossible to do either in irrigated agriculture, or in sea and land trade. By the 9th century include the first independent works on astronomy in Arabic, a special place among them was occupied by "ziji" - collections of astronomical and trigonometric tables (at that time trigonometry was part of astronomy). With the help of these tables, the position of the luminaries in the celestial sphere, the time of solar and lunar eclipses were calculated. They also served to measure time. Among the first zijs is the zij of Al-Khwarizmi, which began with a section on chronology and calendar. This was very important for practical astronomy, since different peoples used different calendars at different times, and universal dating is important for observations. His works on astronomy were based on the works of Indian astronomers. He carried out thorough calculations of the positions of the sun, moon and planets, solar eclipses. The astronomical tables of Al-Khwarizmi were translated into European languages, and later into Chinese. Trigonometric and astronomical tables ("Zij al-Khwarizmi") served as the basis for medieval studies in the field of astronomy both in the East and in Western Europe.
Al-Khwarizmi's book on the astrolabe, the main instrument of astronomical measurements of that time, is also important. "The book on the construction of the astrolabe" has not been preserved and is known only from references in other sources. From the astronomical writings of Al-Khwarizmi, there are also known the “Book on the sundial” and the “Book on the action with the help of the astrolabe” (incompletely included in the work of Al-Ferghani). In sections 41-42 of this book, a special compass was described for determining the time of prayer.
Al-Khwarizmi's contribution to geography
Works on mathematics and astronomy were also associated with the works of Al-Khwarizmi on geography. He is considered the author of the first work on mathematical geography. Al-Khwarizmi was the first to describe in Arabic the inhabited part of the Earth known by that time, gave a map with the coordinates of the most important settlements, with seas, oceans, mountains, rivers.
In many ways, he relied on Greek writings (Ptolemy's Manual of Geography), but his Book of the Picture of the Earth is not just a translation of the writings of his predecessors, but an original work containing a lot of new data. The book included a description of the world, a map and a list of coordinates of the most important places. Despite the fact that the map of Al-Khwarizmi was more accurate than the map of the ancient Greek astronomer, his works did not replace the Ptolemaic geography used in Europe.
Using his own discoveries, Al-Khwarizmi corrected Ptolemy's research on geography, astronomy and astrology. Al-Khwarizmi studied the works of 70 geographers to map the "known world". He also organized scientific expeditions to Byzantium, Khazaria, Afghanistan, under his leadership the length of one degree of the earth's meridian was calculated (very accurately for those times).
Conclusion
It cannot be said that there was no algebra before Al-Khwarizmi. In ancient times, people solved the simplest algebraic problems; there were methods for solving individual specific problems, but Al-Khwarizmi was the first to present algebra as a science of general methods for solving numerical linear and quadratic equations, and gave a classification of these equations.
Mohammed ibn Musa Al-Khwarizmi occupies an important place among the scientists of Central Asia, whose names entered the history of exact natural science. In the ninth century - at the dawn of the dawn of medieval oriental science - the scientist made a great contribution to the development of arithmetic and algebra. Al-Khwarizmi's algebraic treatise was among the first works on mathematics translated in Europe from Arabic into Latin.
The modern name of algebra, as we noted above, comes from the word "al-jabr", and the word "algorithm" comes from the name of Al-Khwarizmi. The works of Al-Khwarizmi for several centuries had a great influence on scientists of the East and West and for a long time served as a model for writing mathematics textbooks.
Historians of science highly appreciate both the scientific and popularization activities of Al-Khwarizmi. The renowned historian of science George Sarton called him "the greatest mathematician of his time, and all things considered, one of the greatest of all time."
And most importantly, Al-Khwarizmi emphasized that he wrote his famous book on algebra (“Al-kitab al-mukhtasar fi hisab al-jabr wal-muqabala”) to serve the practical needs of people in matters relating to inheritance, division property, litigation and commerce. First of all, he considered his work as worship of the Almighty, and only then - as helping people.
May Allah and us be pleasing to Allah and useful to society. Amine!
