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A Concise History of Science in India c7.s5: Study of Arabic and Persian Mathematics in India

A Concise History of Science in India c7.s5

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English

Contents

Study of Arabic and Persian Mathematics in India

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The various Muhammadan houses and dynasties that ruled over extensive tracts of India in the medieval times not unoften patronized science and learning among their subjects. The contents of science and learning, it is needless to say, were what their Arabic and Persian masters of West and Central Asia had written about. Moreover, for a long time after the consolidation of Muhammadan rule in India, such Arabic and Persian science and learning remained confined to Muslim circles of learners and scholars, and it was not until quite late that such learning began to cross-fertilize the traditional sciences which the Hindus continued to cultivate among themselves. This is not to suggest that one group did not show any interest in the science and literature of the other. But the instances of an al-Bīrūnī zealously exploring Hindu works of science and literature, comparing and contrasting them with those of the system he represented, or of a Jagannātha mastering Arabic and Persian and assiduously translating difficult astronomical and mathematical texts into Sanskrit were rare. For the most part the Hindus remained content with the works and commentaries of their learned traditional authors and the Muhammadans hardly felt the need of mastering the language and the sciences of the former.

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As to promotion and patronage of learning, Sultan Mahmūd of the House of Ghazna did much to develop Muhammadan learning through the establishment of ‘a university supplied with a vast collection of curious books in various languages. It contained also a museum of natural curiosities’.a Qutb-ud-dīn, of the ‘Slave’ Dynasty, himself proficient in Arabic, Persian and sciences, established several mosques which, like Christian churches of Medieval Europe, acted as centres of religion and secular learning. Of the Tughluq kings, Ghiyāsuddīn built many public buildings for educational purposes, and provided for stipends to learned men; Muḥammad was skilled in logic, medicine, astronomy and mathematics and Greek philosophy; Fīrūz established at Fīrūzābād a Mādrasah after his name, which, in the beauty of its architecture and scholarly reputation, surpassed all other Indian Mādrasahs of the time.a Fīrūz also showed considerable interest in Sanskrit technical literature and caused a few of them to be translated into Persian. Hindu astronomers also received encouragement in his court. Sultan Sikandar Lodī's reign is important in the literary and scientific history of India in the fact that during his time the Hindus seriously took to the study of Persian in which, as Blochmann observes, they soon attained a great proficiency and even caught up with the Muhammadans in literary excellences.

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a Briggs, I, p. 61.

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In the south, Fīrūz Shāh of the Bahamanī Kingdom was a great scholar and patron of science and learning. He was fond of geometry and botany, among the scientific subjects, used to invite to his court learned men from abroad, and caused an astronomical observatory to be built (A.D. 1407) on the summit of a pass near Daulatābād.

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With the establishment of the Mughal power in India, the Samarqand school of mathematicians and astronomers began to play a prominent part in the study of mathematics and astronomy among the Muhammadans in India. This is clearly mentioned by Bābur himself in his *Memoirs*. Humāyūn had a great liking for astronomy and geography and caused terrestrial and celestial globes to be constructed for the purpose. The enlightened rule of Akbar was also marked by considerable progress in secular learning in which the sciences were not neglected. It was during his reign that *Līlāvatī* was translated into Persian. In the educational system introduced in his time the study of mathematics received due emphasis among the sciences which used to be taught in the following order: morality, arithmetic, accounts, agriculture, geometry, astronomy, art of government, physics, natural philosophy and mathematics. The library of Faizī which, after his death, was transferred to the King's library, contained 4,600 volumes covering different disciplines such as medicine, astrology, astronomy, geometry, philosophy, philology, theology, poetry and music.

Arabic and Persian Mathematical Works of Non-Indian Origin Used in India in Medieval Times

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It is pertinent to ask what authorities and which mathematical works in Arabic and Persian used to be taught and studied in medieval India. In the present state of our knowledge, a satisfactory answer cannot be given to this question, but a good idea may be obtained from the availability of manuscripts of a number of Arabic versions of Euclid's *Elements* and its commentaries, geometrical works of Archimedes and several standard treatises on arithmetic and algebra in different libraries in India.a

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a Law, p. 60.

