In Volume 2: Mathematics; Weights, and Measures; Astronomy, and Astrology; Geography; Medicine; Encyclopaedias, and Miscellanies; Arts and Crafts, Science, Occult Arts

¶ Krause = Stambuler Handschriften islamischer Mathematiker. Von Max Krause (Bremen). (In Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik … herausgegeben von O. Neugebauer, Kopenhagen, und O. Toeplitz, Bonn. Abteilung B: Studien. Band 3—(Schluss-) Heft 4, Berlin 1936, pp. 437–532).

§ 1. Euclid (Eukleides) taught at Alexandria in the reign of Ptolemy i (306–283 bc). Of his Elements only one Arabic recension need be considered here, namely:

Taḥrīr Uqlīdis, as it is commonly called, or Taḥrīr kitāb Uṣūl al-handasah wa-’l-ḥisāb al-mansūb ilā Uqlīdis (beg. al-Ḥ. l. ’l. minhu ’l-ibtidāʾ), in fifteen maqālahs completed in 646/1248 by Naṣīr¹ al-Dīn M. b. M. al-Ṭūsī (see Brockelmann i p. 510, Sptbd. i p. 929; Krause p. 499; D̲h̲arīʿah iii pp. 380 ult.–381).

Persian translations:

(a)

Tarjamah i Taḥrīr i Uqlīdis (beg. Tā ʿināyat i rabbānī ḥijāb i intiẓār), completed in 681/1282–3 by Quṭb al-Dīn Maḥmūd b. Masʿūd al-S̲h̲īrāzī, Naṣīr al-Dīn Ṭūsī’s pupil (who died in 710/1312: see Ency. Isl. under Ḳuṭb al-Dīn (Wiedemann); Brockelmann ii p. 211, Sptbd. ii p. 296), and dedicated to Amīr S̲h̲āh b. Amīr i saʿīd Tāj al-Dīn Muʿtazz b. Ẓāhir: Yenī Jāmiʿ 796 (148 foll. ah 701/1301–2. Krause p. 508 (6)), Nad̲h̲īr Aḥmad 245 (ah 780/1378–9. Bahādur S̲h̲āh, Mōc̲h̲ī Gate, Lahore).

(b)

Taqrīr al-Taḥrīr,² or Tarjamah i Taḥrīr i Uqlīdis (beg. S̲h̲ukr ast mar K̲h̲udāʾī-rā kih az-Ū-st ibtidā), prepared in 1144/1731–2, in Muḥammad S̲h̲āh’s reign, by K̲h̲air Allāh K̲h̲ān b. Luṭf Allāh (cf. pl. i p. 394, ii §§ 27, 145) and divided into fifteen maqālahs: Ethé 2260 (ah 1194/1780).

(c)

Tarjamah i Taḥrīr i Ūqlīdis.³

Edition of Bks. i–vi: Calcutta 1824* (Tarjamah i s̲h̲as̲h̲ maqālah i kitāb i T. i. Ū. kih taʾlīf i K̲h̲wājah N. al-D. i Ṭūsī ast. Hindustani Pr. 262 pp.).

(d)

Taḥrīr i Uqlīdis i manẓūm: Āṣafīyah i p. 808 no. 176.

¶ § 2. Theodosius lived not later than the first century bc (see Ency. Brit., etc.). His Spherics exist in at least three or four Arabic translations⁴ and adaptations (cf. Brockelmann i p. 204³², Sptbd. i p. 366²⁶, 368²⁹; Krause p. 444 (3)). Of interest to students of Persian are:

(1)

Taḥrīr Ukar T̲h̲āūd̲h̲ūsiyūs, in Arabic, completed in 651/1253 by Naṣīr al-Dīn M. b. M. al-Ṭūsī (Ḥ.K̲h̲. ii p. 213; Brockelmann Sptbd. i p. 930¹⁸; Krause p. 502 (n); D̲h̲arīʿah ii p. 276 antepenult., iii p. 383 no. 1383).

Edition of the Arabic text: Tihrān 1304/1886–7 (in a collectaneous volume, Majmūʿat al-Ukarāt wa-’l-kutub al-mutawassiṭāt,⁵ D̲h̲arīʿah iii p. 382 penult., p. 383¹⁶).

Edition of a Persian version of Ṭūsī’s Taḥrīr: Persia (“wa- ṭubiʿat al-tarjamat al-Fārisīyah bi-Īrān aiḍ^an kamā fī baʿḍ al-fahāris”, D̲h̲arīʿah i p. 276 penult.).

(2)

Chanykov 143 (acephalous).

(3)

Rāʾiḍ al-nufūs tarjamah i Ukar i T̲h̲āūd̲h̲ūsiyūs, by G̲h̲ulām-Ḥusain: Āṣafīyah i p. 810 no. 170.

§ 3. Abū ’l-Wafāʾ M. b. M. b. Yaḥyā al-Būzajānī died in 387/ 997 or 388/988 (see Brockelmann i p. 223, Sptbd. i p. 400; Ency. Isl. under Abū ’l-Wafāʾ (Suter); Tatimmat Ṣiwān al-ḥikmah p. 76 and, notes, p. 194; Krause p. 466).

al-Aʿmāl al-handasīyah, in Arabic (see Brockelmann).

Persian translations:

(a)

Tarjamah i kitāb i Abū ’l-Wafā … al-Būzajānī dar aʿmāl i handasīyah (beg. al-Ḥ. l. R. al-ʿā…. a. b. īn tarjamah i k. Abī ’l-Wafā …), by S̲h̲ams al-Dīn Abū Bakr S̲h̲āh b. Najm al-Dīn Maḥmūd S̲h̲āh b. Ḥājī Tāj al-Dīn Kūdak: Blochet 772 (22) (early 17th cent.).

(b)

Tarjamah i Aʿmāl i handasīyah⁶ (beg. al-Ḥ. l. al-Muwaffiq ʿalā ’l-sadād fī ’l-aqwāl), prepared at the instance of Abū Manṣūr Bahāʾ al-Daulah by a translator whose name would perhaps have been ascertainable, if the Mas̲h̲had ms. had not been defective at the end: D̲h̲arīʿah iv p. 79 ult., Mas̲h̲had iii, fṣl. 17, mss., no. 37 (defective at end. Old).

Persian commentary (?): Futūḥāt i g̲h̲aibīyah (beg. Ḥ. i bī-ḥ. K̲h̲udāwandī-rā kih ba-yak fatḥ), if not a commentary, at least a work containing barāhīn i Aʿmāl i handasīyah i Abū ’l-Wafāʾ … Būzajānī, by M. Bāqir ¶ b. Zain al-ʿĀbidīn Yazdī [author of the ʿUyūn al-ḥisāb (i.h. 2152, Majlis 199), who was alive in 1047/1637–8: cf. Brockelmann Sptbd. ii p. 591]: Mas̲h̲had iii, fṣl. 17, mss., no. 144 (defective at end).

