Since the middle of the 20th century, the history of Arabic mathematics evolved as a sub-field of history of science and became an area of a special expertise in which intermingled the skills of confirmed mathematicians with the cultural sense of professional historians. One of the experts who brilliantly emerged in this field was Ahmad Salim Sa‘idan (1914-1991), a Palestinian born in Safad who settled in Amman for a long period of his life. This article, intended as homage to this son of Palestine, presents a biographical sketch and an extensive bibliography of his works on the history of mathematics and astronomy in Islamic civilization.
Figure 1: Front cover of Handsat Ūqlīdis fī aydin ‘arabiya (Euclid's geometry in Arabian hands) by Ahmad Salīm Sa‘īdān (Amman, 1991).
Since the Histoire des mathématiques published beginning from 1758 by the French mathematician Jean-Etienne Montucla, and which is considered unanimously as the first history of mathematics worthy of the name, Arabic mathematics attracted the attention of historians and progressively, especially since the middle of the 20th century, it evolved as a sub-field of history of science and became the area of a special expertise in which intermingled the skills of confirmed mathematicians to the cultural sense of professional historians. The historians engaged in this field came from all over the world. Among them was an Arab and Palestinian who distinguished himself since early 1960s when he began to publish original works that attracted the attention of his colleagues. His articles and soon his books were acclaimed and after few publications in Arabic, his papers appeared (beginning from 1966) in the famous journal of history of science Isis founded by George Sarton. This scholar is Ahmad Salīm Sa'īdān, a Palestinian from Safad who settled in Amman for a long period of his life.
Figure 2: Front cover of Al-Duktūr Ahmad Salīm Sa‘īdān: Mukhtārāt min intājihi al-fikrī, selected and introduced by Khālid Ahmad Jarrār (Amman, 2002).
1. Biographical sketch 
The fate of Sa'īdān as a historian of mathematics came in the context of a real school of history of science which flourished in the Arab world since the 1940s with the publication of historical works by the Egyptian scholars Mustafa Nazif and ‘Ali Mustafa Mushrafa, followed by an ambitious generation of young experts who will have a great career in this field, first at home then abroad, Abdulhamid Ibrahim Sabra and Roshdi Rashed (from Egypt), and Mohammed Souissi and Ahmed Djebbar (from Tunisia and Algeria, respectively), and George Saliba (from Lebanon).
On January 23, 1991, the remarkable historian of medieval Arabic mathematics, Professor Ahmad Salīm Sa'īdān died in Amman, Jordan. Sa'īdān was born in 1914 into an Arabic family in Safad (Palestine). He was a student of the Arabic College in Al-Quds (Jerusalem) and at the American University in Beirut, where he took the degree of Bachelor of Science in mathematics in 1934. Beirut had a strong tradition of studies in the history of Arabic mathematics, and young Sa'īdān was attracted to this field.
After having a Bachelor from London University, his investigations on Arabic mathematics later earned him a Ph.D. from Khartoum University in Sudan. As Professor of mathematics, Sa'īdān taught in Arabic colleges and universities in Palestine, Sudan, and Jordan. After his retirement in 1979, he became President of the University of Abu-Dis in Jerusalem, but he was expelled by the Israeli occupation forces in 1981.
Figure 3: A page from a 13th-century Arabic recension (tahrīr) of Euclid's Elements by Nasīr al-Dīn al-Tūsī. © Edinburgh University Library. (Source).
Sa'īdān was a well known historian in the community of historians of Islamic sciences. His works focused on two fields:
- The edition of original texts in the different fields of mathematics practiced in ancient and medieval times (geometry, algebra and arithmetic); in this sense he edited more than 20 texts (see list below in section 4); and
- The analysis of the original texts with the tools of history of science to reconstruct content and retrace intercultural influences. Thus, his work as a historian of mathematics led him to pay a special interest to the influence exerted on the development of Arabic mathematics by the Indian and Greek traditions. But at the same time, he was aware of the fantastic progress represented by methods of demonstration and mathematical discoveries brought about by Arab and Muslim mathematicians. In this sense, he had an overall view on the Arabic mathematical tradition and tended to cover its two main wings in the Islamic East and West, mainly in his reconstruction of the history of Arabic algebra, from its emergence in the work of Al-Khwarizmi in Baghdad in early 9th century, until its later stage in the works of the mathematicians of the Maghrib, Ibn al-Banna al-Murrakushi (d. 1321) and al-Qalasadi (d. 1406).