Makhach Gitinovasov
Biography of Al-Khwarizmi (full name - Abu Abdullah Muhammad ibn Musa al-Khwarizmi) (arab. ابو عبدالله محمد ابن موسى الخوارزمي IX century; Abdullah's father, Muhammad, son of Musa, a native of Khorezm and) Arab born Abdullah, astronomer, mathematician. There is very little information about the life of the scientist. Al-Khwarizmi (full name - Abu Abdullah Muhammad ibn Musa al-Khwarizmi) (arab. ابو عبدالله محمد ابن موسى الخوارزمي; father of Abdullah, Muhammad, astronomer of Musa, native, Khorezm and) Arab mathematician of the IX century and) There is very little information about the life of the scientist.
The founder of algebra It is generally accepted that the founder of algebra is Abu Jafar Muhammad ibn Musa al-Khwarizmi, who was born approximately in 786. A number of historians argue that his name may indicate that he came from the Khorezm region, located in Central Asia to the south from the Aral Sea. It is generally accepted that the founder of algebra is Abu Jafar Muhammad ibn Musa al-Khwarizmi, who was born around 786. A number of historians argue that his name may indicate that he was from the Khorezm region, located in Central Asia south of the Aral Sea. seas.
Under Caliph al-Mamun (813833), al-Khwarizmi headed the library of the "House of Wisdom" in Baghdad, a kind of Academy. Under Caliph al-Vasik (842847), al-Khwarizmi led an expedition to the Khazars. The last mention of al-Khwarizmi dates back to 847. Under Caliph al-Mamun (813833), al-Khwarizmi headed the library of the "House of Wisdom" in Baghdad, a kind of Academy. Under Caliph al-Vasik (842847), al-Khwarizmi led an expedition to the Khazars. The last mention of al-Khorezmi refers to 847.
The "House of Wisdom" Al-Khwarizmi and his colleague Banu Musa were among the scholars of the "House of Wisdom" in Baghdad. In this academy, they translated Greek scientific manuscripts, studied and wrote essays on algebra, geometry and astronomy. Al-Khwarizmi, who was patronized by Al-Mamun, dedicated two of his works to the Caliph. Al-Khwarizmi and his colleague Banu Musa were among the scholars of the "House of Wisdom" in Baghdad. In this academy, they translated Greek scientific manuscripts, studied and wrote essays on algebra, geometry and astronomy. Al-Khwarizmi, who was patronized by Al-Mamun, dedicated two of his works to the Caliph.
Muhammad Books of Muhammad He wrote the first manual of arithmetic based on the positional principle. In addition, his treatises on algebra and the calendar have been preserved. Muhammad wrote the famous book "Kitab al-jabr wal-muqabala" "The book of restoration and opposition" (dedicated to the solution of linear and quadratic equations), from the name of which the word "algebra" comes from. A treatise on algebra also includes a chapter on geometry, trigonometric tables, and tables of latitudes and longitudes of cities. He wrote the first manual on arithmetic based on the positional principle. In addition, his treatises on algebra and the calendar have been preserved. Muhammad wrote the famous book "Kitab al-jabr wal-muqabala" "The book of restoration and opposition" (dedicated to the solution of linear and quadratic equations), from the name of which the word "algebra" comes from. A treatise on algebra also includes a chapter on geometry, trigonometric tables, and tables of latitudes and longitudes of cities.
His works Diverse scientific interests of al Khorezmi concerned mathematics, theoretical and practical astronomy, geography and history. Not all of his works have survived. Some of them, mentioned by medieval writers, were subsequently lost. Information about the writings of al-Khwarizmi reported by Eastern historians does not always coincide. It has now been established that al-Khwarizmi was the author of the following works: 1. A book on Indian reckoning; 2. A short book on the calculation of al-jabr and al-muqabala; 3. Astronomical tables; 4. Earth picture book; 5. A book about building an astrolabe; 6. A book about actions with the help of an astrolabe; 7. A book about sundials; 8. Treatise on the definition of the era of the Jews and their holidays; 9. History book.
Algorithm The leadership of al-Khwarizmi played a very important role in the development of arithmetic. The name of the author in the Latinized form Algorismus and Algorithmus began to designate in medieval Europe the entire system of decimal arithmetic. The leadership of al-Khwarizmi played a very important role in the development of arithmetic. The name of the author in the Latinized form Algorismus and Algorithmus began to designate in medieval Europe the entire system of decimal arithmetic.