§ 4. Abū ʿAlī al-Ḥusain b. ʿAbd Allāh Ibn Sīnā was born in 370/980 at Afs̲h̲īnah,⁷ a village near Buk̲h̲ārā, and died in 428/ 1037 at Hamadān (see Browne, Lit. Hist, ii pp. 106–11; Ency. Isl. under Ibn Sīnā (de Boer); Brockelmann i pp. 452–8, Sptbd. i pp. 812–28). His pupil ʿAbd al-Wāḥid Jūzajānī,⁸ while editing his master’s work, the Dānis̲h̲-nāmah i ʿAlāʾī, had some additional short notes by Ibn Sīnā on different subjects. Those relating to geometry were collected by him in the risālah described below.

(Risālah dar handasah) (beg. al-Ḥ. l…. c̲h̲. g. K̲h̲wājah i buzurgwār ʿA. al-W. J. kih ān-gāh kih ba-k̲h̲idmat i Raʾīs qaddasa ’llāhu rūḥahu būdam), a short exposition of the elements of Euclid: Ivanow Curzon 565 (20 foll. ah 1228/1813), possibly also Āṣafīyah i p. 820 no. 115 (Muntak̲h̲ab i Tarjamah i Uqlīdis i Ibn i Sīnā. No mention of Jūzajānī in the catalogue).

§ 5. In ʿAlī b. Zaid al-Baihaqī’s Tatimmat Ṣiwān al-ḥikmah, composed circ. 560/1165, Abū Jaʿfar M. b. Aiyūb al-ḥāsib al-Ṭabarī is spoken of (p. 84: cf. Durrat al-ak̲h̲bār p. 59) in the past tense and is placed between Kūs̲h̲yār⁹ and al-Qabīṣī,¹⁰ a position which suggests at least that Baihaqī (whose arrangement is very roughly chronological with exceptions) did not regard him as an author of the recent past. The date 632/1234 given in the Āyā Ṣōfyah catalogue (cf. Brockelmann Sptbd. i p. 859) as that of the composition of the Miftāḥ al-muʿāmalāt is in reality the date of transcription (see Krause p. 492).

(1)

Miftāḥ al-muʿāmalāt (beg. C̲h̲. g…. kih c̲h̲ūn mā bi-pardāk̲h̲tīm az risālah i S̲h̲umār-nāmah), in six sections: Āyā Ṣōfyah 2763 (148 foll. Transcribed from the original at Sīwās in 632/1234–5. Krause p. 492).

Doubtless this author is the same person as S̲h̲. M. b. Aiyūb al-Māzandarānī, who wrote:

(2)

al-Muʾnis fī nuzhat ahl al-majlis, selections from four (untitled?) treatises beginning respectively with the words [a] Sp. K̲h̲udāy-rā kih Maʿbūd i ba-sazā ast Mālik i Fard i Bī-hamtā ast, [b] Ḥisāb i bi-’l-ḍamīrāt u ba-iltibās [sic?] bi-gūyam tā ʿadadī, [c] Masāʾil al-waṣāyā Agar pursand kih Zaid ʿAmr rā waṣīyat kard ba-mālī, [d] Bi-dān aʿazzaka ’llāhu taʿālā kih maʿnī i ¶ ḍarb ba-iṣṭilāḥ i muḥāsibān: Rāmpūr (ah 778/ 1376–7. See Nad̲h̲īr Aḥmad 250).

§ 6. Bhāskara Āc̲h̲ārya,¹¹ of Bīdar in the Deccan, was born in 1114 ad and finished his Sidd’hānta-śirōmani, a course of astronomy, in 1150. Of that course the Līlāwatī is the first section and the Vīja-gaṇita the second.

(1)

Līlāwatī,¹² a Sanskrit work on arithmetic and geometry.

Persian translation: Līlāwatī, or Tarjamah i Līlāwatī (beg. Awwal zi t̲h̲anā-yi Pāds̲h̲āhī gūyam), prepared in 995/1587 at the instance of Akbar by “Faiḍī” (for whom see pl. i § 706): Ethé 1998 (ah 1015/1606), 1999 (ah 1191/1777), 2000 (ah 1193/1779), Ross & Browne 196 (ah 1280/1863–4), Mehren p. 9 no. 18 (1) (ah 1091/1680), Bombay Univ. p. 30 no. 19 (17th cent.?), p. 272 (ah 1206/1791), Lindesiana p. 136 no. 699c (ah 1142/1729), Rieu ii 449b (ah 1190/1777), 804a (18th cent.), Eton 158, Bodleian iii 2697 (ah 1203/1788), 2698, Rehatsek p. 37 no. 69 (ah 1207/1792–3), Berlin 1084 (ah 1210/1796), Cambridge 2nd Suppt. 92 (ah 1212/1798), Ivanow 1694 (ah 1213/1798–9), Bānkīpūr xi 1031 (ah 1244/1828–9), ʿAlīgaṛh Subḥ. mss. p. 21 no. 1 (ad 1836), Āṣafīyah i p. 818 no. 181.

Editions (a) The Lilavati, a treatise on arithmetic, translated into Persian, from the Sanscrit work of Bhascara Acharya, by the celebrated Feizi. (Nusk̲h̲ah i Līlāwatī). Calcutta 1827°* (158 pp.). (b) 1271/1854–5 (Āṣafīyah i p. 820 no. 240).

(2)

Vīja-gaṇita,¹³ a Sanskrit work on algebra.

Persian translations:

(a)

Bīj ganit,¹⁴ or Tarjamah i Bīj ganit (beg. Awwal zi sitāyis̲h̲ i Ilāhī gūyam), composed in 1044/1634–5 by ʿAṭāʾ Allāh “Rus̲h̲dī”¹⁵ b. Aḥmad i Nādir,^16,17 dedicated to S̲h̲āh-Jahān and divided into a muqaddamah and five maqālahs: Blochet i 236 (early 18th cent.), Rieu ii 450b (ah 1141/1728), 804a (18th cent.), Browne Suppt. 208 (King’s 50), r.a.s. P. 194 (ah 1213/1798), Aumer 345, Ethé 2001.

¶ English translation: Bija Ganita: or The Algebra of the Hindus. [Translated from ʿAṭāʾ Allāh’s Persian version.] By E. Strachey. [With notes by S. Davis.] London 1813°* (119 pp.).

(b)

Badr al-ḥisāb: Āṣafïyah i p. 806 no. 182 (ah 1100/ 1688–9).

§ 7. M. G̲h̲aznawī.

Muʾnis al-fuḍalāʾ (beg. Ḥ. u t̲h̲. ān K̲h̲udāy-rā kih mardān i rāh i Ū jān u dil bi-dihand), a mathematical work “composed in the time of Md. B. Bahrām S̲h̲āh”:¹⁸ Rāmpūr (ah 778/1376–7. See Nad̲h̲īr Aḥmad 249).

§ 8. S̲h̲araf al-Dīn Ḥusain b. Ḥasan Samarqandī.

Risālah fī ṭarīq al-masāʾil al-ʿadadīyah (beg. Ahl i īn ṣināʿat rā dar bīrūn āwardan i masāʾil), completed in 632/1235: Istānbūl Sarāy 3455 (12) (4 foll. ah 663/1265. Krause p. 516).