Figure 4: A page from Kitāb al-jabr wa l-muqābala, the first extant algebra text, written in about 825 by Muhammad ibn Mūsā al-Khwārizmī. (Source).
During a career that lasted for several decades, Ahmad Salīm Sa'īdān attended congresses and scientific meetingsy the first prize awarded by the Kuwait Foundation for the Advancement of Science. Besides his work as historian of science, he was also interested in the actual state of science in the Arab world and translated several scientific textbooks. Likewise, he participated to the reflexion on the Arabization of science and on the improvement of teaching science in the Arab universities. In this regard, he was sensitive to the status of Arabic as a scientific language and manifested the desire to see it resuming again its status of vehicle of scientific creation as it was in the past.
Sa'īdān's first well-known paper, "The Rasa'il of Biruni and Ibn Sinan: A rearrangement," appeared in Islamic Culture in 1960. In this paper, he investigated the famous Bankipur manuscript containing many treatises of al-Biruni (973-1048) and his predecessors and contemporaries. In this manuscript, there had been confusion about the pagination of certain treatises by these scientists. In his investigation, Sa'īdān not only straightened this out but also discovered an earlier unknown treatise of Ibrahim Ibn Sinan (908-946) titled al-Masa'il al-mukhtara (Selected Problems).
Figure 5: Page from a manuscript of the Algebra (Maqālah fi al-jabr wa-al muqābalah) of ‘Umar Al-Khayyām (1048-1131). Manuscript on paper, 56 leaves, 13th century. Columbia University Libraries, RBML, Smith Oriental MS 45. (Source).
Five years later in the same journal, Sa'īdān published "The development of Hindu-Arabic arithmetic", a study devoted to the history of Arabic arithmetic with Arabic numerals (called by the Arabs "Indian"). In this paper, he published an English translation of part of an arithmetical treatise he discovered by the 10th-century Syrian mathematician Ahmad al-Uqlidisi dealing with decimal fractions. Thus, Sa'īdān had found the first example in the history of mathematics of the application of decimal fractions, many centuries before Emmanuel Bonfils, Jamshid al-Kashi, and Simon Stevin.
Figure 6: Page from Al-Kitāb al-Fakhrī [the Fakhri book] of the mathematician Al-Karajī (d. 1029) in which he presented geometric demonstrations of an equation. (Source).
Figure 7: Front cover of Muqaddima li-tārīkh al-fikr al-‘ilmī fī al-islām (Introduction to the history of scientific thought in Islam) by Ahmad Salīm Sa‘īdān (Kuwait, 1988, ‘Ālam al-ma‘rifa, No. 131).
In 1966, Sa'īdān published a paper in Isis on Kitab al-Fusul fi al-Hisab al-Hindi (Book of sections on Hindu arithmetic) of Abu Ahmad ibn Ibrahim al-Uqlidisi, which is the earliest extant Arabic arithmetic. This paper gave an analysis of the arithmetical treatise by al-Uqlidisi. Later on, he published a complete English translation in 1978.
During the 1970s, and in parallel with the publication of the volumes of the Dictionary of Scientific Biography in New York, Sa'īdān wrote a series of articles on the medieval Arabic mathematicians Kushyar ibn Labban al-Jili, al-Nasawi, al-Qalasadi, Ya'ish al-Umawi, al-Uqlidisi, and al-Baghdadi. Those entries were either the result of earlier works he already published or the first interest he had for certain names of scholars on who he was going to work in the coming years. This was the case for Al-Umawi, the mathematician of 15th-century Syria from Andalusian origin, of whom Sa'īdān published the treatise of arithmetic in Aleppo in 1981.
