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Mathematics in Ancient and Medieval India c10: Chapter VII Trend of Indo-Persian/Arabic Literature on Mathematics in the Medieval Period

Mathematics in Ancient and Medieval India c10

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English

Chapter VII Trend of Indo-Persian/Arabic Literature on Mathematics in the Medieval Period

c10.2

Vast amount of mathematical literature of the medieval period were written in Persian and Arabic and are now available in different oriental libraries in India. Many standard works were also brought in the Sultanate and Mughal Periods from outside world. Attempt was made during this period to prepare translations and write commentaries on these texts. Sultans and Mughal rulers built up hundreds of *maktabs* for elementary education and *madrasahs* for higher education. There were also institutions which laid special emphasis on special field of study like mathematics, astronomy or medicine. Lahore, Delhi and Lucknow became important centres of learning in the period. Education and activities also grew in Jaunpur, Kashmir, Gujrat, Malwa, Bengal, Bihar, Khandwah, and Deccan. In different *madrasahs* subjects like grammer rhetoric, logic, theology, metaphysics, literature, jurisprudence were mainly taught. The teaching of astronomy, mathematics and medicines were not very satisfactory in these *madrasahs*, and Muslims preferred to attend Hindu institutions to master these subjects¹.

c10.3

¹ Jaggi, O. P. *Science and Technology in Medieval India*. Atma Ram and Sons, Delhi, 1977.

c10.4

Akbar made mathematics compulsory in *madrasahs* for students and issued a *farman*. The study of astronomy and astrology were also encouraged and formed the part of regular courses of study. Inspite of the patronisation, no real effort was taken either to assimilate the knowledge available in Sanskrit sources or from original Persian and Arabic sources were mostly written for people who had no access in standard Sanskrit, Arabic and Persian treatises in mathematics. To what extent the knowledge was available to Indians through Persian and Arabic commentries is yet to be assessed. The following will give an idea of the mathematical activities in the period.

c10.5

Fīrūz Shah ( 1351–1388 A. D. ) of the Bahmani dynasty was a great patron of astronomical studies. He tried to construct an observatory with the help of Hakim Ali Hasan but it was left unfinished because of Hasan’s untimely death.

c10.6

‘Abd al-’Aziz ibn Shams² prepared a Persian versian *Tarjuma-hi Bārāhī* of the *Bṛhat Saṃhitā* of Varāhamihira for Fīrūz Shah. Out of the 104 chapters (*bābs*) in the original, only eight were left out in the translation. He might have written another persian work, *Nujūm al-Hind wa San‘at-i-usṭurlāb* on Indian astronomy and construction of astrolabe. The date of compilation is not available.

c10.7

² Habibullah, A. B. M. ‘Medieval Indo-Persian Literature relating to Hindu Science and Philosophy.’ *Indian Historical Quarterly*, 14, pp. 167–181, 1938.

c10.8

Bābur knew about Ulug Beg's observatory which was established at Samarqand in 1420 A. D. A description of the observatory is given by Bābur in his Memoir, *Bāburnāmā*. Humāyūn had an extraordinary liking for astronomy. He learnt astronomy and mathematics under Turkhan Sufidini, well-known scholar in astronomy and mathematics. He discussed astronomy and mathematics with Sufinini, and could handle problems of mathematics and particularly of astrolabe.

c10.9

Muṣliḥu'd-dīn al-Lārī al-Anṣārī flourished during the reign of Humāyūn ( 1530-40 ). Later he joined the court of Mirzā Shāh Ḥusain Arghun ( 1556 ), the ruler of Sind He wrote a commentary on Alā'ud-dīn 'Alī Qūshji's *Risālah dar Hai'at* entitled *Sharḥ Risālah i Qūshji*. The manuscript is available in the Bankipur Library and State Central Library, Hyderabad.