§ 9. M. ʿAbd al-Karīm (so Palmer) or M. b. ʿAbd al-Karīm (so Ḥ. K̲h̲.) al-Dājī¹⁹ (so Palmer: Ḥ. K̲h̲. omits) al-G̲h̲aznawī.

Tuḥfat al-ṣudūr (beg. (Trinity ms.) al-Ḥ. l. R. al-ʿā … a. b. faʾinna ’l-Nabīya ṣl‘m qāla …: (Cairo ms.) al-Bāb al-awwal fī maʿrifat al-ḍarb), on arithmetic and mensuration “written ad 1247” according to Palmer [i.e. Ramaḍān 644–Ramaḍān 645, but according to Ḥ. K̲h̲. completed in Rabīʿ ii 744, presumably a mistake for 644, i.e. Aug.–Sept. 1246], dedicated to S̲h̲ams al-Daulah and divided into three (so Cairo cat.) or five (so Ḥ. K̲h̲.) maqālahs: Ḥ. K̲h̲. ii p. 230, Cairo p. 510 (ah 670/1271–2. Author’s name not stated in the catalogue), Browne Suppt. 276 (ad 1526 [ah 932–3]. Trinity R.13.29. Palmer p. 61).

§ 10. Naṣīr²⁰ al-Dīn M. b. M. al-Ṭūsī died in 672/1274 (see Durrat al-ak̲h̲bār (takmilah) p. 122; Browne Lit. Hist. ii pp. 484–6; Ency. Isl. under Ṭūsī (Strothmann and Ruska); Brockelmann i pp. 508–12, Sptbd. i pp. 924–33; Krause pp. 494–505; etc.).

(1)

(K. al-ḍarb wa-’l-qismah) (beg. Īn muk̲h̲taṣarī-st dar ḥisāb i Hind u g̲h̲air i ān kih taʿlīq kardah mī-s̲h̲awad bināʾ i ān bar sih maqālat), in three maqālahs each containing eleven faṣls: Istānbūl Sarāy 3327 (3) (51 foll. ah 703/1303–4. Krause p. 497 (12)).

(2)

¶ Jāmiʿ al-ḥisāb²¹ (so in [the heading of?] the Kapūrt’halah ms., which begins Īn muk̲h̲taṣarī-st dar ʿilm i ḥisāb i Hind kih jihat i dūstī taʾlīf kardah mī-s̲h̲awad mus̲h̲tamil bar sih maqālah), in three maqālahs each subdivided into several (c̲h̲and) faṣls, a work apparently similar to, but not identical with, the preceding: Kapūrt’halah (ah 1160/1747. See M. S̲h̲afīʿ’s description in ocm. iii/4 (Aug. 1927) p. 7).

(3)

Kas̲h̲f al-qināʿ ʿan asrār al-qaṭṭāʿ (beg. Lillāhi ’l-ḥ. ʿalā ālāʾihi), an anonymous work (by Naṣīr al-Dīn Ṭūsī according to Ḥ. K̲h̲. v p. 212) on the functions of the sector, dedicated to the great s̲h̲aik̲h̲ al-Muʾaiyad b. Ḥusain and divided into five maqālahs: Bodleian 1498 (ah 1100/1688–9).

(4)

Taḥrīr Ukar T̲h̲āūd̲h̲ūsiyūs, in Arabic: see p. 2. supra.

(5)

Taḥrīr Uqlīdis, in Arabic: see p. 1 supra.

§ 11. Of unknown authorship is:

Lubāb al-ḥisāb fī ʿilm al-turāb: Cambridge 2nd Suppt. 41 (48 foll. Fine old nask̲h̲. 7th/13th cent.).

[P.S. Possibly this work is identical with the Lubāb al-ḥisāb (beg. Sp. u st. mar ān K̲h̲udāʾī [rā] kih muhandis i taqdīras̲h̲) of Maḥmūd b. al-Wuṣūdī yuʿraf bi-Ḥamīd, Tashkent Acad. i 492 (95 foll. 17th cent.)]

§ 12. S̲h̲ams al-Dīn M. b. As̲h̲raf Ḥusainī Samarqandī is said by Ḥ. K̲h̲. to have died about 600/1203–4, a date which may be a hundred years too early. A passage ascribed to him in Leyden iii p. 157 no. 1196 (3) contains a table of fixed stars for the year 645 of the Persian era (ah 675).

As̲h̲kāl al-taʾsīs, an Arabic work on Euclidean geometry (see Brockelmann i p. 468, Supptbd. i p. 850).

Persian translation: Fawāʾid i Jamālī (beg. Ḥ. i bī-ḥ. u t̲h̲. i bī-muntahā u sp. i bī-q. kih qadam i S̲h̲ah-suwār), prepared by Maḥmūd b. M. b. M. b. Qiwām al-Qāḍī al-Wālis̲h̲tānī al-mus̲h̲tahir bi-Maḥmūd al-Harawī al-Haiʾawī [who flourished circ. 838/1434–5: see § 18 infra], dedicated to Amīr Jamāl al-Dīn Sulṭān-Ḥusain [a provincial governor not yet identified] and divided into a muqaddamah and thirty-five theorems (s̲h̲akl): Rieu ii 449a (defective at end. ah 1014–18/1605–9), Āyā Ṣōfyah 1865 (3).

§ 13. Kamāl al-Dīn Ḥasan b. al-Ḥusain al-Ḥakkāk al-Marwazī cannot have lived later than the 8th/14th century.

¶ Murs̲h̲id al-muḥāsibīn, in eight “paragraphes”: Blochet iv 2396 (56 foll. ah 720/1320).

§ 14. For Abū ’l-Muẓaffar G̲h̲iyāt̲h̲ al-Dīn Sulṭān Uwais [presumably the Īlkānī, who reigned 757–76/1356–74] was composed:

(Risālah i misāḥat) (beg. Sp. i bī-q. nit̲h̲ār i bārgāhī … kih Farrās̲h̲ … ba-sar-angus̲h̲t i ījād), in a muqaddamah and twelve bābs: Bānkīpūr xvii 1732 (foll. 1–31. 18th cent.).

§ 15. Quṭb al-Dīn K̲h̲usrau-S̲h̲āh was a disciple of S̲h̲āh Niʿmat Allāh Kirmānī [who died in 834/1431: see pl. i § 1269 n.l.] and a contemporary of Tīmūr.

K̲h̲ulāṣat al-ḥisāb (beg. Naḥmaduka yā Asraʿa ’l-Ḥāsibīn), questions and answers on arithmetic and mensuration in a muqaddamah, two maqālahs and a k̲h̲ātimah: D̲h̲arīʿah vii p. 224 no. 1077, Mas̲h̲had iii, fṣl. 17, mss., nos. 49 (ah 1034/1624–5), 50 (ah 1059/1649).

