Sunday, December 5, 2010

Abū 'l-Walīd Muḥammad bin Aḥmad bin Rushd


Abū 'l-Walīd Muḥammad bin Aḥmad bin Rushd (Arabic: أبو الوليد محمد بن احمد بن رشد‎), better known just as Ibn Rushd (Arabic: ابن رشد‎), and in European literature as Averroes (pronounced /əˈvɛroʊ.iːz/) (1126 – December 10, 1198),

was an Andalusian Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy, geography, mathematics, physics and celestial mechanics. He was born in Córdoba, Al Andalus, modern-day Spain, and died in Marrakech, modern-day Morocco. His school of philosophy is known as Averroism.
http://en.wikipedia.org/wiki/Averroes
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Abū 'l-Walīd Muḥammad bin Aḥmad bin Rushd (Arabic: أبو الوليد محمد بن احمد بن رشد‎), better known just as Ibn Rushd (Arabic: ابن رشد‎), and in European literature as Averroes (pronounced /əˈvɛroʊ.iːz/) (1126 – December 10, 1198),

was an Andalusian Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy, geography, mathematics, physics and celestial mechanics. He was born in Córdoba, Al Andalus, modern-day Spain, and died in Marrakech, modern-day Morocco. His school of philosophy is known as Averroism.
http://en.wikipedia.org/wiki/Averroes

Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani


Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani

was born in Buzjan, Nishapur in 940 C.E. He flourished as a great mathematician and astronomer at Baghdad and died in 997/998 C.E. He learnt mathematics in Baghdad. In 959 C.E. he migrated to Iraq and lived there till his death.

Abul Wafa's main contribution lies in several branches of mathematics, especially geometry and trigonometry. In geometry his contribution comprises solution of geometrical problems with opening of the compass; construction of a square equivalent to other squares; regular polyhedra; construction of regular hectagon taking for its side half the side of the equilateral triangle inscribed in the same circle; constructions of parabola by points and geometrical solution of the equations:

x4 = a and x4 + ax3 = b

Abul Wafa's contribution to the development of trigonometry was extensive. He was the first to show the generality of the sine theorem relative to spherical triangles. He developed a new method of constructing sine tables, the value of sin 30' being correct to the eighth decimal place. He also developed relations for sine (a+b) and the formula:

2 sin2 (a/2) = 1 - cos a , and
sin a = 2 sin (a/2) cos (a/2)

In addition, he made a special study of the tangent and calculated a table of tangents. He introduced the secant and cosecant for the first time, knew the relations between the trigonometric lines, which are now used to define them, and undertook extensive studies on conics.

Apart from being a mathematician, Abul Wafa also contributed to astronomy. In this field he discussed different movernents of the moon, and discovered 'variation'. He was also one of the last Arabic translators and commentators of Greek works.

He wrote a large number of books on mathematics and other subjects, most of which have been lost or exist in modified forms. His contribution includes Kitab 'Ilm al-Hisab, a practical book of arithmetic, al-Kitab al-Kamil (the Complete Book), Kitab al-Handsa (Applied Geometry). Apart from this, he wrote rich commentaries on Euclid, Diophantos and al-Khawarizmi, but all of these have been lost. His books now extant include Kitab 'Ilm al-Hisab, Kitab al- Handsa and Kitab al-Kamil.

His astronomical knowledge on the movements of the moon has been criticized in that, in the case of 'variation' the third inequality of the moon as he discussed was the second part of the 'evection'. But, according to Sedat, what he discovered was the same that was discovered by Tycho Brache six centuries later. Nonetheless, his contribution to trigonometry was extremely significant in that he developed the knowledge on the tangent and introduced the secant and cosecant for the first time; in fact a sizeable part of today's trigonometry can be traced back to him.
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Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani

was born in Buzjan, Nishapur in 940 C.E. He flourished as a great mathematician and astronomer at Baghdad and died in 997/998 C.E. He learnt mathematics in Baghdad. In 959 C.E. he migrated to Iraq and lived there till his death.

