Tuesday, May 15, 2018

The works of al-Kashi

Ghiyath aI-DIn Jamshid al-Kashi, an eminent Iranian mathematician and astrono­mer of the 15th century, left his birthplace Kashan for Samarkand in A.D. 1421 and joined the scientific circle of Ulugh Beg.

He is a scientist at an observatory and learning center established in Samarkand by the prince Ulugh Beg, a grandson of the Mongol conqueror Tamerlane.

Al-Kashi worked at many areas of science —astronomy, algebra and geometry. The first known scientific event in Al-Kashi’s life is his observation of an eclipse of the moon, made in Kashan on June 2, 1406. The day is precise, since Al-Kashi dated many of his works with the exact date on which they were completed.

In 1407, the scientist completed a work, named ‘Sullam Al-sama’. The full title of the work means The Stairway of Heaven, on Resolution of Difficulties Met by Predecessors in the Determination of Distances and Sizes (of the heavenly bodies).

In 1410-1411, he wrote Mukhtasar dar ilm-i hay’at-Compendium of the science of astronomy dedicated to Sultan Iskandar, one of the rulers of Timurid dynasty.

In 1413-1414, al-Kashi wrote Khaqani zij and dedicated it to Ulugh Beg. In the introduction of this book al-Kashi complains about living in poverty while working on mathematics and astronomy, and he says he could not have completed this work without Ulugh Beg’s support.

Kashi’s work “Nuzhat al-hada’iq’ completed in 1416, described an instrument ‘tabaq al-manatiq’ (equatorium) used for the determination ofthe position of the planets (longitude and latitude) on the ecliptic and a second instrument ‘lauh al-ittisalat’, used to compute the conjunctions of the planets.

On March 2, 1427, Al-Kashi completed a monumental book in Arabicon arithmetic called Mift ̄ah al-his ̄ab. His book Mift ̄ah al-his ̄ab (Key to Arithmetic) provides sufficient knowledge of mathematics for those who are working on astronomy, surveying, architecture, accounting and trading.

Al-Kashi provided accurate trigonometric tables. He also expressed the theorem in a suitable form for the modern usage. In French, the law of cosines in named theorem d'Al-Kashi after al-kashi unification of the exiting works on the subject.

All great discoveries of Al-Kashi were unknown in Europe and only in the 19th and 20thcenturies they were studied by the historians of science.
The works of al-Kashi
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