Al-Khwarizmis Planisphere

Al-Khwarizmis Planisphere

Al Khwariz Algebra PAGE

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Al Khwariz Algebra PAGE

Ancient text in new outlook by Al Khwarizmi

Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus' Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems.

Arabic mathematics ALGEBRA

Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before..

root is given by the steps,

In modern notation this process, with 'x' the "thing" (shay') or "root", is given by the steps,
(10 − x)2 = 81x
x2 + 100 = 101x
Let the roots of the equation be 'p' and 'q'. Then , pq = 100 and

So a root is given by (10 − x)2 = 81x
x2 + 100 = 101x
Let the roots of the equation be 'p' and 'q'. Then , pq = 100 and

So a root is given by




Several authors have also published texts

Compare with modern mathematical notation

The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes,
If some one say: You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts.

method of solving linear and quadratic equations

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)
by dividing out the coefficient of the square and using the two operations al-jabr and al-muqābala ("balancing"). Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x2 = 40x − 4x2 is reduced to 5x2 = 40x. Al-muqābala is the process of bringing quantities of the same type to the same side of the equation. For example, x2 + 14 = x + 5 is reduced to x2 + 9 = x.

Al Khwarizmi Latin Book

The Compendious Book on Calculation by Completion and Balancing is a 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.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,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.
This book is considered the foundational text of modern algebra. It provided an exhaustive account of solving polynomial equations up to the second degree,and introduced 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.

AL Jabr BOOKS

Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala ( الكتاب المختصر في حساب الجبر والمقابلة

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Muslim scientists experiments

Muslim scientists placed a greater emphasis on experimentation than previous ancient civilizations (for example, Greek philosophy placed a greater emphasis on rationality rather than empiricism), which partly arose from the emphasis on empirical observation found in the Qur'an and Sunnah, and the rigorous historical methods established in the science of hadith.In addition, there was greater emphasis on combining theory with practice in the Islamic world, where it was common for those studying the sciences to be artisans as well, something that was "considered an aberration in the ancient world",thus Islamic experts in the sciences were usually expert makers of truments that would enhance their powers of observation and calculation. Muslim scientists thus combined precise observation, controlled experiment and careful records with a new approach to scientific inquiry which led to the development of the scientific method.In particular, the empirical observations and experiments of Ibn al-Haytham (Alhacen) in his Book of Optics is seen as the beginning of the modern scientific method, which he first introduced to optics and psychology. Rosanna Gorini writes:

"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable.

Other early experimental methods were developed by Geber (for chemistry), Muhammad al-Bukhari (for history and the science of hadith),Al-Kindi (for the Earth sciences), Avicenna (for medicine), Abū Rayhān al-Bīrūnī (for astronomy and mechanics), Ibn Zuhr (for surgery)[83] and Ibn Khaldun (for the social sciences).The most important development of the scientific method, the use of experimentation and quantification to distinguish between competing scientific theories set within a generally empirical orientation, was introduced by Muslim scientists.

Ibn al-Haytham, a pioneer of modern optics,used the scientific method to obtain the results in his Book of Optics. In particular, he combined observations, experiments and rational arguments to show that his modern intromission theory of vision, where rays of light are emitted from objects rather than from the eyes, is scientifically correct, and that the ancient emission theory of vision supported by Ptolemy and Euclid (where the eyes emit rays of light), and the ancient intromission theory supported by Aristotle (where objects emit physical particles to the eyes), were both wrong.[85] It is known that Roger Bacon was familiar with Ibn al-Haytham's work. Ibn al-Haytham is featured on the 10,000 Iraqi dinar note.

Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing in order to verify theoretical hypotheses and substantiate inductive conjectures. Ibn al-Haytham's scientific method was similar to the modern scientific method in that it consisted of the following procedures:[87]

1. Observation
2. Statement of problem
3. Formulation of hypothesis
4. Testing of hypothesis using experimentation
5. Analysis of experimental results
6. Interpretation of data and formulation of conclusion
7. Publication of findings

The development of the scientific method is considered[by whom?] to be fundamental to modern science and some — especially philosophers of science and practicing scientists — consider earlier inquiries into nature to be pre-scientific. Some consider Ibn al-Haytham to be the "first scientist" for this reason

Muslim scientists experiments

Muslim scientists placed a greater emphasis on experimentation than previous ancient civilizations (for example, Greek philosophy placed a greater emphasis on rationality rather than empiricism), which partly arose from the emphasis on empirical observation found in the Qur'an and Sunnah, and the rigorous historical methods established in the science of hadith.In addition, there was greater emphasis on combining theory with practice in the Islamic world, where it was common for those studying the sciences to be artisans as well, something that was "considered an aberration in the ancient world",thus Islamic experts in the sciences were usually expert makers of intruments that would enhance their powers of observation and calculation. Muslim scientists thus combined precise observation, controlled experiment and careful records with a new approach to scientific inquiry which led to the development of the scientific method.In particular, the empirical observations and experiments of Ibn al-Haytham (Alhacen) in his Book of Optics is seen as the beginning of the modern scientific method, which he first introduced to optics and psychology. Rosanna Gorini writes:

"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable.

Other early experimental methods were developed by Geber (for chemistry), Muhammad al-Bukhari (for history and the science of hadith),Al-Kindi (for the Earth sciences), Avicenna (for medicine), Abū Rayhān al-Bīrūnī (for astronomy and mechanics), Ibn Zuhr (for surgery)and Ibn Khaldun (for the social sciences).The most important development of the scientific method, the use of experimentation and quantification to distinguish between competing scientific theories set within a generally empirical orientation, was introduced by Muslim scientists.