Al-Khwarizmi also wrote a treatise on Indo-Arabic numerals. The Arabic text has been lost. His Latin translation Algoritmi de numero Indorum and the English counterpart Al-Khwarizmi on the Hindu Art of Calculation gave rise to the mathematical term "algorithm" (from Al-Khwarizmi's name in the title of the book). Al-Khwarizmi also wrote a treatise on Indo-Arabic numerals. The Arabic text has been lost. His Latin translation Algoritmi de numero Indorum and the English counterpart Al-Khwarizmi on the Hindu Art of Calculation gave rise to the mathematical term "algorithm" (from Al-Khwarizmi's name in the title of the book).
Arithmetic “The most easy and useful thing in arithmetic, for example, that which a person constantly requires in matters of inheritance, inheritance, division of property, litigation, trade relations or when measuring land, digging channels, geometric calculations, and also in other cases. ". “The easiest and most useful thing in arithmetic, for example, what a person constantly needs in matters of inheritance, inheritance, division of property, litigation, trade relations or when measuring land, digging canals, geometric calculations, and also in other cases” .
Conceived as an initial guide to practical mathematics, "Al-jabr wal-muqabala" in its first part begins with the consideration of equations of the first and second degree, and then in the two final sections moves on to the practical application of algebra in matters of measurement and inheritance. Conceived as an initial guide to practical mathematics, "Al-jabr wal-muqabala" in its first part begins with the consideration of equations of the first and second degree, and then in the two final sections moves on to the practical application of algebra in matters of measurement and inheritance.
The book begins with an introduction to natural numbers, followed by a presentation of the main theme of the first section of the book of solving equations. All presented equations are linear or quadratic and consist of numbers, their squares and roots. It is interesting to note that in all the books of Al-Khwarizmi, mathematical calculations are recorded exclusively with the help of words, not a single symbol, therefore, was used by him. The book begins with an introduction to natural numbers, followed by a presentation of the main theme of the first section of the book of solving equations. All presented equations are linear or quadratic and consist of numbers, their squares and roots. It is interesting to note that in all the books of Al-Khwarizmi, mathematical calculations are recorded exclusively with the help of words, not a single symbol, therefore, was used by him.
A) the squares are equal to the roots; b) squares are equal to numbers; c) roots are equal to numbers; d) squares and roots are equal to numbers, for example, x x = 39; e) squares and numbers are equal to roots, for example, x = 10x; f) roots and numbers are equal to squares, for example, 3x + 4 = x 2. a) squares are equal to roots; b) squares are equal to numbers; c) roots are equal to numbers; d) squares and roots are equal to numbers, for example, x x = 39; e) squares and numbers are equal to roots, for example, x = 10x; f) roots and numbers are equal to squares, for example, 3x + 4 = x 2.
The transformation is carried out through two operations al-jabr and al-muqabala (opposition). Al-Khwarizmi uses the word "al-jabr" in the meaning of "replenishment" to denote the process of transferring a negative number from one part of the equation to another. The transformation is carried out through two operations al-jabr and al-muqabala (opposition). Al-Khwarizmi uses the word "al-jabr" in the meaning of "replenishment" to denote the process of transferring a negative number from one part of the equation to another.
So, using one of the examples of Al-Khwarizmi himself, by means of "al-jabr" the equation x 2 \u003d 40x 4x 2 is reduced to the form 5x 2 \u003d 40x. The term "al-muqabala" means "opposition" and is used by Al-Khwarizmi to refer to the process of reducing equal terms in both sides of the equation. For example, applying the al-muqabala operation twice, we bring the equation x + x 2 = x to the form 21 + x 2 = 7x. So, using one of the examples of Al-Khwarizmi himself, by means of "al-jabr" the equation x 2 \u003d 40x 4x 2 is reduced to the form 5x 2 \u003d 40x. The term "al-muqabala" means "opposition" and is used by Al-Khwarizmi to refer to the process of reducing equal terms in both sides of the equation. For example, applying the al-muqabala operation twice, we bring the equation x + x 2 = x to the form 21 + x 2 = 7x. Example
Further, Al-Khwarizmi shows how to solve six standard types of equations using algebraic methods of solution and geometric proofs. Further, Al-Khwarizmi shows how to solve six standard types of equations using algebraic methods of solution and geometric proofs.
