This fascinating compendium is important in understanding the scholarly environment which characterised Qazwin shortly after becoming the Safavid capital under Shah Tahmasp (r.1524-76). Written in balanced naskh and nasta’liq scripts, it is densely filled throughout with diagrams and tables coloured in red, blue and gold. The margins of the manuscript reveal an important aspect of this volume, in that the scribe copied this book from a copy of Al-Kashi’s autograph manuscript.
In some marginal notes we find references to the original comments made by Al-Kashi (the word hashia refers to additions which Al-Kashi made to his own text in his copy, see for example f.12a or 26b). To this first layer of notes by Al-Kashi, the scribe of the master copy of our manuscript added his personal notes and observations, which are full of references to other scientific works by scholars such as Euclid, Archimedes, Al-Tusi and Ptolemy. The accuracy of these references leads us to hypothesise that he was a mathematician as well, perhaps from Al-Kashi’s entourage while he was in Samarqand. A third layer of marginal remarks are those made by the current scribe, who diligently preserved the knowledge transmitted in the margins of the first two copies, to which he added his observations throughout.
The authors of the compendium
Ghiyath al-Din Jamshid Mas’ud al-Kashi (circa 1380-1429 AD) was born towards the last quarter of the fourteenth century in Kashan, Persia, and dedicated all his life to the study of mathematics and astronomy. He is recorded as working under the patronage of a local vizir in 1407 (to whom he dedicated the work Sullam al-sama) and a few years later for Iskander, sultan of Isfahan and Fars (to whom he dedicated Mukhtashar dar ‘ilm-I hay’at, a compendium of science and astronomy). But it was under the patronage of the great Timurid ruler Ulugh Beg in Samarqand that Jamshid al-Kashi composed the most famous works of his career, which are still used as references today. He joined the madrasa founded by Ulugh Beg between 1417 and 1420 and was able to work in the great observatory commissioned by the ruler in 1424. He remained in Samarqand until he was murdered on 22 June 1429.
Qadi Zade al-Rumi (c.1364–1436) was born in Bursa, Turkey, and was the son of a judge. He moved to Samarqand under Timur and was the astronomy teacher of Ulugh Beg, leading his observatory in Samarqand. He was a contemporary of Jamshid al-Kashi and the two scholars worked together, Al-Rumi compiling many commentaries on Al-Kashi’s works.Their close collaboration is witnessed in the treatise by Al-Kashi entitled Risala al-watar wa’l-jaib which might have been concluded by Al-Rumi after Al-Kashi’s death.
The texts in the compendium
Miftah al-hisab. Translated as 'Key to Computation', this monumental treaty was completed in 1427 and dedicated to Ulugh Beg. The treatise is divided into five books and doesn’t deal only with mathematics but includes also arithmetic and astronomical and physical measurements.
After presenting the arithmetic of integers and fractions (books I and II), Al-Kashi proposes a methodical theory of decimal fractions, along with the known and used sexagesimal arithmetic (books II and III). The decimal fractions, introduced by Al-Kashi, became a revolution for the world of mathematics and were absorbed quickly by his contemporaries. This system is mentioned in Ottoman literature in the last quarter of the fifteenth century, which means that the Miftah al-hisab must have travelled to Istanbul shortly after having been published and was quickly integrated in the basic knowledge of mathematics of the time. It is worth remembering that the mathematician 'Ali Qushji, a colleague of Al-Kashi in Samarqand, moved from the Timurid court to the Ottoman one in 1471, likely bringing with him a deep knowledge of Al-Kashi’s works (see Ozdural in Necipoğlu 1998, p.107). Another interesting aspect of Al-Kashi’s work is the attention devoted to the specific weight of various materials and gems (book IV), which are reported in tables taken from works by Al-Khawwam al-Baghdadi and Al-Farisi (Tzvi Langermann 2018, p.88-89).
The earliest known copy of the Miftah al-hisab, dated just two years before the present work (965 AH/1558 AD) is now in Leiden (OR.185). A copy dated 1559 and produced in Persia, is now in the National Library of Israel, inv. no.Ms.Yah.224 (published in Tzvi Langermann 2018, p.89). Therefore, the present manuscript appears to be the third earliest copy recorded. A further copy dated 1575-76 is now in the Bibliothèque Nationale, Paris (inv. no.Arabe5020). For a full list of other copies of this manuscript please see Rosenfeld & Ihsanoglu 2003, p.269 and Brockelmann GAL II 273.
Risala al-muhitiyya, a treatise on the circumference. This was completed in 827 AH/1424 AD and discusses the values of π and the implication of the use of the wrong value for π when it is used to calculate the circumferences of very large circles (such as celestial spheres). The manuscript to hand contains only the fourth section of the Risala, which deals with calculations, which are made in sexagesimal fractions, then transferred into decimal fractions. The autograph manuscript is now in the Astane Qudse Razawi Library in Mashhad, Iran (inv. no.162, and illustrated in Azarian 2004). Other copies of this treatise are recorded in Rosenfeld & Ihsanoglu as being in Istanbul (inv. no.AM 756), and Tehran (inv. no642/4).
Nuzhat al-hada’iq, a treatise on the methods of constructions of the instrument called 'plate of heaven' (known today as an equatorium), to determine the position of the planets, the sun and the moon. This work was composed before Al-Kashi’s arrival to Samarqand and picked up again in 1426, when he reviewed the first version and dedicated it to Ulugh Beg. The current manuscript bears the second version and it is one of the earliest known copies. A further manuscript attributed to the fifteenth century is now in the Chester Beatty Library, Dublin (inv. no.3640/2).
Risala fi istikhraj jayeb daraja wahida, a treatise on the sine of one degree. This work by Qadi-Zade al-Rumi, copied from Qadi-zade's original copy, deals with the value of the sine of one degree, a topic which was also extensively discussed by Al-Kashi in his now lost Risala al-watar wa al-jaib. This treatise by Al-Rumi was indeed inspired by Al-Kashi’s work.
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