c10.10

The *Līlāvatī* gained wide popularity in India and was held in esteem in the time of Akbar ( 1556-1605 ). It is under his order, Abul Faizī, his court poet, prepared a Persion translation *Tarjamah-i-Līlāvatī* in 1587 A. D. ( A. H. 996–6 ). This is mentioned in *Āīn-i-Akbari*.

c10.11

Mullāchānd was also the court astronomer of Akbar. He wrote a work on astronomical table, *Tashīlāt*. This is referred by Farīd-ud-Dīn in *Zīj-i-Shāh-jahānī* and Jai Singh Sawāi in *Zīj-i-Muḥammad Shāhī*. Nīlakaṇṭha Jyotirvid who flourished in the court of Akbar compiled a *Tājik* work in which a large number of Persian technical terms were introduced.

c10.12

'Aṭāu'llah Qārī ( Qadiri ? ) flourished during the reign of Barhān Niṣām Shāh, ruler of Aḥmadnagar (1591–1595). His *Risāla dar Maʻrifat-i Aʻmāl-i Rubʻmujayyā-i Āfāqī* deal with sine quadrant. The manuscript is available in the State Central Library, Hyderabad and Azad Library, Aligarh.

c10.13

A Persian translation of the *Bījagaṇita* entitled *Tarjamah-i-Bij* was made in India in 1634-35 A. D. by Atāullāh Rashīdī, son of Ustad Aḥmad Nādir, the builder of Taj Mahal He was originally a resident of Lahore and had his education under his father, and Makramat Khan, who was well-known for his knowledge in mathematics. The work was dedicated to Shāhjahān (1628–1659). The Persian version was translated into English by Edward Strachey in 1813 A. D. From the traslation it appears that it is not a faithful translation of the *Bījagaṇita* but is a mixture of text, commentary and some interpolation. The same author wrote perhaps two other works viz. *Khasinatril Aʻdad* dealing with arithmetic, algebra, and applied geometry. Some discussion is also available on some astronomical problems. The other work is *Khulasah-i-Baz* dealing with arithemetic, mensuration and algebra in verse form. The manuscript copies are available in Bankipur and British Museum.

c10.14

Farīd'd-dīn Maʼsud, son of Ḥāfis Ibrāhim Munajim was the court astronomer of Shāhjahān. He was considered as a great scholar in mathematics, astronomy, geometry. etc. He wrote perhaps two works viz. *Sirājul Istikhrai* and *Zij-i Shāhjahānī* in 1629 A. D. The former deals with eras, calculations of dates and principles of computation of almanacs. The latter is on calendars and astronomical tables. The manuscripts of both the works are available in the State Central Library, Hyderabad.

c10.15

Lutfu'llah Muhandis, the brother of Atā'ullāh Rashīdī (c. 1634) and the second son of Ustad Aḥmad, was also well-known for his interest in mathematics and other sciences. His *Muntakhab* is a short versified translation of Bahā'ud-dīn Āmuli's mathematical work *Khulāṣatu'l Ḥisāb* and was written in Persian in 1681 A. D. The copies of the manuscripts are available in the Asiatic Society of Bengal, Bankipur, British Museum, Azad Library (Aligarth) and Salarjang Library (Hyderabad). His *Risāla dar Jawāb i-Sawali* on geometry in question answer form and *Risāla-i-Arsmatiqi* on properties of numbers are still available in the Rampur Library and Saidiyah Library (Hyderabed). He wrote *Taqwim Luṭifi*, on almanac and *Tarjuma Kitāb Suwar-i-Kawakib*, a commentary on the celebrated astronomical work *Suwaru'l Kawākib*. The manuscript is available in Rampur Rida Library (U. P.) and Azad Library (Aligarh).

c10.16

Hāji Kha'ullah, son of Aman'ullah and brother of Mulla Murshid Makramat Khan in the beginning of 17th century A. D. (died in 1649) wrote a commentary on the work of mathematics is entitled *Sharḥ-i-Kitāb-i-Haji Kalil*. A copy is available in the Rampur Library.