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Thus we have in the Bankipur library the *Sharḥ Uqlīdas*, a critical commentary on Euclid's *Elements* in Arabic by Aḥmad b. ‘Umar at-Karābīsī (*c.* A.D. 840), a distinguished mathematician of the Middle East and author of several works. Of the several works produced by Abū-l-Ḥasan Thābit b. Qurra (d. A.D. 901), a few noticed in Indian libraries include the *Kitāb Arshīmīdas fī'd-Dawā’iri'l-Mutamāssah*, the *Kitāb Arshīmīdas fī Uṣuli'l Handasah*, both geometrical works by Archimedes, and the *Uqlīdas*. Thābit b. Qurra, besides being a physician, mathematician and astronomer of repute, was one of the greatest translators from Greek and Syriac into Arabic. In mathematics his favourite originals were the works of Apollonius, Archimedes, Euclid and Ptolemy. His works revived, in particular, the study of parabolas, paraboloids and amicable numbers. Mention may be made of *Ar-Risālah fī Auna'l-Ashkāla Kullahā mina'd-Dā'irah*, a work on the geometry of circles by Naṣr. b. ‘Abdullah (*c.* tenth century) who flourished in Baghdad.

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Next we turn to Abū Bakr M. b. Ḥasan al-Karkhī (d. *c.* A.D. 1019 to 1029), a contemporary of Śrīdharācārya, and one of the greatest Muslim mathematicians. A copy of his famous algebra *Kitāb al-Fakhrī fī-l-Ḥisāb Jabr-i-Wa'l-Muqābilah* has turned up in the library of the Osmania University. Largely based on Diophantos, *al-Fakhrī* deals with quadratic equations and equations of higher powers of the type

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$x2n+axn = b,$

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of which he was the first to have given the solutions. He gave the summation of the squares and the cubes of natural numbers as follows:b

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$₁n i² = (₁n i)(2n+1)/3$ $₁n i³ = (₁n i)²$

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Unlike other Arabic mathematical works al-Karkhī's were free from Hindu elements.

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Of al-Bīrūnī's (973–1048) mathematical works we possess his *al-kitāb fī Istikhrāji'l-Autār fī'd-Dā'irah bi-Khawāssi'l-Khaṭṭi'l Munḥani'l-Wāqi‘fihā*, a treatise on the chords of a circle, *al-Maqālah fī Rāshikāli'l Hind*, an arithmetical work on the rule of proportions based on Hindu works, and *Riyāḍatu'l-Fikr Wa'l-‘Aql*, a general work dealing with typical mathematical problems. Al-Bīrūnī's refinements in trigonometry and his construction of accurate sine tables from 0° to 90° at the intervals of 15ʹ are well known. In this connection he also gave several trigonometrical relations. Accordingly, a special importance attaches to his treatise on the chords among the Indian collection of his mathematical works.

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a A manuscript survey has been carried out by the Medieval Unit of the History of Sciences under the Indian National Science Academy, a preliminary draft of which has been made available to the author for use in this section.

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b Sarton, I, pp. 718–19.

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The same is true of ‘Umar b. Ibrāhīm al-Khayyāmī’s *Maqālah fī-l-Jabr-i* (*c.* A.D. 1110), one of the greatest medieval works on algebra. Important features of ‘Umar’s algebra are: an admirable classification of equations, geometric and algebraic solutions of quadratic and higher power equations, development of binomial series with positive integral exponents, geometrical postutates, etc. His classification of equations was based on the number of terms, e.g. trinomial, quadrinomial, etc. He made significant contributions to the solution of cubic equations which he arranged in 27 groups. The following are a few examples of his quadrinomial cubic equations: $x³+bx² = cx+d$ $x³+cx = bx²+d$ $x³+d = bx²+cx$

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‘Umar solved the above types of equations by finding the intersection of the conics. Such geometrical methods of solving algebraic equations paved the way for the development of analytical geometry at the hands of Descartes in the seventeenth century. In Europe, Renaissance mathematicians like Scipio del Ferro (1465–1526), Tartaglia (1500–57) and Cardano (1501–76) succeeded for the first time in solving cubic equations.

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An arithmetical treatise *Ghunyatu’l-Hussāb fī ‘Ilmi’l-Ḥisāb* by Aḥmad b. Thābit (*c.* twelfth century) who flourished somewhere in the Middle East is noticed in the Bankipur collection. The work deals with multiplication, division, ratio and proportion, extraction of roots, transactions, mensuration and excavation problems. Treatment of conic sections forms part of his mensuration. The author’s another arithmetical work was *‘Umdatu’r-Rā’id*.