Ibn al-Haytham, a pioneer of modern optics,used the scientific method to obtain the results in his Book of Optics. In particular, he combined observations, experiments and rational arguments to show that his modern intromission theory of vision, where rays of light are emitted from objects rather than from the eyes, is scientifically correct, and that the ancient emission theory of vision supported by Ptolemy and Euclid (where the eyes emit rays of light), and the ancient intromission theory supported by Aristotle (where objects emit physical particles to the eyes), were both wrong. It is known that Roger Bacon was familiar with Ibn al-Haytham's work. Ibn al-Haytham is featured on the 10,000 Iraqi dinar note.

Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing in order to verify theoretical hypotheses and substantiate inductive conjectures. Ibn al-Haytham's scientific method was similar to the modern scientific method in that it consisted of the following procedures:

1. Observation
2. Statement of problem
3. Formulation of hypothesis
4. Testing of hypothesis using experimentation
5. Analysis of experimental results
6. Interpretation of data and formulation of conclusion
7. Publication of findings

The development of the scientific method is considered[by whom?] to be fundamental to modern science and some — especially philosophers of science and practicing scientists — consider earlier inquiries into nature to be pre-scientific. Some consider Ibn al-Haytham to be the "first scientist" for this reason

Europeans helped by islamics cience

Growth of European science was helped by islamicscience and European scholars learning which they could only find among Muslims, especially in Islamic Spain and Sicily. These scholars translated new scientific and philosophical texts from Arabic into Latin.

One of the most productive translators in Spain was Gerard of Cremona, who translated 87 books from Arabic to Latin, including Muhammad ibn Mūsā al-Khwārizmī's On Algebra and Almucabala, Jabir ibn Aflah's Elementa astronomica, al-Kindi's On Optics, Ahmad ibn Muhammad ibn Kathīr al-Farghānī's On Elements of Astronomy on the Celestial Motions, al-Farabi's On the Classification of the Sciences, the chemical and medical works of Razi, the works of Thabit ibn Qurra and Hunayn ibn Ishaq,and the works of Arzachel, Jabir ibn Aflah, the Banū Mūsā, Abū Kāmil Shujā ibn Aslam, Abu al-Qasim, and Ibn al-Haytham (including the Book of Optics).

Other Arabic works translated into Latin during the 12th century include the works of Muhammad ibn Jābir al-Harrānī al-Battānī and Muhammad ibn Mūsā al-Khwārizmī (including The Compendious Book on Calculation by Completion and Balancing), the works of Abu al-Qasim (including the al-Tasrif), Muhammad al-Fazari's Great Sindhind (based on the Surya Siddhanta and the works of Brahmagupta), the works of Razi and Avicenna (including The Book of Healing and The Canon of Medicine), the works of Averroes, the works of Thabit ibn Qurra, al-Farabi, Ahmad ibn Muhammad ibn Kathīr al-Farghānī, Hunayn ibn Ishaq, and his nephew Hubaysh ibn al-Hasan, the works of al-Kindi, Abraham bar Hiyya's Liber embadorum, Ibn Sarabi's (Serapion Junior) De Simplicibus,the works of Qusta ibn Luqa, the works of Maslamah Ibn Ahmad al-Majriti, Ja'far ibn Muhammad Abu Ma'shar al-Balkhi, and al-Ghazali,the works of Nur Ed-Din Al Betrugi, including On the Motions of the Heavens,Ali ibn Abbas al-Majusi's medical encyclopedia, The Complete Book of the Medical Art,Abu Mashar's Introduction to Astrology,the works of Maimonides, Ibn Zezla (Byngezla), Masawaiyh, Serapion, al-Qifti, and Albe'thar. Abū Kāmil Shujā ibn Aslam's Algebra, the chemical works of Geber, and the De Proprietatibus Elementorum, an Arabic work on geology written by a pseudo-Aristotle. By the beginning of the 13th century, Mark of Toledo translated the Qur'an and various medical works.

Science medieval Islamic world

The ancient world have their origins in the medieval Islamic world, with the most notable examples being: the public hospital (which replaced healing temples and sleep temples) and psychiatric hospital, the public library and lending library, the academic degree-granting university, the astronomical observatory as a research institute (as opposed to a private observation post as was the case in ancient times),and the trust

The first universities which issued diplomas were the Bimaristan medical university-hospitals of the medieval Islamic world, where medical diplomas were issued to students of Islamic medicine who were qualified to be practicing doctors of medicine from the 9th century. Sir John Bagot Glubb wrote:

"By Mamun's time medical schools were extremely active in Baghdad. The first free public hospital was opened in Baghdad during the Caliphate of Haroon-ar-Rashid. As the system developed, physicians and surgeons were appointed who gave lectures to medical students and issued diplomas to those who were considered qualified to practice. The first hospital in Egypt was opened in 872 AD and thereafter public hospitals sprang up all over the empire from Spain and the Maghrib to Persia."

The Guinness Book of World Records recognizes the University of Al Karaouine in Fez, Morocco as the oldest university in the world with its founding in 859.Al-Azhar University, founded in Cairo, Egypt in the 10th century, offered a variety of academic degrees, including postgraduate degrees, and is often considered the first full-fledged university.

A number of distinct features of the modern library were introduced in the Islamic world, where libraries not only served as a collection of manuscripts as was the case in ancient libraries, but also as a public library and lending library, a centre for the instruction and spread of sciences and ideas, a place for meetings and discussions, and sometimes as a lodging for scholars or boarding school for pupils. The concept of the library catalog was also introduced in medieval Islamic libraries, where books were organized into specific genres and categories.