al-Kharaqī, Abū Bakr

al-Kharaqī, Abū Bakr astronomy cosmology chronology geography magic squares Bahāʾ al-Dīn Abū Bakr Muḥammad b. Aḥmad al-Kharaqī (d. 553/1158-9) was a mathematician, astronomer, and well-rounded scholar of Persian origin who wrote two books on astronomy and several mathematical treatises. Bahāʾ al-Dīn Abū Bakr Muḥammad b. Aḥmad al-Kharaqī (d. 553/1158-9) was a mathematician, astronomer, and well-rounded scholar of Persian origin, probably from Kharaq (or Khiraq), near Marw, to which city he was summoned by the Khwārazmshāh (either Quṭb al-Dīn Muḥammad, r. 490-521/1097-1127, or his son Atsïz, r. 521-51/1127-56). Ghalandari has established that he died in 553/1158-9; he has been confused or identified with a contemporary, Shams al-Dīn al-Kharaqī (d. 533/1138-9). Al-Kharaqī wrote two books on astronomy. The shorter of the two, al-Tabṣira fī l-hayʾa (“Enlightenment on cosmology”), had a relatively wide readership, as is evidenced by the many manuscript copies, including transcriptions into Hebrew characters, a Hebrew translation, and a short commentary by Aluʾel (David) ben Yeshaʿ (fl. ninth/fifteenth century?), a Yemenite Jew (for the transcriptions and Aluʾel's commentary, see Langermann, 150; the Hebrew translation is found in Vatican City, Vatican Library, MS Vat. Ebr. 389, ff. 61a-123a). In astronomy, he follows the physicist and mathematician Ibn al-Haytham (d. 430/1039) “in the division of all of the orbs, deferents, circles, and solid spheres, and the manner in which they cause the stars embedded within them to revolve, along with their motions, in the order in which they are found in reality, without limiting myself to imaginary circles,” as was done by the ancient astronomers. Like other writers in the genre, he is motivated by the desire to know how in reality the Heavenly bodies carry out their motions. He likens the dilemma to knowing that a person travelled from one place to another, but not knowing whether he went on foot or on horseback. The section on geography is particularly rich. In the longer Muntahā l-idrāk fī taqāsīm al-aflāk (“Ultimate attainment in the division of the orbs”) (ed. Ghalandari), al-Kharaqī considerably expands the bounds of the haʾya genre. In addition to sections on cosmology (hayʾat al-ʿālam) and geography (hayʾat al-arḍ)—common features in the hayʾa tradition, including in his own Tabṣira—he includes a section on chronology. Al-Kharaqī is modest in presenting his own contribution. He first surveys the field, citing many authorities by name, then signals issues that have not been treated sufficiently, to which he turns his attention and adds what he can. This book is valuable for both its original contributions and its citation of otherwise unavailable sources. For example, he introduces the section on chronology by defining an epoch (taʾrīkh) as a period that can be traced to a starting point, which is the appearance of a religious community, a state, a natural disaster, or some other of the “heavenly signs and earthly markers,” which can happen at any moment; and, when it does occur, it is taken as the starting point for the time that follows thereafter. In his discussion of the Flood date, he critically reviews the literature, especially the views of Abū Maʿshar (Albumasar, d. 272/886), the foremost astrologer of classical Islam, and his disciple Ibn al-Bāzayār (fl. third/ninth century), and cites from the former’s Kitāb al-ulūf (“Book of thousands”). One among several mathematical treatises ascribed to al-Kharaqī is extant, Talkhīṣ fī l-ʿadad al-wafq, a monograph on magic squares. It is divided into three sections: (1) strong magical squares, in which the columns, rows, and diagonals of the sub-squares also add up to a constant; (2) ordinary magical squares, which do not possess this property; and (3) various rarities. It displays the sophistication Islamic mathematicians of his era had achieved in this field. In the introduction to the Tabṣira, he mentions a book on logic that he is preparing, although nothing further is known about it, and no other evidence of it appears in the historical record. [ceds 557 words] Y. TZVI LANGERMANN BIBLIOGRAPHY Sources Hanif Ghalandari, A survey of the works of hayʾa in the Islamic period with a critical edition, translation and commentary of the treatise Muntahā l-idrāk fī taqāsīm al-aflāk written by Bahāʾ al-Dīn al-Kharaqī (d. 553 AH/1158 AD), Ph.D. diss., University of Tehran 2012 (Persian with edition of the Arabic text). Studies Y. Tzvi Langermann, Arabic writings in Hebrew manuscripts. A preliminary relisting, Arabic Sciences and Philosophy 6/1 (1996), 137-60; Jacques Sesiano, Herstellungsverfahren magischer Quadrate aus islamischer Zeit (III), Sudhoffs Archiv 79/2 (1995), 193-226; E. Wiedemann and K. Kohl, Einleitung zu Werken von al-Charaqī, Sitzungsberichte der Physikalisch‐ Medizinischen Sozietät in Erlangen 58-9 (1926-7), 203-18, repr. in E. Wiedemann, Aufsätze zur arabischen Wissenschaftsgeschichte (Hildesheim 1970), 2:628-36; E. Wiedemann and J. Samsó, al-K̲h̲araḳī, EI2.