c10.17

Sh. Muḥammad (17th century A. D.), son of Sh. Muḥammad Saīd flourished under emperor Aurangzeb (1659–1709) He wrote in Arabic *Shārḥ as Sirajiya*, an incomplete commentary on as-Sajāwandi's algerbaical treatise known as *Sirājīya*. The manuscript is available in the Asiatic Society of Bengal.

c10.18

Dharma Nārāyan ibn Kalyānmal Kayath wrote a Persian commentary in 1663–64 A.D. at Etawah on the *Līlāvatī* under the title *Badā’ i-i-Funūn* and dedicated to Alamgir Aurangzeb (1659–1709). The copies of manuscripts are listed by C. A. Story. This shows that the *Līlāvatī* received recognition among the Mughal emperors. Manuscript copies of Faizi’s version are deposited in the British Museum, India Office Library and John Rylands Library in Manchester to mention a few. Another version *Dastūr al Ḥisāb: Tarjuma-i-Līlāvatī* was prepared by Amīn b Shaikh Muḥammed Sa’īd in 1678 A. D. The incomplete Manchesther copy has been translated by Winter and Mirza, the work contains a selection of examples taken from the *Līlāvatī*. The examples include problems on investigation of mixture, rule of three, inverse proportion, compound proportion etc. and concern primarily business transaction.

c10.19

Khawāja Bahādur Husain Khān Bahādur flourished during the reign of Aurangzeb and later went to Qulīch Khān. He learnt astronomy and astrology under S. Alavi Khān Zubadatul Munajjimin Ṭāliqānī. He is known for his two works viz. *Sharḥ-i zīj-i Nizāmī* (commentary on *Zīj-i Nizāmī*) and *Zīj-i Nizāmī* (astrological and astronomical table). The scholar has studied of both Indian and non-Indian works. The copies of both the works are available in the State Central Library.

c10.20

Nand Rām, son of Hiranand Ka’isth flourished during the reign of Mughal emperor Aurgangzeb and wrote a work on accountancy, *Ain-i-Siyaq* in 1680 A. D. One copy of the manuscript is available in the State Central Library, Hyderabad.

c10.21

M. Husain s|o Khalilullāh (d. 1696) was born at Bījāpur and studied under M. Zubair at Bījāpurī. He was appointed principal of Madrasah-i-Maḥmūd in Bidar by Aurgangzeb in 1686 A. D. He produced *Ujalatur Rub* in Arabic which deals with application of quadrant for recording various astronomical data. The manuscript is available at Sa-Idiyah Library, Hyderabad

c10.22

Rājā Jayasiṃha (1693-1743) flourished under the patronization of Maḥammad Shāh (1719-1748 A. D.) and tried to rectify and improve the almanacs already constructed by his predecessors.¹ He started organising new observations with the help of the Muslim, Hindu and European experts. After seven years of observations in Delhi, Jaipur, Mathura, Benares, and Ujjain, he deputed Padre Manoel with some competent hands to Europe who brought back with them the astronomical tables of De la Hire. He was also familiar with Euclid’s *Elements of Geometry*, Ptolemy’s *Almagest*, certain writings on astrolabe, the tables of Ulugh Beg of Samarkand and Flamsteed’s *Historia Celestis Britannica*. The materials are compiled in his *Zīj-i Jādīd -i Muḥammad Shāhī*, which was completed in 1727 A. D.

c10.23

¹ Kaye G. R (1) *The Astronomical Observatories of Jai Singh*, Archaeological Survey of India, New Imperial Series No. 40, Calcutta, 1918.
(2) *A Guide to Old Observatories at Delhi, Jaipur, Ujjain & Benares*, Calcutta, 1920.

c10.24

The manuscript is available at the Oriental Library, Bankipur and British Museum. Under his patronization, Samrāṭ Jagannāth translated Ptolemy's *Syntaxis* as *Siddhāntasāra Kaustubha*, Euclid's *Elements* as *Rekhāgaṇita*, Kewal Ram (Gujrathi Brāhman) translated De la Hire's table as *Jai Vinod Vibhag Sāraṇi*, Ulugbeg's tables as *Tārā Sāraṇi*. Pundarik Ratnākar, a Maharastrian Brahmin wrote *Jai Singh Kalpadrum* dealing with Purāṇic facts.