Abul Wafa's main contribution lies in several branches of mathematics, especially geometry and trigonometry. In geometry his contribution comprises solution of geometrical problems with opening of the compass; construction of a square equivalent to other squares; regular polyhedra; construction of regular hectagon taking for its side half the side of the equilateral triangle inscribed in the same circle; constructions of parabola by points and geometrical solution of the equations:

x4 = a and x4 + ax3 = b

Abul Wafa's contribution to the development of trigonometry was extensive. He was the first to show the generality of the sine theorem relative to spherical triangles. He developed a new method of constructing sine tables, the value of sin 30' being correct to the eighth decimal place. He also developed relations for sine (a+b) and the formula:

2 sin2 (a/2) = 1 - cos a , and
sin a = 2 sin (a/2) cos (a/2)

In addition, he made a special study of the tangent and calculated a table of tangents. He introduced the secant and cosecant for the first time, knew the relations between the trigonometric lines, which are now used to define them, and undertook extensive studies on conics.

Apart from being a mathematician, Abul Wafa also contributed to astronomy. In this field he discussed different movernents of the moon, and discovered 'variation'. He was also one of the last Arabic translators and commentators of Greek works.

He wrote a large number of books on mathematics and other subjects, most of which have been lost or exist in modified forms. His contribution includes Kitab 'Ilm al-Hisab, a practical book of arithmetic, al-Kitab al-Kamil (the Complete Book), Kitab al-Handsa (Applied Geometry). Apart from this, he wrote rich commentaries on Euclid, Diophantos and al-Khawarizmi, but all of these have been lost. His books now extant include Kitab 'Ilm al-Hisab, Kitab al- Handsa and Kitab al-Kamil.

His astronomical knowledge on the movements of the moon has been criticized in that, in the case of 'variation' the third inequality of the moon as he discussed was the second part of the 'evection'. But, according to Sedat, what he discovered was the same that was discovered by Tycho Brache six centuries later. Nonetheless, his contribution to trigonometry was extremely significant in that he developed the knowledge on the tangent and introduced the secant and cosecant for the first time; in fact a sizeable part of today's trigonometry can be traced back to him.

Abu'l-Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani


Abu'l-Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani,

born in Farghana, Transoxiana, was one of the most distinguished astronomers in the service of al-Mamun and his successors. He wrote "Elements of Astronomy" (Kitab fi al-Harakat al-Samawiya wa Jawami Ilm al-Nujum i.e. the book on celestial motion and thorough science of the stars), which was translated into Latin in the 12th century and exerted great influence upon European astronomy before Regiomontanus. He accepted Ptolemy's theory and value of the precession, but thought that it affected not only the stars but also the planets. He determined the diameter of the earth to be 6,500 miles, and found the greatest distances and also the diameters of the planets.

Al-Farghani's activities extended to engineering. According to Ibn Tughri Birdi, he supervised the construction of the Great Nilometer at al-Fustat (old Cairo). It was completed in 861, the year in which the Caliph al-Mutawakkil, who ordered the construction, died. But engineering was not al-Farghani's forte, as transpires from the following story narrated by Ibn Abi Usaybi'a.

Al-Mutawakkil had entrusted the two sons of Musa ibn Shakir, Muhammad and Ahmad, with supervising the digging of a canal named al-Ja'fari. They delegated the work to Al-Farghani, thus deliberately ignoring a better engineer, Sind ibn Ali, whom, out of professional jealousy, they had caused to be sent to Baghdad, away from al-Mutawakkil's court in Samarra. The canal was to run through the new city, al-Ja'fariyya, which al-Mutawakkil had built near Samarra on the Tigris and named after himself. Al-Farghani committed a grave error, making the beginning of the canal deeper than the rest, so that not enough water would run through the length of the canal except when the Tigris was high. News of this angered the Caliph, and the two brothers were saved from severe punishment only by the gracious willingness of Sind ibn Ali to vouch for the correctness of al-Farghani's calculations, thus risking his own welfare and possibly his life. As had been correctly predicted by astrologers, however, al-Mutawakkil was murdered shortly before the error became apparent. The explanation given for Al-Farghani's mistake is that being a theoretician rather than a practical engineer, he never successfully completed a construction.