§ 16. Ṣalāḥ al-Dīn²² Mūsā b. M. b. Maḥmūd, called Qāḍī-zādah i Rūmī, collaborated with G̲h̲iyāt̲h̲ al-Dīn Jams̲h̲īd in the astronomical observations carried out for Ulug̲h̲ Bēg at Samarqand and continued the work after his colleague’s death [not earlier than 830/1427, the date of the completion of Jams̲h̲īd’s Miftāḥ al-ḥussāb], but died himself before the conclusion of the observations [i.e. doubtless before 841/1437–8, which according to Rieu is taken as the starting point of several of the tables in Ulug̲h̲ Bēg’s Zīj]. The incorrect date 815 given for his death by Ḥ. K̲h̲. is mentioned in the S̲h̲aqāʾiq as that of his commentary on the As̲h̲kāl al-taʾsīs (cf. Ahlwardt v 5943). [al-S̲h̲aqāʾiq al-Nuʿmānī- yah (Cairo 1310) i pp. 17–20, Rescher’s trans. pp. 7–8; Rieu ii p. 456; Barthold (tr. Hinz) Uluġ Beg und seine Zeit pp. 150–1, 162–4; Brockelmann ii p. 212.]

Risālah dar ḥisāb (beg. T̲h̲anā-yi bī-muntahā K̲h̲udāwandī rā-st): Mas̲h̲had iii, fṣl. 17, mss., no. 94.

§ 17. Abū ’l-Wafāʾ b. Saʿīd was alive in 823/1420 (see below).

Muk̲h̲taṣar i mus̲h̲tamil bar misāḥat i abʿād u suṭūḥ u mujassamāt u bar kaifīyat i aʿmāl i Hindī: Leningrad Mus. Asiat. (ah 959/1551, transcribed from an autograph of 823/1420. See Mélanges asiatiques iii (St. Petersburg 1859) p. 500).

¶ § 18. Maḥmūd b. M. b. Qiwām al-qāḍī al-Wālis̲h̲tānī,²³ commonly called Maḥmūd al-Harawī al-Haiʾawī,²⁴ was the author of an astronomical work, al-G̲h̲iyāt̲h̲īyah, mentioned by Ḥ. K̲h̲., who says that it was composed for G̲h̲iyāt̲h̲ al-Dīn Saiyidī Aḥmad al-Harawī [i.e. evidently G̲h̲. al-D. Saiyidī A. b. K̲h̲wājah Niẓām al-Dīn Aḥmad Andak̲h̲ūdī, who in 838/1434–5 became joint vizier to S̲h̲āh-Ruk̲h̲ and who died in 839/1435–6: see Dastūr al-wuzarāʾ pp. 357–8]. His translation of M. b. As̲h̲raf Samarqandī’s As̲h̲kāl al-taʾsīs has already been mentioned (pl. ii § 12).

(Muk̲h̲taṣar dar ʿilm i ḥisāb) (beg. Baʿd az ḥ. (Paris sp.) u st. i (Bodl. adds ḥaḍrat i) Parwardgār u durūd bar k̲h̲ulāṣah i nataʾij i haft u c̲h̲ahār), in a muqaddamah and two maqālahs: Bodleian 1525 (foll. 113b–133b. ah 862/1457), Blochet ii 772 (2) (early 17th cent.).

§ 19. S̲h̲araf al-Dīn ʿAlī Yazdī died in 858/1454 (see pl. i § 356).

Ḥisāb al-ʿuqūd (beg. Baʿd az ḥ. i Parwardgārī-kih aṣnāf): Mas̲h̲had (not in the published volumes of the catalogue apparently, but see D̲h̲arīʿah vii p. 11 no. 39). [p.s. See p. 25 (47)].

§ 20. ʿAlāʾ al-Dīn ʿAlī b. M. al-Qūs̲h̲jī died at Istānbūl in 879/ 1474–5 (see pl. ii § 112).

(Risālah dar ʿilm i ḥisāb), or “Fārsī Ḥisāb” (beg. al-Ḥ. l. R. al-ʿā…. a. b. īn kitāb mus̲h̲tamil-ast), on arithmetic and geometry in three maqālahs ((1) dar ḥisāb i ahl i Hind, (2) dar ḥisāb i ahl i tanjīm, (3) dar misāḥat): Bodleian 1528 (ah 932/1526. List of maqālahs and bābs), 1529 (ah 995/ 1587), 1530–3, Ivanow Curzon 570 (ah 958/1551), 1st Suppt. 896 (fragment), Leningrad Mus. Asiat. (ah 979/1571–2. See Mélanges asiatiques iii (St. Petersburg 1859) p. 499), Blochet iv 2364 (2) (ah 984/1576), 2363 (1) (ah 1063/1653), ii 783 (1) (Maqālah ii), iv 2180 (2), Mas̲h̲had iii, fṣl. 17, mss., nos. 77 (ah 1020/1611), 76 (ah 1031/1622), 72, 75, Mehren p. 9 no. 17 (2) (ah 1160/1747), Ethé 2254 (8) (ah 1169/1756), 2242–5, Madrās 503–4, Lahore Panjāb Univ. (see ocm. x/3 (May 1934) p. 99), Rieu Suppt. 421 (2), ʿAlīgaṛh Subḥ. mss. p. 21 nos. 4, 5, Berlin 81 (6), Brelvi-Dhabhar p. 57 no. 1, Peshawar 1724 (5).

Editions: 1266/1850 (Mīzān al-ḥisāb, by Mullā ʿAlī Qūs̲h̲jī. Āṣafīyah i p. 820 no. 284); 1269/1852–3 (Risālah i ḥisāb, by Qūs̲h̲jī. Āṣafīyah i p. 810 no. 62).

¶ § 21. [K̲h̲air al-Dīn] K̲h̲alīl b. Ibrāhīm.

(1)

Miftāḥ i kunūz i arbāb i qalam u miṣbāḥ i rumūz i aṣḥāb i raqam (beg. S̲h̲. u sp. sawāzār i ḥaḍratī-st kih d̲h̲āt i Ū az ṣifat i imkān), on some arithmetical operations invented by the author, composed in the reign of Sulṭān M. b. Murād b. M. [i.e. Muḥammad ii, ah 855–86/1451–81] and divided into a muqaddamah, ten faṣls and a k̲h̲ātimah: Ḥ. K̲h̲. vi p. 29 nos. 12599 (where the author is called K̲h̲air al-Dīn), 12600, Blochet ii 771 (ah 904/1498), Bodleian 1905 (6) (ah 914/1508. Chapter headings given), Rieu ii 449b (17th cent.).

(2)

Mus̲h̲kil-gus̲h̲āy i ḥussāb u muʿḍil-numāy i kuttāb: Āyā Ṣōfyah 2731.

(3)

Muk̲h̲taṣar fī ’l-ḥisāb, possibly identical with one of the preceding: Istānbūl Esmī K̲h̲ān Sulṭān 294.

(4)

Risālah fī ’l-ḥisāb, doubtless identical with one of the preceding: Asʿad Efendī 3158.