Al-Khwarizmi continues further research in the field of algebra in Hisab al-jabr wal-muqabala, studying how the application of the laws of algebra can be extended to arithmetic solutions of algebraic objects. For example, he shows how to multiply expressions of the form Al-Khwarizmi continues his research in algebra in Hisab al-jabr wal-muqabala, studying how the application of the laws of algebra can be extended to arithmetic solutions of algebraic objects. For example, it shows how expressions like (a + bx) (c + dx) should be multiplied. (a + bx) (c + dx).
Geography And, finally, Al-Khwarizmi was the author of a significant work in the field of geography, where he defined the latitude and longitude of 2402 settlements of the world as the basis of the world map. Al-Khwarizmi also wrote a number of other lesser-known works on topics such as the astrolabe, chronology and sundials. Finally, Al-Khwarizmi was the author of a significant work in the field of geography, where he determined the latitude and as the basis of the world map. Al-Khwarizmi also wrote a number of other lesser-known works on topics such as the astrolabe, chronology, and sundials.
I have compiled a short book on the calculus of algebra and almuqabala,
Al-Khwarizmi
containing simple and complex questions of arithmetic,
because people need it
During the Early Middle Ages, Central Asia became the world center of sciences, which gave the world numerous scientists.
Among the famous scientists of that time is al-Khwarizmi Muhammad bin Musa(full name Abu Abdullah Muhammad ibn Musa al-Khwarizmi).
Information about the life of al-Khwarizmi, unfortunately, has survived very little.
It is known that he was born on the territory of present-day Uzbekistan in Khorezm (present-day Khiva) around 800 AD. e.
Khorezmi Mohammed bin Musa spent a significant part of his life at the court of the Baghdad caliph al-Mamun, a great patron of sciences. He headed the library of the House of Wisdom in Baghdad, a sort of Baghdad academy.
(presumably in 783 - 850)
In the library of the House of Wisdom, Muhammad wrote numerous works on astronomy and mathematics.
In world science, Mohammed bin Musa is known for his treatise on mathematics « About numbers and actions with them.
In this work, for the first time, a systematic presentation of arithmetic based on the decimal positional calculus is given. And although the original Arabic text has been lost, thanks to its translation from Arabic into Latin in the 12th century, European scientists first became acquainted with the Indo-Arabic way of counting. From now on "Arab» numbers have forever entered European and world mathematics.
The second treatise of ben Musa is a textbook of mathematics, published by him under the title " Kitab al-jabr wal muqabala" about 830, devoted mainly to the solution of equations of the first and second degree. Ben Musa emphasized that he wrote his book to help people solve their problems in everyday life. He considered such important issues for that time as the division of inheritance, merchant accounts, court cases, trade transactions, etc.
The scientist gave a classification of numerical linear and quadratic equations and a method for solving them.
The method used by Mohammed bin Musa consists of two operations. The first operation, which he calls "al-jabr", that is, restoration, consists in eliminating negative quantities from the equation by adding expressions opposite to these negative quantities on both sides of the equation. The second operation is called "val-muqabala", that is, opposition.
In fact, the actions of al-jabr and almuqabala are the current transfer of terms of the equation from one part of the equation to another and the reduction of similar terms.
These two operations allowed al-Khwarizmi to reduce any algebraic equation of the first and second degree to six canonical forms.
These equations were written down by him verbally, the solution of these equations al-Khwarizmi also expressed in the form of verbal rules.
If the Greeks solved quadratic equations in a purely geometric way, then al-Khwarizmi's method is almost algebraic. He can solve any quadratic equation according to its general rule (find positive roots), and uses the drawing only to explain the validity of his rhetorical solution. And this is a colossal step forward in comparison with the geometric algebra of the Greeks.
If we translate the descriptive methods for solving six types of linear and quadratic equations given by al-Khwarizmi into our modern mathematical language, we will get well-known formulas by which we can find the roots of equations.
The name Khorezmi, in its Latinized form Al-Khwarizmi, is immortalized in the universally known mathematical term algorithm. Algorithm is a slightly modified form of the name Alkhorezmi, under the influence of the Greek word "arithmos" - number.
The name of Khorezmi bin Musa is also associated with another important mathematical concept - algebra. Algebra is the Latinized name for the al-jabr operation used by Khorezmi Mohammed bin Musa when solving equations. In his mathematical works, Khorezmi bin Musa gave rise to a new branch of mathematics - algebra.