The Fihrist of Ibn al-Nadim, written in 987, ascribes only two works to Al-Farghani: (1) "The Book of Chapters, a summary of the Almagest" (Kitab al-Fusul, Ikhtiyar al-Majisti) and (2) "Book on the Construction of Sun-dials" (Kitab 'Amal al-Rukhamat).

The Jawami, or 'The Elements' as we shall call it, was Al- Farghani's best-known and most influential work. Abd al-Aziz al-Qabisi (d. 967) wrote a commentary on it, which is preserved in the Istanbul manuscript, Aya Sofya 4832, fols. 97v-114v. Two Latin translations followed in the 12th century. Jacob Anatoli produced a Hebrew translation of the book that served as a basis for a third Latin version, appearing in 1590, whereas Jacob Golius published a new Latin text together with the Arabic original in 1669. The influence of 'The Elements' on mediaeval Europe is clearly vindicated by the presence of innumerable Latin manuscripts in European libraries.

References to it by medieval writers are many, and there is no doubt that it was greatly responsible for spreading knowledge of Ptolemaic astronomy, at least until this role was taken over by Sacrobosco's Sphere. But even then, 'The Elements' of Al-Farghani continued to be used, and Sacrobosco's Sphere was evidently indebted to it. It was from 'The Elements' (in Gherard's translation) that Dante derived the astronomical knowledge displayed in the 'Vita nuova' and in the 'Convivio'.
Add a caption
Abu'l-Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani,

born in Farghana, Transoxiana, was one of the most distinguished astronomers in the service of al-Mamun and his successors. He wrote "Elements of Astronomy" (Kitab fi al-Harakat al-Samawiya wa Jawami Ilm al-Nujum i.e. the book on celestial motion and thorough science of the stars), which was translated into Latin in the 12th century and exerted great influence upon European astronomy before Regiomontanus. He accepted Ptolemy's theory and value of the precession, but thought that it affected not only the stars but also the planets. He determined the diameter of the earth to be 6,500 miles, and found the greatest distances and also the diameters of the planets.

Al-Farghani's activities extended to engineering. According to Ibn Tughri Birdi, he supervised the construction of the Great Nilometer at al-Fustat (old Cairo). It was completed in 861, the year in which the Caliph al-Mutawakkil, who ordered the construction, died. But engineering was not al-Farghani's forte, as transpires from the following story narrated by Ibn Abi Usaybi'a.

Al-Mutawakkil had entrusted the two sons of Musa ibn Shakir, Muhammad and Ahmad, with supervising the digging of a canal named al-Ja'fari. They delegated the work to Al-Farghani, thus deliberately ignoring a better engineer, Sind ibn Ali, whom, out of professional jealousy, they had caused to be sent to Baghdad, away from al-Mutawakkil's court in Samarra. The canal was to run through the new city, al-Ja'fariyya, which al-Mutawakkil had built near Samarra on the Tigris and named after himself. Al-Farghani committed a grave error, making the beginning of the canal deeper than the rest, so that not enough water would run through the length of the canal except when the Tigris was high. News of this angered the Caliph, and the two brothers were saved from severe punishment only by the gracious willingness of Sind ibn Ali to vouch for the correctness of al-Farghani's calculations, thus risking his own welfare and possibly his life. As had been correctly predicted by astrologers, however, al-Mutawakkil was murdered shortly before the error became apparent. The explanation given for Al-Farghani's mistake is that being a theoretician rather than a practical engineer, he never successfully completed a construction.

The Fihrist of Ibn al-Nadim, written in 987, ascribes only two works to Al-Farghani: (1) "The Book of Chapters, a summary of the Almagest" (Kitab al-Fusul, Ikhtiyar al-Majisti) and (2) "Book on the Construction of Sun-dials" (Kitab 'Amal al-Rukhamat).

The Jawami, or 'The Elements' as we shall call it, was Al- Farghani's best-known and most influential work. Abd al-Aziz al-Qabisi (d. 967) wrote a commentary on it, which is preserved in the Istanbul manuscript, Aya Sofya 4832, fols. 97v-114v. Two Latin translations followed in the 12th century. Jacob Anatoli produced a Hebrew translation of the book that served as a basis for a third Latin version, appearing in 1590, whereas Jacob Golius published a new Latin text together with the Arabic original in 1669. The influence of 'The Elements' on mediaeval Europe is clearly vindicated by the presence of innumerable Latin manuscripts in European libraries.