§ 22. G̲h̲iyāt̲h̲ al-Dīn ʿAlī b. ʿAlī Amīrān [Ḥusainī Iṣfahānī] composed his Asrār al-ḥurūf (Āṣafīyah ii p. 1674, Browne Pers. cat. 133 (2)) in 870/1465–6, his well-known Dānis̲h̲-nāmah i jahān (Browne Coll. M. 1, Bodleian 1456, Ethé 2173–4, 718, Rieu ii 439, Edwards col. 108, etc., etc.) in 871/1466–7 in Badak̲h̲s̲h̲ān,²⁵ and his Tadbīr-nāmah i anfus u āfāq, an ethical work (Madrās i 423), in 885/1480.

Durrat al-misāḥah (beg. Bandagī i ḥaqīqī ʿAlīm i Ḥakīmī rā), on the elements of geometry and mensuration, compiled at the request of a Wazīr Niẓām al-Dīn Darwīs̲h̲ ʿAlī for the instruction of an architect S̲h̲ihāb al-Dīn K̲h̲wājagī, dedicated in 890/1485 to Abū ’l-Fatḥ Sulṭān Maḥmūd G̲h̲āzī “Ruler of Īrān and Tūrān” [the Tīmūrid, who ruled in 899–900/ 1494, but was Governor of Māzandarān from 864/1460] and divided into a muqaddamah (on the general principles of mensuration), four maqālahs (on the measurement of (1) plain surfaces, (2) spherical surfaces, (3) irregular curved surfaces, (4) the surfaces of solid bodies) and a k̲h̲ātimah (some elementary algebraic rules): Ivanow Curzon 572 (54 foll. ah 953/1546).

§ 23. Malik-Muḥammad b. Sulṭān-Ḥusain Iṣfahānī received an ijāzah from ʿAlī b. Hilāl al-Karakī in 984/1576–7 (D̲h̲arīʿah i p. 223).

(Risālah dar jabr u muqābalah u qawāʿid i istik̲h̲rāj i majhūlāt i ʿadadīyah) (beg. al-Ḥ. l. al-Malik al-ʿAllām), composed as a supplement to Qūs̲h̲jī’s Risālat al-ḥisāb (cf. pl. ii § 20): D̲h̲arīʿah v p. 88 no. 357, Mas̲h̲had iii, fṣl. 17, mss., no. 64 (ah 1096/1685).

¶ § 24. Bahāʾ al-Dīn M. b. Ḥusain al-ʿĀmilī died at Iṣfahān in 1031/1622 (see Browne Lit. Hist. iv pp. 426–8; Brockelmann ii p. 414, Sptbd. ii p. 595; pl. i § 1236(4), ii § 130).

(1)

K̲h̲ulāṣat al-ḥisāb, an Arabic compendium of arithmetic (see Brockelmann for mss., Arabic commentaries and printed editions).

Persian translations and commentaries:

(a)

Mūḍiḥ al-K̲h̲ulāṣah (beg. al-Ḥ. l. R. al-ʿā.), by M. Amīn Najafī Ḥijāzī Qummī, a pupil of Bahāʾ al-Dīn al-ʿĀmilī, in whose lifetime the commentary was written: D̲h̲arīʿah iv p. 493 no. 2210 (Tauḍīḥ K̲h̲. al-ḥ.), Mas̲h̲had iii, fṣl. 17, mss., no. 171 (not later than ah 1166/1753).

(b)

S̲h̲arḥ i K̲h̲ulāṣat al-ḥisāb (beg. Ḥamdī kih maqdūr na-bās̲h̲ad ḥaṣras̲h̲), an anonymous commentary (without the Arabic text) completed possibly in 1081/1670: Bānkīpūr xi 1033 (ah 1226/1811), 1034 (19th cent.).

(c)

Muntak̲h̲ab (a chronogram = 1092/1681. Beg. Al-ḥ. l. R. al-ʿā. wa-’l-ṣ. wa-’l-s. ʿalā Rasūlihi), composed by Luṭf Allāh “Muhandis” (for whom see § 31 infra) at the request of Mīr M. Saʿīd b. M. Yaḥyā: Bānkīpūr xvii 1731 (ah 1096/1685), Rieu ii 451a (ah 1130/1718), Ethé 2254 (5) (ah 1145/ 1733), 2253, Cambridge 2nd Suppt. 90 (2) (late 18th cent.), Lindesiana p. 125 no. 705c (ah 1240/1824–5), Āṣafīyah i p. 820 no. 211 (ah 1243/1827–8), Ivanow 1st Suppt. 898 (ah 1256/ 1840), Madrās 180 (a).

(d)

Tarjamah i K̲h̲ulāṣat al-ḥisāb (beg. Ḥamdī kih hīc̲h̲ ʿadadī iḥṣā-yi ān na-kunad), an anonymous paraphrase and commentary: Ethé 2251 (ah 1107/1696), Bānkīpūr xi 1032 (ah 1111/1699), Chanykov 126, 128 (a).

(e)

Faiḍ al-Wahhāb fī s̲h̲arḥ K̲h̲ulāṣat al-ḥisāb (beg. T̲h̲. u ḥ. i bī-ḥ. kih aqsām u anwāʿ i ʿadad), composed by Niẓām al-Dīn Aḥmad b. M. ʿAbd Allāh al-s̲h̲ahīd at the request of ʿAbd al-Wahhāb K̲h̲ān [possibly Nawwāb ʿA. al-W. K̲h̲ān, for whose perusal the ms. Ethé 2251 (an anonymous commentary on the K̲h̲ulāṣat al-ḥisāb) was transcribed at Arcot in 1107/ 1696]: Ethé 2252 (Muqaddamah and first two bābs only. 82 foll.).

(f)

G̲h̲āyah i juhd al-ḥussāb²⁶ (a chronogram = 1130/1718. Beg. K̲h̲ulāṣat al-ḥisāb li-l-muḥāsib …) by M. Zamān Faiyāḍ, al-muk̲h̲āṭab bah T̲h̲ālit̲h̲, b. M. Ṣādiq Anbālajī Dihlawī Shāfiʿī Ḥanafī:²⁷ Bānkīpūr xi 1035 (19th cent.).

(g)

¶ Taḥrīr al-Ṣadr, by Ṣadr al-Dīn M. b. Zabardast K̲h̲ān, who flourished about 1135/1722–3 (see pl. i § 1466): Lahore Panjāb Univ. (14 foll. N.d. See ocm. x/3 (May 1934) p. 100).

(h)

S̲h̲arḥ i K̲h̲ulāṣat al-ḥisāb, by K̲h̲wājah M. Māh [doubtless identical with M. Māh, author of the Mirʾāt al-ḥisāb (Āṣafīyah i p. 820 no. 96)]: Āṣafīyah i p. 816 no. 167 (ah 1221/1806).

(j)

S̲h̲arḥ i K̲h̲ulāṣat al-ḥisāb, by Mīrzā Muḥammad Bēg: Āṣafīyah i p. 816 no. 192 (ah 1250/1834–5).

