# Al-Sijzi Abu Sa‘id Ah?mad Ibn Muh?ammad Ibn ‘Abd Al-Jalil

# AL-SIJZī ABū SA‘īD AḤMAD IBN MUḤAMMAD IBN ‘ABD AL-JALīL

(*b*. Sijistän. Persia. ca. 945; d. ca. 1020)

*geometry, astronomy, astrology*.

Al-Sijzī is also known as al-Sijazī, al-Sijzī, or al-Sijarī. The following evidence indicates that he was an older contemporary of al-BĪrŪnĪ (973–ca. 1050): he is not mentioned in Ibn al-NadĪm’s *Fihrist* (987), but al-BĪrŪnĪ quoted him in his *Chronology*. Al-BÏrünÏ wrote to al-SijzÏ on the determination of the *qibla* (direction of Mecca, for prayer) and on a proof by his teacher Mansūr ibn Irāq for the theory of the transversal figure. Conversely, al-SijzÏquoted three propositions by al-BÏrünĪ in his treatise on trisecting an angle, which he ended with five problems of al-BÏrünÏ. Around 969 al-Sijzī had written and copied mathematical works at Shīrāz, a later version of which is in Paris (Bib. Nat. arabe 2457). Presumably around the same time (*ca*. 967) he composed his*Kitāb al-qirānāt* (“Book of the Conjunctions”), which contains references to an even earlier work of his, *Muntakhab Kitāb al-ulūf* (“Summary of the Thousands of Abū Ma‘shar”). In 969–970 al-Sijzī assisted at the observations of the meridian transits in Shīrāz conducted by ‘Abd al-Rahmān al-Sūfī.

Al-Sijzī may have spent some time in Khurāsān, since he answered questions by mathematicians of that region. He dedicated works to the Sayyid Amīr Abū Ja ‘far Ahmad ibn Muhammad, a prince of Balkh (*d*. 1019) (L. Massignon, *Opera omnia*, I [Beirut, 1963], 650–666), and to the Buwayhid Caliph ‘Adud al-Dawla (Shīrāz-Baghdad, 949–983).

Al-Sijzī’s main scientific activity was in astrology, and he had a vast knowledge of the older literature. He usually compiled and tabulated, adding his own critical commentary. Al-Sijzī summarized three works by Abū Ma‘har and wrote on the
second of the five books ascribed to Zoroaster in his *Kitāb Zarādusht ̣uwar darajāt al-falak* (“The Book of Zoroaster on the Pictures of the Degrees of the Zodiac”). In his *Kitāb al-qirānāt*, which treats general astrology and its history, he used Sassanid material and sources from the time of Hārūn al-Rashīd and from the late Umayyad period. In *Zā’irjāt*, a book on horoscopes, he gave tables based on Hermes, Ptolemy, Dorotheus, and “the moderns.” Al-Sijzī’s tables, together with those of Ptolemy, are quoted by Ịtiyāzu I;D’n Mụammed in his *Judicial Astrology* (Trinity College, Cambridge). Al-Bīrūnī described in his *Kitāb fī istīāb* three degenerate astrolabes constructed by al-Sijzī: one fish-shaped, one anemone-shaped, and one skiff-shaped.

Al-Sijzī’s mathematical papers are less numerous but more significant than his astrological ones, and he is therefore better known as a geometer. He wrote original treatises on spheres and conic sections, the construction of a conic compass, and the trisection of an angle by intersecting a circle with an equilateral hyperbola. This method became widely accepted: Abū’l-Jūd, for example, describes it in the Leiden manuscript Or 168(13). Al-Sijzī mentioned several other methods for solving this problem, including one by “mobile geometry,” which he ascribed to the ancients; but he omitted any reference to Pappus. His treatise on proportions in the transversal figure is especially useful for astronomy, and his emphasis on the position of the lines was new and important. Al-Sijzī constructed the regular heptagon according to the same principle as that used by al-Qūhī. He also wrote articles on subdividing segments and several letters on problems related to the work of Euclid and Archimedes.

## BIBLIOGRAPHY

I. Original Works. Al-Sijzī’s available mathematical MSS are listed in F. Sezgin, *Geschichte des arabischen Schrifttums*. V. (Leiden, 1974), 331–334. On the astrological MSS see M. Krause, “Stambuler Handschriften islamischer Mathematiker,” in *Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik*, B.3 (1934), 468–472: and W. Thomson and G. Junge. *The Commentary of Pappus on Book X of Euclid’s Elements* (Cambridge, 1930), 48–51. C. Brockelmann. *Geschichte der arabischen Literatur*. I (Leiden, 1943), 246–247: and supp. I (Leiden, 1937), 388–389, lists a few more MSS and additional copies. Neither mentions *Kitāb al-qirānāt wa tahāwīl sinī al-ālam*. a MS that David Pingree dealt with in *The Thousands of Abū ‘ Mashar* (London, 1968). In this work Pingree also discusses the *Muntakhab Kitāb al-ulūf*, which was partly translated by E. S. Kennedy in “The World-Year of the Persians,” in *Journal of the American Oriental Society*, **83** , no. 3 (1963), 315–327. Translations or discussions of mathematical treatises are found in: F. Woepcke. *L’Algèbre d’Omar Alkhayāmī* (Paris, 1851), 117–127; and “Trois traités arabes sur le compas parfait,” in *Notices et extraits de la Bibliothèque nationale*.**22** , part *i* (1874), 112–115; C. Schoy, “Graecoarabische Studien,” in *Isis*, **8** (1926), 21–40: H. Bürger and K. Kohl, “Thabits Werk über den Transversalensatz,” in *Abhandlungen zur Geschichte der Naturwiśsenschaften und der Medizin*. 7 (1924), 49–53; and L. A. Sédillot, “Notice de plusieurs opuscules mathématiques.” in *Notices et extraits de la Bibliothèque nationale*, **13** (1838). 136–145. Edited by the Osmania Oriental Publications Bureau is *Risāla fī ‘l-shakl al-gattaā* (“On the Transversal-Theorem”: Hyderabad, 1948).

II. Secondary Literature. There are few biographical references to al-Sijzī. On the observations in Shīrāz see al-Bīrūnī. *Tạd̄d nihāt al-amākin li-tashinh masāfāt al-masākin* (Cairo, 1962), 99; and E. S. Kennedy. *A Commentary Upon Bīrūnī’s Kitāb Tahdīd al-Amākin* (Beirut, 1973), 42. On al-Sijzī as an astrologer see Pingree (see above), 21–26, 55, 63–67, 70–127. On his mathematics consult Sezgin (see above), 43–51; and the notes of G. Bergsträsser in “Pappos Kommentar zum Xten Buch von Euklid’s Elementen.” in *Islam*, **21** (1938), 195–198. On his astrolabes see Josef Frank. “Zur Geschichte des Astrolabs,” in *Sitzungsberichte der Physikalisch-medizinischen Sozietät in Erlangen*. **50–51** (1918–1919), 290–293: and al-Bīrūnī. *Al-Qānūn al Mas’dī*. **I** (Hyderabad, 1954), introduction, 17–18.

Yvonne Dold-Samplonius

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