The scientific heritage of Khorezmi had a great influence on the development of mathematics and other sciences and firmly entered the treasury of human culture.
Of great importance for the astronomy of that time was his book on the astrolabe (an instrument for determining latitude). The collection of astronomical and trigonometric tables compiled by him was translated into Chinese and European languages.
Al-Khwarizmi also made a significant contribution to geography. He is considered the author of the first work on mathematical geography. For the first time in Arabic, he described the inhabited part of the Earth known by that time, gave a map with the coordinates of the most important settlements, with seas and oceans, mountains and rivers.
And his Earth picture book - not just a translation of the works of predecessors, but an original work containing a lot of new data. He organized scientific expeditions to Byzantium, Khazaria, Afghanistan. Under his leadership, the length of one degree of the earth's meridian was calculated.
But, despite the wide range of his scientific interests, the main science of his life is mathematics.
The brilliant scientist was the first to give a systematic presentation of arithmetic as a science based on the decimal system of calculus, he was the first to present algebra as a science of general methods for solving numerical linear and quadratic equations.
Renowned historian of science George Sarton characterizes al-Khwarizmi in this way: “… greatest mathematician of his time , and if you take into account all the circumstances, and one of the greatest scientists of all time».
« He influenced mathematical thinking more than any other medieval writer.- Philip Hitty (1886-1978), famous American scientist, professor at Princeton University.
T.A. Fedorenko
Mathematical geography- part of general geography, the ultimate goal of which is:
1) determination of the type and size of the Earth;
2) determining the position of some point on the globe in relation to the geometric area, as a limited earth's surface;
3) determining the position of the globe at a given time in world space.
Biography
There is very little information about the life of the scientist. Born presumably in Khiva in 780. In some sources, al-Khwarizmi is called "al-majusi", that is, a magician, from which it is concluded that he came from a family of Zoroastrian priests who later converted to Islam. The homeland of al-Khorezmi is Khorezm, which included the territory of modern Uzbekistan and part of Turkmenistan.
The last mention of al-Khwarizmi dates back to 847, when Caliph al-Wasik died. Al-Khwarizmi is mentioned among those present at his death. It is generally accepted that he died in 850.
Scientific activity
Al-Khwarizmi was born in an era of great cultural and scientific upsurge. He received his primary education from the outstanding scientists of Maverannahr and Khorezm. At home, he got acquainted with Indian and Greek science, and in Baghdad he ended up as a fully established scientist.
In 819, al-Khwarizmi moved to the suburb of Baghdad, Kattrabbula. In Baghdad, he spent a significant period of his life, heading the "House of Wisdom" (Arab. "Bayt al-hikma") under Caliph al-Mamun (813-833). Before becoming caliph, al-Mamun was the governor of the eastern provinces of the Caliphate and it is possible that from 809 al-Khwarizmi was one of the court scholars of al-Mamun. In one of his writings, al-Khwarizmi praised al-Ma'mun, noting that "the love of science and the desire to bring scientists closer to him, extending the wing of his patronage over them and helping them in clarifying what is unclear to them, and in facilitating what is difficult for them.
The "House of Wisdom" was a kind of Academy of Sciences, where scientists from Syria, Egypt, Persia, Khorasan and Maverannahr worked. It contained a library with a large number of old manuscripts and an astronomical observatory. Here, many Greek philosophical and scientific works were translated into Arabic. At the same time, Khabbash al-Khasib, al-Fargani, Ibn Turk, al-Kindi and other prominent scientists worked there.
By order of Caliph al-Mamun, al-Khwarizmi worked on the creation of tools for measuring the volume and circumference of the earth. In 827, in the Sinjar desert, al-Khwarizmi took part in measuring the length of the arc degree of the earth's meridian in order to clarify the circumference of the Earth, found in antiquity. The measurements made in the Sinjar desert remained unsurpassed in accuracy for 700 years.
Around 830, Muhammad ibn Musa al-Khwarizmi produced the first known Arabic treatise on algebra. Al-Khwarizmi dedicated two of his works to the caliph al-Mamun, who provided patronage to the scientists of Baghdad.
Under Caliph al-Vasik (842-847), al-Khwarizmi led an expedition to the Khazars. The last mention of it refers to 847.