(k)

Tarjamah i K̲h̲ulāṣat al-ḥisāb (Ḥ. i nā-maḥdūd Aḥadī-rā kih āḥād i mufradāt), in a muqaddamah, twelve bābs and a k̲h̲ātimah, by M. Ṣādiq b. ʿAbd al-ʿAlī Tabrīzī: Bānkīpūr xi 1036 (19th cent.).

(l)

Tarjamah i K̲h̲ulāṣat al-ḥisāb (beg. (without preface) Naḥmaduka yā Man lā yuḥīṭu bi-jamʿi niʿamihi ʿadad—Sp. mī-kunam Tu-rā ai Ān-kih iḥāṭah na-mī-kunad ba-farāham āwardan i niʿmathā-yi Ū hīc̲h̲ ʿadad), by Raus̲h̲an ʿAlī Jaunpūrī:²⁸ Būhār 223 (ah 1227/1812), ʿAlīgaṛh Subḥ. mss. p. 21 no. 2 (ah 1249/1833–4), Lahore Panjāb Univ. (see ocm. x/3 p. 100), Āṣafīyah iii p. 338 no. 371.

Editions: (1) The Khoolasut-ool-hisab: a compendium of arithmetic and geometry; in the Arabic language, by Buha,e-ood-deen, of Amool [sic] … with a translation into Persian and commentary by … Muoluwee Ruoshun Ulee, of Juonpoor; to which is added a treatise on algebra, by Nujm-ood-deen Ulee²⁹ Khan … Revised and edited by Tarinee Churun Mitr, Muoluwee Jan Ulee and Ghoolam Ukbur … Calcutta 1812° (477 pp.); (2) Calcutta, Ṭibbī Pr. 1261/1845* (Tarjamah i K̲h̲. al-ḥ. 423 pp.).

(m)

Kanz al-ḥisāb s̲h̲arḥ i K̲h̲ulāṣat al-ḥisāb, by “S̲h̲āh-zādah Farhād b. Walī-ʿahd”, i.e. evidently Farhād Mīrzā, who died in 1888 (see pl. i § 259): Tihrān 1257/ 1841 (Āṣafīyah i p. 818 no. 245).

(n)

Tas̲h̲rīḥ al-ḥisāb (beg. al-Ḥ. l. ’l. minhu ’l-mabdaʾ), by M. ʿAlī, called Nāẓim al-S̲h̲arīʿah, Kirmānī: D̲h̲arīʿah iv p. 188.

(o)

Unidentified translations and commentaries: Browne Suppt. 438 (ah 1124/1712. Christ’s Dd. 3. 16), Cambridge 2nd Suppt. 405 (18th ¶ cent.), Āṣafīyah i p. 816 no. 123 (S̲h̲arḥ i K̲h̲. al-ḥ. ah 1236/1821), Lindesiana p. 125 no. 705b (the Arabic text? ah 1240/1824–5).

Edition of a translation: K̲h̲. al-ḥ. [Ṭihrān] 1295/1878 (144 foll. Karatay p. 118).

(2)

Risālah dar ḥisāb (beg.… a. b. īn kitāb mus̲h̲tamil ast bar sih muqaddamah dar ḥisāb i ahl i Hind u ān mus̲h̲tamil bar muqaddamah u dū bāb. Muqaddamah dar ṣuwar i aʿdād), ascribed in the colophon to Bahāʾ al-Dīn al-ʿĀmilī: Maʿārif ii 237 (28 foll. ah 1270/1854).

(3)

Tuḥfah (beg. al-Ḥ. l. R. al-ʿā…. a. b. bar ḍamāʾir i ūlī ’l-abṣār huwaidā u ẓāhir ast kih taḥqīq i miqdār i kur az ahamm i muhimmāt ast), a short tract dealing mainly with the kur and the misāḥat i ḥauḍhā, dedicated to S̲h̲āh Ṭahmāsp (ah 930–80/1523–72)³⁰ and divided into twelve faṣls: D̲h̲arīʿah iii p. 402 no. 1443, Bānkīpūr xvii 1733 (foll. 32b–47a. 18th cent.).

§ 25. S. Luṭf Allāh al-Ḥusainī was a contemporary of Bahāʾ al-Dīn al-ʿĀmilī (for whom see § 24 supra).

Risālah dar ḥisāb (beg. al-Ḥ. l. al-Maḥmūd), arranged like Bahāʾī’s K̲h̲ulāṣat al-ḥisāb: D̲h̲arīʿah vii p. 7 no. 19, Mas̲h̲had iii, fṣl. 17, mss., no. 97 (ah 1105/1693–4).

§ 26. Ḥasan Muḥammad b. Rājī Muḥammad al-Firs̲h̲aurī³¹ al-ʿAbbāsī al-Kujrātī al-Sarkijī,³² the author of the Laṭāʾif al-fuyūḍ, is probably the same person as Ḥ. M. b. R. M. ʿAbbāsī, who transcribed the i.o. ms. Ethé 1032 (Kullīyāt i ʿAṭṭār) in 1025/1616.

Laṭāʾif al-fuyūḍ (beg. Sp. i bī-q. u minnathā-yi bī-muntahā mar K̲h̲āliqī rā), in two maqālahs: Mas̲h̲had iii, fṣl. 17, mss., no. 152 (breaking off in Bāb 7 of Maqālah ii. Classified as Riyāḍī but without further specification of the subject).

¶ § 27. Nādir al-ʿAṣr³³ ustād Aḥmad i Miʿmār i Lāhaurī, who died in 1059/1649,³⁴ was revealed to us not long ago³⁵ as the architect of the Rauḍah i Mumtāz-Maḥall (the “Taj Mahall”)³⁶ at Āgrah.

Risālah i Aḥmad i Miʿmār: ʿAlīgaṛh Subḥ. mss. p. 21 no. 3 (47 foll. ad 1836. Under Ḥisāb but without further information).

§ 28. ʿAṭāʾ Allāh “Rus̲h̲dī”³⁷ b. ustād Aḥmad i miʿmār i Lāhaurī (cf. pl. ii § 27) was the elder brother of Luṭf Allāh “Muhandis” (for whom see §§ 31, 75, 141).

(1)

K̲h̲ulāṣah i rāz (beg. S̲h̲. i bī-ḥ. ba-Wāḥid i Azalī), a metrical work on arithmetic, algebra and mensuration in ten bābs, beginning with eulogies of S̲h̲āh-Jahān (ah 1037–69/ 1628–59) and Prince Dārā-S̲h̲ukōh (for ¶ whom see pl. i § 1321), the latter being the dedicatee: Bānkīpūr xvii 1730 (ah 1097/1686), Rieu ii 451a (ah 1130/1718).

(2)

Tarjamah i Bīj ganit (ah 1044): see p. 4 supra.

§ 29. M. Amīn b. M. Saʿīd al-ʿAlawī.

Iʿjāz al-ḥisāb (beg. al-Ḥ. l. ’l. mattaʿanā bi-naʿmāʾihi bilā ḥisāb), composed in 1072/1661–2, in the reign of Aurangzēb, and divided into a muqaddamah, two maqālahs and a k̲h̲ātimah: Rāmpūr (Nad̲h̲īr Aḥmad 244).