c10.25

Muḥammad Zaman Fayyad, son of M. Sadiq al-Anbalaji ad-Dehlawī wrote in 1718 A. D. his *Ghayat-i Juhdu'l Ḥisāb*. The manuscript is available in the Bankipur and Rampur Libraries. He was a native of Ambala and later on resided at Delhi. He wrote several other books in mathematics and astronomy. His *Taḥrīru'l Ashkāl li Hal-li Sharḥ-i Ashkālu't Ta'* *sis li Ṭusī* is a super-commentary on the commentary by Ṭusī on the *Ashkālu't Ta'* *'sis*, a geometrical work of *Shamsu'd-Dīn* M. b. Ashraf Husaini. The manuscript is available in the Rampur Library.

c10.26

‘Imāmu'd-dīn Ḥusain (b. 1701 ), the eldest son of Luṭfu'llāh Muhandis was a well-known astronomer. He wrote many works on astronomy, of which his *at-Tā' liqāt alā Sharḥi'l-Mulakhkhasi'l Chagmīnī* is a commentary on the *al-Mulakhkhas fi'l Hai'al* of *Qāḍī Zadah ar-hūmī* and *at-Taṣrīh fi sharhi Taṣrīḥ* is a commentary on *Taṣrīḥu'd-dīn Aflāk* of Bahā'ud-dīn Āmūli.

c10.27

Mirzā Khairullāh Muhandis (c. 1700-1740 ), the second son of Luṭfalla Muhandis of Lahore and nephew of ‘Ata’ Allāh Rushdī (c. 1634) was astronomical adviser to Jayasiṃha ( 1693-1743 ) and wrote a *Sharḥ* on the latter's *Zīj-i-Muḥammad Shāhī*. He also translated a copy of *Almagest* and wrote a commentary on it. A manuscript of *Almagest* with his commentary is available at the Raza Library, Rampur.

c10.28

Abu'l Khairu'llah son of Luṭfu'llah Muhandis was appointed head of the observatory at Delhi by emperor Mohammad Shāh in 1718. His *Taqrību't Taḥrīr*, is a Persian translation of Naṣirud-dīn's Arabic version on Ptolemy's *Almagest*. He compiled with the help of Nizāmu'd-dīn at Barjandī's commentary on Ṭusi's above work. The manuscript is available at the Bankipur Library. He wrote another commentary on the *Zīj-i-Muḥammad Shāhī*.

c10.29

Mulchand, son of Harihar Prasad flourished during the reign of Muḥammad (1719-1748), ruler of Delhi. His *Ḥisāb Nāmāh*, a treatise on arithmetic was written in Delhi. One copy of the manuscript is available in State Central Library.

c10.30

Anand Ram Mukhlis, son of Rajah Mardi Ram of Allahabad flourished during the reign of Muḥammad Shāh (1719-1748). His work *Dasturu'l Amal* chiefly dealing with accountancy was written in first half of 18th century in Persian. It contains information on weights and measure, zodiacal signs, Hindu science and śāstras in tabulated form. He quoted profusely about his teacher Mirza Bedi in the work.

c10.31

Inderman, a native of Hisar wrote his *Dastur-i-Ḥisāb* in 1767 A. D. It is a treatise in five *maqalah* and a *khatimah*. One copy is available at Bankipur Library.

c10.32

Muhammad Barkat flourished in Lahore in 1782 A. D. and was well-known for his *Sharḥ Taḥrīr-u usuli'l Handasat-i wa'l Ḥisāb*, a commentary in Arabic on the first book of *Euclid* and *Al-Hashiyah'ala Uqlidas*, a gloss on the *Euclid*. The manuscripts are available in the Osmania University Library.