Contribution to world science
Al-Khwarizmi was the first to present algebra as an independent science of general methods for solving linear and quadratic equations, and gave a classification of these equations.
Historians of science highly appreciate both the scientific and popularization activities of al-Khwarizmi. The famous historian of science J. Sarton called him "the greatest mathematician of his time and, all things considered, one of the greatest of all times."
The works of al-Khwarizmi were translated from Arabic into Latin, and then into new European languages. Various textbooks on mathematics were created on their basis. The works of al-Khwarizmi played an important role in the development of the science of the Renaissance and had a fruitful influence on the development of medieval scientific thought in the countries of the East and West.
Astronomy
Al-Khwarizmi is the author of serious works on astronomy. In them, he talks about calendars, calculations of the true position of the planets, calculations of parallax and eclipses, compiling astrological tables (zij), determining the visibility of the moon, etc. The works of Indian astronomers formed the basis of his works on astronomy. He carried out thorough calculations of the positions of the sun, moon and planets, solar eclipses. The astronomical tables of al-Khwarizmi were translated into European, and later, Chinese, languages.
Geography
In the field of geography, al-Khwarizmi wrote the book “The Book of the Picture of the Earth” (Kitab surat al-ard), in which he clarified some of the views of Ptolemy. The book included a description of the world, a map and a list of coordinates of the most important places. Despite the fact that al-Khwarizmi's map was more accurate than the map of the ancient Greek astronomer, his works did not replace the Ptolemaic geography used in Europe. Using his own discoveries, al-Khwarizmi corrected Ptolemy's studies of geography, astronomy and astrology. To map the "known world" al-Khwarizmi studied the work of 70 geographers.
Earth picture book
His writings on geography were also associated with works on mathematics and astronomy. Al-Khwarizmi's "The Book of the Picture of the Earth" - the first geographical work in Arabic and the first work on mathematical geography - had a strong influence on the development of this science.
For the first time in Arabic, he described the inhabited part of the Earth known by that time, gave a map with 2402 settlements and coordinates of the most important settlements. In many ways, he relied on Greek writings (Geography of Ptolemy), but his Book of the Picture of the Earth is not just a translation of the writings of his predecessors, but an original work containing a lot of new data. He organized scientific expeditions to Byzantium, Khazaria, Afghanistan, under his leadership the length of one degree of the earth's meridian was calculated (very accurately for those times), but his main scientific achievements are related to mathematics. In the Book of the Picture of the Earth, latitude and longitude were defined.
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AL-KHOREZMI(783–850). The full name is Abu Abdallah (or Abu Jafar) Muhammad ibn Musa al Khorezmi in Arabic means the father of Abdallah (or the father of Jafar) Muhammad, the son of Musa from Khorezm, one of the greatest scientists (mathematician, astronomer, historian, geographer) of the Middle Ages. Almost no biographical information about him has been preserved, it is only known that he was born at the end of the 8th century. (presumably in Khiva), and died in the second half of the 9th century. The given years of life are conditional. In some sources, he is called "al-majusi", i.e. magician, from this it is concluded that his ancestors were magicians, priests of the Zoroastrian religion, widespread in those days in Central Asia.
The homeland of Al-Khorezmi is Khorezm, a vast region of Central Asia, which corresponds to present-day Uzbekistan, part of Karakalpakstan and part of Turkmenistan. Like many other Central Asian scientists, he worked in the "House of Wisdom" in Baghdad, the capital of the Arab Caliphate. The "House of Wisdom" was a kind of Academy of Sciences, where scientists from many Arab countries worked, there was a rich library of old manuscripts and an astronomical observatory.
It is considered established that Al-Khwarizmi was the author of 9 works: 1. Indian arithmetic book(or Indian Counting Book); A short book on the calculus of algebra and almuqabala; Astronomical tables (Zij); Earth picture book; A book about building an astrolabe; A book about actions with the help of an astrolabe; sundial book; Treatise on the definition of the era of the Jews and their holidays; history book.
Of these books, only 7 have come down to us - in the form of texts either by Al-Khwarizmi himself or by his Arabic commentators, or in translations into Latin.
