Chapter 7 Kāshānī’s Equatorium Employing Different Plates for Determining Planetary Longitudes Hamid Bohloul Ghīyāth al-Dīn Jamshīd ibn Mas‘ūd ibn Maḥmūd ibn Muḥammad Kāshānī (or al-Kāshī), the fifteenth-century Iranian astronomer and mathematician, is known nowadays for his precise calculation of π and Sin 1°, and for his con- tribution to Ulugh Beg’s observatory at Samarkand. In 818 H (1416 CE), most probably in his home town of Kāshān, he invented an equatorium,1 and wrote an Arabic treatise on its construction and use. The treatise had the title Nuzhat al-Ḥadāʾiq (Excursion to the Gardens) and the equatorium was called Ṭabaq al-Manāṭiq (Plate of the Deferents). In the Nuzha, he also described another instrument, named Lawḥ al-Ittiṣālāt (Plate of Conjunctions). The main pur- pose of both instruments was to reduce the amount of calculation astrologers needed to do. About ten years later, while Kāshānī was working at Samarkand Observatory, he wrote an Arabic supplementary tract to the Nuzha, in which he added a set of ten appendices. Most of them describe new methods of construction and give simple and more precise instructions for using the equatorium. During the reign of Sultan Bayezid II (from 1481 to 1512), most probably in Istanbul, an anonymous astronomer composed an untitled Persian treatise about Kāshānī’s equatorium, and dedicated it to the Sultan.2 Having found the only manuscript of this Persian treatise, the late Edward S. Kennedy surmised that the original work of Kāshānī was lost.3 He started his investigation of the equatorium using the Persian text and published two papers, one on the Plate of Conjunctions in 1947,4 and the other on the equatorium in 1950.5 In 1951 1 Equatoria were similar to standard astrolabes in appearance and in the Middle Ages were generally used for determining planetary longitudes without numerical calculations. 2 The only extant manuscript of this treatise is now preserved at Princeton University Library, Garret collection, no. 75. See Mohamad E. Moghadam, Yahya Armajani, Descriptive Catalog of the Garret Collection of Persian, Turkish and Indic Manuscripts Including some Miniatures in the Princeton University Library (under the supervision of Philip K. Hitti), Princeton University Press, Princeton, 1939, pp. 35–36. 3 Edward S. Kennedy, “Al-Kāshī’s ‘Plate of Conjunctions’ ”, Isis 38 (1947), pp. 56–59: 57. 4 Ibid. 5 E.S. Kennedy, “A Fifteenth-Century Planetary Computer: Al-Kāshī’s ‘Ṭabaq Al-Manāṭeq’ I. Motion of the Sun and Moon in Longitude”, Isis 41 (1950), pp. 180–183. © Koninklijke Brill NV, Leiden, 2019 | doi:10.1163/9789004412842_008 Kāshānī’s Equatorium 123 he discovered that a manuscript of Kāshānī’s Nuzha was preserved in the India Office Library in London, but he carried on his research without paying much attention to this original work of Kāshānī. The result was two more papers in the same year, 1951.6 It was only in his last paper in 1952 that he included some information about the original Arabic text.7 Eventually, in 1960 he published a book on the instrument entitled The Planetary Equatorium of Jamshīd Ghīyāth al-Dīn al-Kāshī,8 which included a facsimile of the Persian text, an English translation and a commentary. Kennedy also discussed briefly some of the appendices Kāshānī published in the supplementary tract. As nearly all of Kennedy’s contribution is based on the Persian treatise of the anonymous Ottoman astronomer, it is worth studying Kāshānī’s own text to learn more about his equatorium and his scientific career. In the present chapter I describe some of the features of the original text and explain how the three additional plates described in the Nuzha can be used to find the true lon- gitudes of the superior planets (Mars, Jupiter and Saturn) and of Venus. I also show how the equatorium can be used for different geographical longitudes. 1 The Nuzhat al-Ḥadāʾiq Nuzhat al-Ḥadāʾiq, which has no dedication, consists of an introduction, two articles on the equatorium, and a conclusion on the Lawḥ al-Ittiṣālāt, an ingenious device for performing linear interpolation to pinpoint graphically the time of day at which a planetary conjunction will be observed at a cer- tain terrestrial longitude. The list of extant manuscripts of Nuzhat al-Ḥadāʾiq, sorted into chronological order, is as follows: 1. Tehran, Malik National Library, MS 3180.5, copied in 830 H (1427 CE), pp. 319–357 plus the supplementary tract pp. 358–382. 2. Dublin, Chester Beatty Library, MS 3640.2, (probably) copied in the fifteenth century, fols. 112v–126v. 3. Tehran, Central Library of Tehran University, MS 2508, copied in 964 H (1557 CE), pp. 1–40 plus the supplementary tract pp. 41–58. 6 E.S. Kennedy, “A Fifteenth-Century Lunar Eclipse Computer”, Scripta Mathematica 17 (1951), pp. 91–97; E.S. Kennedy, “An Islamic Computer for Planetary Latitudes”, Journal of the American Oriental Society 71 (1951), pp. 13–21. 7 E.S. Kennedy, “A Fifteenth-Century Planetary Computer: al-Kāshī’s Ṭabaq al-Manāṭeq”, Isis 43 (1952), pp. 42–50: 45. 8 E.S. Kennedy, The Planetary Equatorium of Jamshīd Ghīyāth al-Dīn al-Kāshī, Princeton University Press, Princeton, 1960..