c10.33

Khwajah Muḥammad was a native of Hydarabad and dedicated his arithmetical work, *Mir'atu'l 'Ḥisāb* in 1786 A. D. to Mumtazu'd Daulah M. A. 'Zamu'd-Din Khan Bahādur Muzaffar Jung, commander in chief of Nizāmud Dīn Mir. Nizām 'Alikhan Fath Jung, ruler of Hyderabad. The manuscript is available at the Azad Library, State Central Library, Rampur Library and Mashriqi Kutub Khanah Salar Jung (Hyderabad). He wrote also a commentary *Sharḥ-i-Khulāsatu'l Ḥisāb* on the *Khulāṣatu'l Ḥisāb* of *Bahā'ud-Dīn 'Āmulī'*. The manuscript is available in the State Central Library.

c10.34

Raushan Ali (fl. second half of the 18th century) was born at Jaunpur. He taught at Calcutta. Madrasah and Fort William College. He wrote a number of works in mathematics and other subjects. Some of these works are *Risālah fi Jabr wa Muqablah* (on Algebra), *Risāla-i-Ḥisāb* (a treatise on arithmetic) *Tarjumḥ-i Khulāṣatu'l Ḥisāb* (a translation of Bahā'ud-dīn Āmulī's mathematical treatise). The manuscript is available in Rampur Library.

c10.35

Karim Bakhsh made a selection from a larger treatise, *Umudu'l Ḥisab* for a Deccan Prince Arastu Jah. Three copies of the manuscripts are available in the Sa Idiyah Library, Hyderabad.

c10.36

Nawab Shamsu'ul Umara Fakhru'd-dīn Khān Bahādur (b. 1785) was a decendant of Farīdu'd-dīn Mas'ud al-Ajudhani. His grand father migrated to Hyderabad and was appointed an officer under Asaf Jah Nizam, first founder Nizam of Hyderabad (died in 1748). He took interest in propagating western knowledge to India. He wrote two works viz. *Risālah der Bayan i Amal-i Qite*, a treatise on the construction of the sector and *Sham su'l Handasah*, a work on geometry mensuration and trigonometry. The copies of both these manuscripts are available in State Central Library, Hyderabad.

c10.37

M. Ḥusain Isfahani Landani, son of S. Abdu'l-'Azim Isfahani Landani flourished during the days of Asifu'lmulk Sikandar Jāh Bahādur. He wrote his *Risālah-i Haī'at-i Angrezī* in 1797 A. D. on European astronomical system specially English and French. The manuscript is available in State Central Library, Hyderabad and Rampur Library, U. P.

c10.38

Sayyid Nuru'l Asfiyah (c. 1800 A. D.) was born at Aurangabad. He lived for a considerable time with Nawab ali Khān at Karnal and later on shifted to Hyderabad and joined the service under Nawab Shamesu'ul Umara. He wrote *Risālah-i-Nuru'l Ḥisāb*, a treatise on arithmetic. The manuscript is available in the State Central Library, Hyderabad.

c10.39

Sh. Aḥmad b. M. Maghribi Tilimsani al-Ansari as-Sa'imi (c. 1814) was attached as collector in the Department of Revenue of Madras. He composed several treatises on mathematics and astronomy. His *A'zamu'l-Ḥisāb* is a treatise on mathematics, now available in the State Central Library. The *Zubdatu'l Ḥisāb* is another mathematical treatise available in Asiatic Society in four chapters dealing with arithmetic, measurements, finding an unknown quantity and some essentials relating to arithmetic. He perhaps wrote another work *Mir’atu’l-’Alam* on mathematics. The manuscript is available in the State Central Library.