§ 30. Mēdnī-Mal b. D’haram-Narāyan (or, according to Ivanow, D’haram-Dās Narāyan) b. Kalyān-Mal Kāyat’h³⁸ Saksēnah.³⁹

Badāʾiʿ i funūn (beg. Jahān jahān niyāyis̲h̲ i Wāḥid al-Qahhārī), on arithmetic, composed in 1074/1663–4, the sixth year of Aurangzēb’s reign, at Itāwah, based mainly on the Līlāwatī, and divided into nine (or ten) bābs: Blochet iv 2178 (breaks off in Bāb viii. 18th cent.), Ivanow 1497 (18th cent.), Āṣafīyah i p. 806 nos. 312 (ah 1262/1846), 155, Ethé 2259 (breaks off in Bāb iv).

§ 31. Luṭf Allāh “Muhandis” wrote a concise Arabic commentary on the K̲h̲ulāṣat al-ḥisāb (mss.: Loth 761, Rāmpūr i p. 416) as well as a Persian translation of ʿAbd al-Raḥmān al-Ṣūfī’s Ṣuwar al-kawākib (ms.: Berlin 332 (3)) and an ethical work Siḥr i ḥalāl composed in 1070/1659 (mss.: Bombay Univ. p. 47 no. 27 (cf. Islamic culture xi/2 p. 207 n.3), Ḥaidarābād, M. G̲h̲aut̲h̲’s private library (Islamic culture, ibid.)). For his Āsmān i suk̲h̲un see pl. i § 1093, and for his dīwān pl. ii § 28, where some information will be found concerning his father and other relations.

(1)

K̲h̲awāṣṣ i aʿdād (beg. al-Ḥ. l…. mī-g. faqīr L.A. mutak̲h̲alliṣ bi-M.), in four maqālahs: Rieu ii 451a (foll. 100–7. ah 1130/1718), Ḥaidarābād Saʿīdīyah Library (see Islamic culture xi/2 (April 1937) p. 207¹²).

(2)

Muntakhab (ah 1092): see p. 10 supra.

§ 32. M. Zamān b. M. Ṣādiq Anbālajī Dihlawī S̲h̲āfiʿī Ḥanafī, already mentioned (pl. ii § 24 (1) (f)) as the author of a commentary written in 1130/1718 on the K̲h̲ulāṣat al-ḥisāb, composed in 1120/1708–9 a treatise on astronomy (Blochet iv 2370).

Irtifāʿ al-jibāl: Āṣafīyah i p. 806 no. 70. [p.s. See p. 77, n. 166].

¶ § 33. ʿAṭāʾ Allāh.⁴⁰

K̲h̲azīnat al-aʿdād (a chronogram = 1178/1764–5. Beg. al-Ḥ. l. ’l. j. al-s̲h̲amsa ḍiyāʾ^an), on arithmetic, algebra and practical geometry, in a muqaddamah, two miftāḥs, ten bābs, one kac̲h̲kūl and a k̲h̲ātimah: Bombay Univ. p. 249 no. 170.

§ 34. Indarman [Ḥiṣārī].

Dastūr i ḥisāb [ḥussāb?] (beg. Ḥ i bī-ʿadd D̲h̲āt i Īzadī rā kih dar ṣūrat) composed during a visit to Delhi, completed in 1180/1766–7 (the chronogram, however, Guldastah i dānis̲h̲wari = 1090), and divided into a muqaddamah, five maqālahs and a k̲h̲ātimah: Bānkīpūr xi 1037 (217 foll. 5 Rajab 14th year of S̲h̲āh-ʿĀlam [1186/1772]).

§ 35. M. Ṣalāḥ al-Dīn b. Diyānat K̲h̲ān Jahāndār-S̲h̲āhī presumably flourished in the later years of the eighteenth century and perhaps in the earlier years of the nineteenth, since the epithet Jahāndār-S̲h̲āhī⁴¹ doubtless refers to his father Diyānat K̲h̲ān and not to himself.

Kifāyat al-jabr (beg. al-Ḥ. l. ’l. Huwa Asraʿ al-Ḥāsibīn), in a muqaddamah, thirteen bābs and a k̲h̲ātimah: Bānkīpūr xi 1038 (ah 1227/1812).

§ 36. G’hāsī Rām Dihlawī.

Majmaʿ al-ḥisāb, composed in 1202/1787–8 and divided into nine bābs: Lahore Panjāb Univ. (ah 1266/1850. See ocm. x/3 (May 1934) p. 100).

§ 37. Karīm-bak̲h̲s̲h̲.

(1)

ʿUmdat al-ḥisāb: Āṣafīyah i p. 818 no. 1035

(2)

Intik̲h̲āb i ʿUmdah, composed in 1204/1789–90 for Arasṭū-Jāh:⁴² Āṣafīyah i p. 806 no. 191 (ah 1204/1789–90, autograph).

§ 38. Qāḍī ’l-Quḍāt M. Najm al-Dīn K̲h̲ān “T̲h̲āqib” b. M. Ḥamīd al-Dīn Kākōrawī, a raʾīs of Kākōrī (cf. pl. i § 1378 fn.), died on 13 Rabīʿ ii 1229/4 April 1814 at Benares, when on his way from Calcutta to Kākōrī after retiring from the post of Qāḍī ’l-Quḍāt. He translated into Persian two sections of the Fatāwā-yi ʿĀlamgīrī (see Edwards) and wrote also a short treatise on Indian eras (Rieu iii 1013b, Ivanow 1504) and an Arabic qaṣīdah included in the Nafḥat al-Yaman ¶ (cf. pl. i § 308, n. 181). [Riyāḍ al-wifāq (summarised in Sprenger p. 166); Ṣubḥ i guls̲h̲an p. 96; Raḥman ʿAlī pp. 233–5].

Risālah dar jabr u muqābalah, (beg. Ai ān-kih turā-st d̲h̲ihn i t̲h̲āqib), a short metrical work interspersed with illustrations, etc., in prose: Būhār 223 (2) (ah 1227/1812 probably), Ivanow Curzon 579 (1) (early 19th cent.), ʿAlīgaṛh Subḥ. mss. p. 21 no. 1 (ah 1249/1833–4), Lahore Panjāb Univ. (ah 1256/1840. See ocm. x/3 (May 1934) p. 101).

Edition: Calcutta 1812° (appended to the K̲h̲ulāṣat al-ḥisāb of Bahāʾ al-Dīn al-ʿĀmilī. See pl. ii p. 11).

§ 39. Dīwān Kānhjī Kāyast’h ʿAẓīmābādī.⁴³

K̲h̲izānat al-ʿilm (beg. Ḥamdī c̲h̲ū marātib i ʿadad), on arithmetic, geometry and astronomy, composed in 1229/1814 at ʿAẓīmābād (i.e. Patna), dedicated to Francis Hākns [probably Hawkins] and divided into a muqaddamah, ten bābs and a k̲h̲ātimah: Ethé 2261 (ah 1230/1815), Ellis Coll. M 218 (ah 1230/1815).