In 1974, Sa'īdān published an article in Isis, "The arithmetic of Abu ‘l-Wafa", devoted to the arithmetical treatise of the famous Baghdad mathematician and astronomer al-Buzgani (940-998). The complete Arabic text of this treatise, based on manuscripts held at Leiden University and the Cairo National Library, was edited by Sa'īdān in Amman in 1971 together with an introduction, commentary, and ample references to the Arithmetic of al-Karaji (d. ca. 1030). The treatise of al-Buzgani is a very famous arithmetical text containing the only known instance of negative numbers.
Figure 8: Page from a Latin version of Euclid's Elements, Liber elementorum in artem geometria (Venice, 1482). This Latin version is thought to have been translated from Arabic by the English scholar Adelard of Bath (12th century), with a commentary by Campanus of Novara. (Source).
At a conference devoted to the millennium of al-Biruni held in Karachi, Pakistan in 1973, Sa'īdān lectured on "The trigonometry of al-Biruni". Three years later, at the International Symposium for the History of Arabic Science in Aleppo, his lecture was on "Number theory and series summation in two Arabic texts". In 1977, he published the Cartography of al-Biruni and the Treatise on Amicable Numbers by Thabit ibn Qurra (836-901). The year after, he published "Theory of numerical triangles of al-Khazin," a study on the theory of Pythagorean triples in the treatises of Abu Ja'far al-Khazin (d. ca. 965; not to be confused with Al-Khazini, d. ca. 1120).
Sa'īdān also edited the complete mathematical treatises of Ibrahim Ibn Sinan, the genius mathematician of the 10th century who was the grand-son of Thabit ibn Qurra, together with an introduction and commentary. These treatises played an important role in the history of geometry since Ibn Sinan's treatise On the mensuration of a parabola is the first in the history of mathematics to use a general affine transformation of plane figures (polygons and segments of parabolas), and his treatise on the construction of conic sections is the first to employ a plane projective transformation mapping a circle onto a hyperbola.
Figure 9: Nasīr al-Dīn al-Tūsī's (d. 1274 CE) record of Euclid's proof of the Pythagorean Theorem. (Source).
Figure 10: Extract from an Arabic mathematical text on the concept of the decimal fractions, which is attributed to Stevin (around 1600), whilst the existence of such fractions in Arabic mathematical works is attested as early as the 10th century. (Source). See: Seeking Science from the Lands of Islam by George Saliba.
In his obituary of Sa'īdān, Boris R. Rosenfeld, a notable historian of Arabic sciences, wrote as a conclusion: "My correspondence with Sa'īdān began when he was living in Khartoum and I was in Moscow. We often exchanged copies of Arabic manuscripts, printed texts, and our own publications. The death of Sa'īdān is an enormous loss for historians of mathematics around the world" .
2. Publications of A. S. Sa'īdān on Arabic mathematics and astronomy
Many of the late Professor Sa'īdān's books and articles contain editions of medieval Arabic texts on arithmetic, algebra, geometry and astronomy. A large number of these editions seem to be virtually unknown outside of the Arabic world, although his works were privileged sources of work for his colleagues, the professional historians of Islamic science.
2.1. Critical editions
- 1968: Nasir al-Din al-Tusi, Jawami' al-hisab bi-'l-takht wa-'l-turab. Beirut: The American University, 1968, 292 pp.
- 1971: Ta'rikh ‘iim al-hisab al-arabi. Al-juz' al-awwal: hisab al-yad [History of Arabic arithmetic. Part 1. Finger reckoning. Amman: Jam'iyat ‘ummal al-matabi' al-ta'awuniyya (in Arabic). [Includes Abu ‘l-Wafa al-Buzgani, Kitab fima yahtaj ilayhi al-'ummal wa-'l-kutab min ‘ilm al-hisab (On the science of arithmetic necessary for scribes, workers and others)].