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Abū Ja‘far Nāṣīr-al-dīn al-Ḥasan aṭ-Ṭūsī (1201–74) of Khorasan, the celebrated mathematician, astronomer and founder director of the Marāgha Observatory, was the most popular authority among the Muhammadan scientific circles, particularly in the days of the Mughal rule. His *Taḥrīr-u Uqlīdas*, Arabic version of the *Elements*, is available in manuscript copies in several libraries, being published from Calcutta in 1824. *Taḥrīr*, as Thomas Heath pointed out, was not a translation of Euclid’s text but a rewritten Euclid based on the older Arabic translations.a Jagannātha’s Sanskrit translation was based on this Arabic version. His other works of which manuscript copies have been found in India include *Maqālah-i-Arshīmīdas fī Taksīri’d-Dā’irah* and *Kitābu’l-Kurah* *Wal-Uṣṭuwānah*, both based on Archimedes' geometrical works, and another tract on conic sections *Ar-Risālatu'l-Qiṭā‘ fī ‘Ilmi'l-Handasah*.

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a Heath, I, p. 78.

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Finally we shall mention two works, both on arithmetic, of which several copies are available in Indian libraries. The ‘*Uyūn’l Ḥisāb* by Zainu'l-‘Ābidīn (*c.* a.d. 1460) treats, among others, of the arithmetic of whole numbers, fractions, mensuration, solution of unknown quantities by the method of *Khaṭā'ain* and algebra. Bahā'u'ddīn al-‘Āmulī (1547–1621) of Iran wrote an excellent arithmetic *Khulāṣatu'l-Ḥisāb*, of which several copies are available in Indian libraries. The work was published from Calcutta in 1862, the Arabic text with a German translation by Nesselmann appeared from Berlin in 1843 and a French translation by Marre from Rome in 1864.

Works by Indian Mathematicians

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The rich storehouse of Arabic and Persian mathematical literature was thus available to the Indian Muslims for a long period of time. They had also access to Hindu works in Arabic translations and commentaries as well as in their originals whenever they cared for them. But their own production, either in the form of original work or commentaries, appears far from impressive. Only from the sixteenth century do we notice some degree of activity resulting in the production of a few commentaries and translations.

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In 1555, Abū Isḥāq b. ‘Abdu’llāh, a mathematician of Golkonda, wrote *Sharḥu'sh-Shamsīyah* as a commentary on an arithmetical work *ash-Shamsīyah* by Ḥasan an-Nīshāpūrī, a pupil of aṭ-Ṭūsī. In 1587, Abū'l-Faiz Faizī, the poet laureate of Akbar, translated the *Līlāvatī* into Persian. For a Persian translation of Bhāskara's *Bījagaṇita*, the Muslim scholars had to wait for about half a century. In 1634–35, ‘Aṭau’llāh Rashīdī, son of Ustād Aḥmad Nādir, who took part in the construction of the Taj, rendered this service. Mīr M. Hāshim b. Qāsim al-Ḥusainī wrote a commentary entitled *Sharḥ Taḥrīr-u-Uṣūli'l-Handasah Wa'l-Ḥisāb* on aṭ-Ṭūsī's geometrical work *Taḥrīr-u-Uṣūlī* (1635). *Badāi'ul-Kanūn* (1663–64) by Medhnī Mal b. Dhram Dās Nārain b. Klliyān Mal Kāysth is an arithmetical treatise based on Bhāskara's *Līlāvatī*. In 1684, Ismatu’llāh as-Sahāranpūrī wrote a treatise entitled *Ḍābiṭ Qawā'idu'l-Ḥisāb* in which both arithmetical and algebraic problems were treated. Bahāu'ddin al-Amuli's arithmetic *Khulāṣatu'l-Ḥisāb* was commented upon in the seventeenth century by Luṭfu’llāh Muhandis in his *Sharḥ Khulāṣatu'l-Ḥisāb* and in the eighteenth century (a.d. 1770) by Amīnu’ddīn al-Lāhorī in his *Lawāmi'ul-Lubāb fī Sharḥ Khulāṣatu'l-Ḥisāb*. Towards the end of the eighteenth century (a.d. 1797) Farīdu'd-Dīn Aḥmad Khān Bahādur, Superintendent of Mādrasah ‘Āliyah and holder of important political appointments, wrote a work on geometrical compass entitled *Dar Ṣan‘ati-Parkār Ma'Fawā'idu'l-Afkār*.

Cites (3)