c10.40

Abul Qāsim ( Ghulam Hussain ), son of Fath M. Al-Karbala-i wrote his *Jami’i Bahādur Khānī*¹ in 1834 A. D. He was born at Jaunpur in 1790-91 A. D. and had his lesson in mathematics under his father and some contemporary scholars in mathematics. He spent most of his time with the princes of Benares and Murshidabad The work is devoted to mathematics and astronomy in six chapters viz. science of geometry, optics, arithmetics, practical gemoetry dealing with the measurement and division of circle, heavenly bodies, horoscope and calendar. The work starts with the element of geometry and arithmetic according to Hindus, then European methods of decimal fractions, logarithms, trigonometrical tables and then gives a system of astronomy first according to Hindus, then according to Ptolemy, then according to Copernicus together with an account of astronomical instruments and calculations on astronomical almanacs. The copies of manuscripts are available in the Asiatic Society of Bengal, State Central Library, Salarjung Library, Hyderabad. He wrote several other works viz. *Sharzhala Tahrīr-i Uqlīdas* (commentaries to Euclid) and *al-Mijisṭī* (commentary to *Almagest* of Ptolemy ). *Anīsu’l-Aḥbāb* *fi Bayān-i Masā'il-i Usṭurlāb* (commentary on the Bahāud-dīn Āmulī's treatise on *Sufaiḥah*), *Iṣṭilāḥātu't Taqwin* (on compilation of almanacs) and *Zīj-i-Bahādur Khānī* (on astronomical tables).

c10.41

¹ Tytler, John. ‘Analysis and Specimens of a Persian Work on Mathematics and Astronomy, *Royal Asiatic Society of Great Britain and Ireland*, 5, pp. 254-72, 1837.

c10.42

To sum up, the present chapter gives an incomplete survey of the Persian and Arabic literature on mathematics during the medieval period in India. It is by no means complete. The Persian and Arabic literatures were produced mostly under the patronage of Mughal rulers.¹ Many standard works were brought from outside India. Some of these are *Khulāṣtu'l Ḥisāb* of Bahā'ud-Dīn Āmulī (c. 1547-1621) written originally in Arabic in Iran, *Taḥrīr-i-Uqlidas* and *al-Mijisṭī*, Arabic version of Euclid's *Elements* and Ptolemy's *Almagest* by Nasīru'd-dīn aṭ-ṭūsi etc. besides some others on acountancy, which attracted attention of many Indian scholars.

c10.43

¹ Storey, C. A. *Persian Literature*, Vol. 2, pp. 1, 4–5, London, 1938.

c10.44

Attempt has been made to translate and write commentaries on these texts. Similar attempts have been tried to make translations of *Bṛhatsaṃhitā*, *Līlāvatī* and *Bījagaṇita* in the period, but very few attempts have been made to make a comparison with the available knowledge in Sanskrit sources. These were written mainly for readers of Persian who knew no other language and had no access in standard Sanskrit, Arabic and Persian treatises in mathematics. Only a partial attempt has been made by Muniśvara and Kamalākara, Jagannātha Paṇḍita and Rājā Jayasiṃha to make a synthesis of the available Indian knowledge, and that of Ptolemy and Euclid. The account gives an idea of both Hindu and Islamic traditions in India as well as their activities in the form of writing commentaries on older Indian and some Persian texts, which helps us to some extent to assess the trend of literature. The activities of the Indian scholars in mathematics also attracted the attention of European scholars viz. Giovanni Dominique Cassini (1691-1699), Le Gentil (1772), Robert Barker (1777), Joseph Tieffenttaler (1785-1789), Bailey (1787), William Jones (1790), Samuel Devis (1790-1892) and John Bentley (1799), who tried to make assessment of Indian activities by writing translation of the text, writing articles in French, Latin and German languages. Sen¹ has made a resumé of these activities. But the assessment of the actual contribution in the period deserves more intensive research. This is very important because this will help us to assess correctly the proportion of cultural interdependence in the field of mathematical knowledge.

c10.45

¹ Sen, S. N. 'Scientific Works, in Sanskrit, translated into Foreign languages and Vice Versa in the 18th and 19th century A. D.' *Indian Journal of History of Science*, 7. No. 1, pp 44-70, 1972.

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