- 1971: "‘Ilm al-Hisab ‘inda I-'Arab" [The science of arithmetic among the Arabs]. ‘Alam al-fikr (Kuwayt) vol. 2, pp. 161-194 (in Arabic).
- 1973: Ta'rikh ‘iim al-hisrib ai-'arabi. ‘Al-juz' al-thani. AI-fusul fi i-hisdb al-Hindi li-Abi ‘I-Hasan Ahmad ibn Ibrrahim al-Uqlidisi [History of Arabic arithmetic. Part 2. The chapters on Indian Arithmetic by al-Uqlidisi]. Amman: University of Jordan Press (in Arabic).
- 1977: Kitab al-a'dad al-mutahdbba ii-Thabit ibn Qurra. Amman: The Jordanian University [In Arabic]
- 1977: "Kitab tastih al-suwar wa-tabtikh al-kuwar li-Abi ‘l-Rayhan al-Biruni al-mutawaffa sanat 440H", Dirasat (Amman: The Jordanian University) vol. 4, N° 1-2 (in Arabic).
- 1978: Abū al-Hasan Ahmad b. Ibrāhīm al-Uqlīdīsī, The Arithmetic of al-Uqlīdisī: The story of Hindu-Arabic Arithmetic as Told in Kitab al-fusul fi al-hisab al-Hindi written by Abu al-Hasan Ahmad ibn Ibrahim al-Uqlidisi written in Damascus in the year 341 (A.D. 952/3). Translated and annotated by A. S. Sa'īdān. Dordrecht/Boston: D. Reidel (xvii+492 pp. ; 25 cm).
- 1978: "Hawla khawas al-a'dad li-Abi Ja'far Muhammad ibn al-Husayn". Dirasat (Amman: The Jordanian University) vol. 5, N°. 2, pp. 7-49 (in Arabic).
- 1981: Marasim al-intisab fi ma'alim al-hisab li- Ya'ish b. Ibrahim al-Amawi. Aleppo: Institute for the History of Arabic Science (series "masadir wa-dirasat fi tarikh al-'ulum al-'arabiya wa-'l-islamiya, silsilat al ulum al riyadhiya", 2), 128 pp., 24 cm.
- 1982: "Risalatan fi ‘l-handasa tunsaban ila Arshimidis" [two treatises in geometry attributed to Archimedes]. Majallat ma'had al-makhtutat al-'arabiyya vol. 26, pp. 571-623 (in Arabic).
- 1983: Rasa'il Ibn Sinan [The Treatises of [Ibrahim] Ibn Sinan]. Edition of the Arabic unicum MS kept at Bankipur library (published previously in Haydarabad in 1948). Kuwait: Kuwait: The National Council for Culture, Arts and Letters; Arabic Heritage Department (series "al-silsila al-turathiya", 6), 375 pp., 25 cm (in Arabic, with English summaries).
- 1984: Ta'rikh ‘ilm al-hisab ‘inda I-'arab. Al-Juz' al-thalith: al-hisab fi ‘l-Andalus wa-'l-Maghrib [History of arithmetic among the Arabs. Part 3. Arithmetic in Andalus and the Maghrib]. Amman: Dar al-Furqan (series "tarikh al-'ulum ‘inda al-'arab", 3), 252 pp., 25 cm (in Arabic, with English summary).
- 1985: Al-takmila fi al-hisab li-'Abd al-Qahir ibn Tahir al-Baghdadi ma'a risala lahu fi ‘l-misaha. Tahqiq wa-dirasa muqarana. Kuwait: Institute of Arabic Manuscripts, 7+389 pp., 25 cm (in Arabic, with English summaries).
- 1985: Al-fusul fi ‘l-hisab al-hindi li-Abi al-Hasan Ahmad al-Uqlidisi. Amman: Al-lajna al-urduniya li-ta'rib wa-'l-tarjama wa-n-nashr, 1973, 536 pp., 26 cm (2nd edition 1984 (Aleppo: Institute for the History of Arabic Science, photographic reprint with a few changes; in Arabic).