References to it by medieval writers are many, and there is no doubt that it was greatly responsible for spreading knowledge of Ptolemaic astronomy, at least until this role was taken over by Sacrobosco's Sphere. But even then, 'The Elements' of Al-Farghani continued to be used, and Sacrobosco's Sphere was evidently indebted to it. It was from 'The Elements' (in Gherard's translation) that Dante derived the astronomical knowledge displayed in the 'Vita nuova' and in the 'Convivio'.

Abu al-Hasan Ali ibn Sahl Rabban al-Tabari


Abu al-Hasan Ali ibn Sahl Rabban al-Tabari
(علی ابن سهل ربان طبری) (c. 838 – c. 870 CE)
was a Muslim hakim, Islamic scholar, physician and psychologist of Jewish or Zoroastrian descent, who produced the first encyclopedia of medicine. He was a pioneer of pediatrics and the field of child development.

His works
Tuhfat al-Muluk ("The King's Present")
a work on the proper use of food, drink, and medicines.
Hafzh al-Sihhah ("The Proper Care of Health"), following Greek and Indian authorities.
Kitab al-Ruqa ("Book of Magic or Amulets")
Kitab fi al-hijamah ("Treatise on Cupping")
Kitab fi Tartib al-'Ardhiyah ("Treatise on the Preparation of Food")

On the Quran he said: "When I was a Christian I used to say, as did an uncle of mine who was one of the learned and eloquent men, that eloquence is not one of the signs of prophethood because it is common to all the peoples; but when I discarded (blind) imitation and (old) customs and gave up adhering to (mere) habit and training and reflected upon the meanings of the Qur'an I came to know that what the followers of the Qur'an claimed for it was true. The fact is that I have not found any book, be it by an Arab or a Persian, an Indian or a Greek, right from the beginning of the world up to now, which contains at the same time praises of God, belief in the prophets and apostles, exhortations to good, everlasting deeds, command to do good and prohibition against doing evil, inspiration to the desire of paradise and to avoidance of hell-fire as this Qur'an does. So when a person brings to us a book of such qualities, which inspires such reverence and sweetness in the hearts and which has achieved such an overlasting success and he is (at the same time) an illiterate person who did never learnt the art of writing or rhetoric, that book is without any doubt one of the signs of his Prophethood.
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Abu al-Hasan Ali ibn Sahl Rabban al-Tabari
(علی ابن سهل ربان طبری) (c. 838 – c. 870 CE)
was a Muslim hakim, Islamic scholar, physician and psychologist of Jewish or Zoroastrian descent, who produced the first encyclopedia of medicine. He was a pioneer of pediatrics and the field of child development.

His works
Tuhfat al-Muluk ("The King's Present")
a work on the proper use of food, drink, and medicines.
Hafzh al-Sihhah ("The Proper Care of Health"), following Greek and Indian authorities.
Kitab al-Ruqa ("Book of Magic or Amulets")
Kitab fi al-hijamah ("Treatise on Cupping")
Kitab fi Tartib al-'Ardhiyah ("Treatise on the Preparation of Food")

On the Quran he said: "When I was a Christian I used to say, as did an uncle of mine who was one of the learned and eloquent men, that eloquence is not one of the signs of prophethood because it is common to all the peoples; but when I discarded (blind) imitation and (old) customs and gave up adhering to (mere) habit and training and reflected upon the meanings of the Qur'an I came to know that what the followers of the Qur'an claimed for it was true. The fact is that I have not found any book, be it by an Arab or a Persian, an Indian or a Greek, right from the beginning of the world up to now, which contains at the same time praises of God, belief in the prophets and apostles, exhortations to good, everlasting deeds, command to do good and prohibition against doing evil, inspiration to the desire of paradise and to avoidance of hell-fire as this Qur'an does. So when a person brings to us a book of such qualities, which inspires such reverence and sweetness in the hearts and which has achieved such an overlasting success and he is (at the same time) an illiterate person who did never learnt the art of writing or rhetoric, that book is without any doubt one of the signs of his Prophethood.