Al-Khwarizmi's work on arithmetic played an important role in the history of mathematics, and although its original Arabic text has been lost, the content is known from a Latin translation of the 12th century, the only manuscript of which is kept in Cambridge. In this work, for the first time, a systematic presentation of arithmetic based on the decimal positional number system is given. The translation begins with the words "Dixit Algorizmi" (said by Algorizmi). In Latin transcription, the name of Al-Khwarizmi sounded like Algorizmi or Algorizmus, and since the essay on arithmetic was very popular in Europe, the author's name became a household name - medieval European mathematicians so called arithmetic based on the decimal positional number system. Later, this was the name of any system of calculations according to a certain rule, now this term means a prescription that specifies the process of calculations, starting from arbitrary initial data and aimed at obtaining a result completely determined by these initial data.
Algebraic book of Al-Khwarizmi ( Kitab muhtasab al-jabr and wal-muqabala) consists of two parts - theoretical (the theory of solving linear and quadratic equations, some questions of geometry) and practical (application of algebraic methods in solving household, commercial and legal problems - division of inheritance, drawing up wills, division of property, various transactions, land measurement , canal construction). The word al-jabr (replenishment) meant the transfer of a negative term from one part of an equation to another, and it is from this term that the modern word "algebra" arose. Al-mukabala (contrast) is the reduction of equal terms in both parts of the equation. The doctrine of linear and quadratic equations inherited from Eastern mathematicians became the basis for the development of algebra in Europe.
The geometric part of the treatise is devoted mainly to measuring the areas and volumes of geometric figures (triangle, square, rhombus, parallelogram called a rhomboid, circle, circle segment, quadrilateral with different sides and angles, parallelepiped, circular cylinder, prism, cone).
The leading place among the exact sciences in the medieval East was occupied by astronomy as one of the most necessary sciences in practice; it was impossible to do without it either in irrigated agriculture, or in sea and land trade. By the 9th c. include the first independent works on astronomy in Arabic, a special place among them was occupied by ziji - collections of astronomical and trigonometric tables (at that time trigonometry was part of astronomy), with the help of these tables the positions of the stars in the celestial sphere, solar and lunar eclipses were calculated, they served and for measuring time. Among the first zijs is the zij of Al-Khwarizmi, which began with a section on chronology and the calendar - this was very important for practical astronomy, since different peoples used different calendars at different times, and dating is important for observations. There were lunar, solar and lunar-solar calendars, and the beginning of the chronology in various systems referred to an arbitrarily chosen event. This led to many different eras, different peoples dated the same event differently, in accordance with the era adopted by them. Al-Khwarizmi described the Arabic lunar calendar, the Julian calendar - the calendar of the "rums" (Romans and Byzantines). He also compared various eras, among them one of the oldest that existed in India, the "Iron Age", which Al-Khwarizmi called the "era of the flood" with the beginning in 3101 BC. The Seleucid era or "Alexander's era" (Seleucus is one of the generals of Alexander the Great) began on October 1, 312 BC. The era of Hijra (migration) accepted in Islamic countries began on July 16, 622, the day of Muhammad's migration from Mecca to Medina. He considered both the Christian and Spanish eras and the rules for transferring dates from one era to another.
Al-Khwarizmi's book on the astrolabe, the main instrument of astronomical measurements of that time, is also important.
His writings on geography were also associated with works on mathematics and astronomy; Al-Khwarizmi is considered the author of the first work on mathematical geography. For the first time in Arabic, he described the inhabited part of the Earth known by that time, gave a map with the coordinates of the most important settlements, with seas, oceans, mountains, rivers. In many ways, he relied on Greek writings ( Geography Ptolemy), but his Earth picture book- not just a translation of the works of predecessors, but an original work containing a lot of new data. He organized scientific expeditions to Byzantium, Khazaria, Afghanistan, under his leadership the length of one degree of the earth's meridian was calculated (very accurately for those times), but his main scientific achievements are related to mathematics.
It cannot be said that there was no algebra before Al-Khwarizmi, in ancient times people solved the simplest algebraic problems, there were methods for solving individual specific problems, but Al-Khwarizmi first introduced algebra as a science of general methods for solving numerical linear and quadratic equations, gave a classification of these equations, which was essential for "pre-letter" algebra.
Historians of science highly appreciate both the scientific and popularization activities of Al-Khwarizmi. The famous historian of science J. Sarton called him "the greatest mathematician of his time and, all things considered, one of the greatest of all times."
Elena Malishevskaya