- 1986: Ta'rikh ‘ilm al-jabrfi I-'slim al-'arabi. Dirasa muqdrana ma'a tahqiq li-ahamm kutub al-jabr al-'arabiyya [History of Algebra in medieval Islam. A comparative study, with the edition of the most important books of Arabic algebra]. 2 vols. in Arabic, paginated serially. Vol. 1 English title: Algebra in Eastern Islam. Study built upon Al-Fakhri of Al-Karaji. Vol. 2 English title: Algebra in Western Islam. A study of Ibn Badr and Ibn al-Banna. Kuwait: al-Majlis alwatani li I-thaqafa wa-'I-funun wa-'I-adab (series "al-silsila al-turathiyya", 15), 1986, 2 vols., 626 pp., 24 cm.
- 1991: Handasat Uqilidis fi aydin arbiya: Kitab al-'usul li-Uqlidis ma'a idhafat al-Nayrzi ma'a Kitab tajrid Uqlidis li-'Ali b. Ahmad an-Nasawi [Geometry of Euclid in Arabian hands]. Amman: Dar al-Bashir, 1991, 598 pp., 24 cm.
2.2. Commentaries and analysis of scientific texts
- 1960: "Hawla rasa'il al-Biruni" [On the treatises of Al-Biruni]. Majallat ma'had al-makhttutat al-'Arabiyya (Review of the Institute of Arabic Manuscripts) vol. 6, pp. 307-312.
- 1960: "The Rasa'il of Biruni and Ibn Sinan: A rearrangement". Islamic Culture vol. 34, pp. 173-175.
- 1961: "AI-Usul al-ighriqiyya li-'l-'ulum al-riyadiyya ‘inda ‘I-'arab" [The Greek roots of the mathematical sciences among the Arabs]. Majallat ma'had al-makhttutat al-'Arabiyya vol. 7, pp. 81-110 (Survey article; in Arabic].
- 1962: "Al-Athar al-hindi fi ‘I-riyadiyyat al-'arabiyya [The Indian influence in Arabic mathematics]. Al-Abhath vol 15, pp. 409-477 (Detailed survey; in Arabic).
- 1963: "Tara'if al-hisab li-Abi Kamil Shuja' ibn Aslam al-Misri", Majallat ma'had al-makhttutat al-'Arabiyya vol. 9, pp. 291-320 (in Arabic).
- 1965: "The development of Hindu-Arabic arithmetic". Islamic Culture vol. 39, pp. 209-221.
- 1966: The Development of Hindu-Arabic Arithmetic. Ph.D. Thesis, Khartoum University.
- 1966: "The Earliest Extant Arabic Arithmetic: Kitāb al-Fusūl fī al Hisāb al Hindī of Abū al-Hasan, Ahmad ibn Ibrāhīm al-Uqlīdisī." Isis vol. 57, pp. 475-490.
- 1967: "Risalatan fi l-hisab al-'arabi" [Two treatises on Arabic arithmetic]. Majallat ma'had al-makhttutat al-'Arabiyya 13, 41-158. [In Arabic].
- 1967: "Jawami' al-hisab bi ‘I-takht wa I-turab". Al-Abhath (Beirut) vol. 20, pp. 91-163, 213-292 (in Arabic).
- 1968: "Finger reckoning in an Arabic poem". The Mathematics Teacher vol. 61, pp. 707-708.
- 1974: "The Arithmetic of Abū ‘l-Wafā [al-Buzgānī]." Isis vol. 65, pp. 367-375.
- 1978: "Number Theory and Series Summations In Two Arabic Texts." In: Proceedings of the First International Symposium for the History of Arabic Science, April 5-12, 1976. Volume II: Papers in European Languages, edited by Ahmad Y. al-Hassan et. al. Aleppo: Institute for the History of Arabic Science, Aleppo University, pp 145-163.
- 1979: "The Trigonometry of Al-Bīrūnī". In: Al-Bīrūnī Commemorativ