Edition: Khazánat ul ilm, or The Treasury of Science, being a course of instruction in the various branches of Mathematics … Printed up to the 492nd page under the supervision of Dr. J. Tytler⁴⁴ … and completed … under the … supervision of … Mansúr Ahmed Bardwání. Calcutta 1837°* (654 pp.).

§ 40. ʿAbd al-Raḥīm “ʿAbdū” Gōrak’hpūrī, otherwise known as ʿAbd al-Raḥīm Dahrīyah, travelled through Afg̲h̲ānistān with Mountstuart Elphinstone and W. Fraser [1808–9] and died in Calcutta. The Kār-nāmah i Ḥaidarī (for which see pl. i § 1078) is described as “his famous work” in the Catalogue of the Arabic and Persian manuscripts in the library of the Calcutta Madrasah, p. 105. In that library are preserved five small volumes dated 1825 and 1826 containing his Persian translations from the Mathematical Course of Charles Hutton.

S̲h̲igarf bayān,⁴⁵ a miscellany containing inter alia (1) a history of the genesis and evolution of the human race (foll. 1–28b), (2) a brief autobiography (foll. 28b–32a), (3) an Arabic treatise on astronomy (foll. 40a–58b), (4) five important reasons for translating into Arabic and Persian the standard European works on astronomy, geography, and mathematics (foll. 62a–65a), (5) reasons for preferring the work of Simpson to ¶ that of Naṣīr al-Dīn Ṭūsī on Euclid’s elements (foll. 69a–70): Calcutta Madrasah 175.

§ 41. Nawwāb S̲h̲ams al-Umarāʾ Mīr Fark̲h̲undah ʿAlī K̲h̲ān died in 1249/1833–4 according to the Āṣafīyah catalogue.

Tabdīl i suṭūḥ.

Edition: 1251/1835–6 (Āṣafīyah i p. 806 no. 13).

§ 42. M. Irtaḍā ʿAlī K̲h̲ān died in 1251/1835–6 (see pl. i § 1381).

Nuqūd al-ḥisāb (beg. Ba-ḥamd i Wāḥid i Rabb al-barāyā), on arithmetic with special reference to the Hindu system, completed in 1235/1819 and divided into a muqaddamah, seven bābs and a k̲h̲ātimah: Ivanow 1st Suppt. 902 (ah 1241/1826).

Edition: 1260/1844 (Āṣafīyah i p. 820 no. 95).

§ 43. Abū ’l-Qāsim al-mus̲h̲tahir bi- G̲h̲ulām-Ḥusain b. Fatḥ-Muḥammad Karbalāʾī Jaunpūrī is the author of (1) Anīs al-aḥbāb, a commentary on Bahāʾ al-Dīn al-ʿĀmilī’s Arabic treatise on the astrolabe, (2) Iṣṭilāḥāt al-taqwīm, and (3) Zīj i Bahādur-K̲h̲ānī (for which see § 161 infra).

Jāmiʿ i Bahādur-K̲h̲ānī (beg. ʿAnbarīn ṭirāzī kih), completed in 1249/1833 and divided into a muqaddamah, six k̲h̲azīnahs ((1) geometry, (2) optics, (3) arithmetic, (4) mensuration, (5) astronomy, (6) astronomical tables and almanacs) and a k̲h̲ātimah: D̲h̲arīʿah v p. 43 no. 176, Ivanow Curzon 580 (mid-19th cent.), Rieu iii 1038a (extracts only. Circ. ad 1850).

Edition: A Book styeled Jamy Bahadur Khanee containeing four sciences of Mathematicks that is Geomatry, Optics, Arithmetics and Stronomy. Selected out of the Arabic and Eenglish authors, didecated to Rajah Khan buhadur Khan Dalaour jung … in the year 1834 … By Golam hosin of Jan pore. Calcutta 1835° (720 pp.).

Description (probably of this work): Analysis and specimens of a Persian work on mathematics and astronomy [author: Maulawī G̲h̲ulām-Ḥusain], by the late John Tytler⁴⁶ (in jras. iv (1837) pp. 254–72).

§ 44. Ḥakīm Sirāj al-Dīn Ḥasan.

Dastūr al-ḥisāb (or al-ḥussāb), composed in 1250/1834–5: Āṣafīyah i p. 810 no. 207.

¶ § 45. S. Nūr al-Aṣfiyā [b. Nūr al-ʿUlā b. Qamar al-Dīn] Aurangābādī (for whose grandfather see pl. i §§ 36, 1369) died at Ḥaidarābād on 20 D̲h̲ī-Qaʿdah 1255/25th January 1840⁴⁷ (see Gulzār i Āṣafīyah pp. 371–3, where nothing is said about works written by him).

(1)

Nūr al-ḥisāb: Āṣafīyah i p. 812 no. 215 (ah 1223/ 1808).

(2)

Nūr al-muḥāsibīn: Āṣafīyah i p. 820 no. 144.

§ 46. It may be conjectured that Ḥāfiẓ Aḥmad b. M. Mag̲h̲ribī Tilimsānī Anṣārī Ṣāʾimī dedicated his work Aʿẓam al-ḥisāb to Nawwāb Aʿẓam al-Umarāʾ M. G̲h̲aut̲h̲ K̲h̲ān “Aʿẓam” (d. 1855: see pl. i § 1209).⁴⁸

(1)

Aʿẓam al-ḥisāb: Āṣafīyah i p. 806 no. 139.

(2)

Mirʾāt al-ʿālam: Āṣafīyah i p. 820 no. 71 (ah 1262/ 1846. Under Riyāḍī, but without further particularization of the subject).

(3)

Zubdat al-ḥisāb (beg. al-Ḥ. l.… a. b. ʿilm i ḥisāb bihtarīn i ʿulūm i ʿaqlī ast), a short work in a muqaddamah and four maqālahs: Ivanow 1st Suppt. 899 (ah 1290/1874), Āṣafīyah iii p. 338 no. 394.

Edition: 1270/1853–4 (Āṣafīyah i p. 814 no. 63).

§ 47. Mīrzā Jaʿfar K̲h̲ān Mus̲h̲īr al-Daulah (for whom see pl. i § 1422) died in Jumādā ii 1279/Nov.–Dec. 1862 (D̲h̲arīʿah vii p. 5 antepenult).

(Kitāb al-ḥisāb)⁴⁹ in a muqaddamah, six bābs and a k̲h̲ātimah, composed in 1262/1846, dedicated to Muḥammad S̲h̲āh Qājār, and said (D̲h̲arīʿah vii p. 4²³) to be the first Persian work on modern arithmetic: D̲h̲arīʿah vii p. 5 no. 9 (where the work is not expressly said to have been published).

§ 48. Nawwāb S̲h̲ams al-Umarāʾ Bahādur Amīr i Kabīr M. Fak̲h̲r al-Dīn K̲h̲ān, born in 1780, was eleven years old when his father, Abū ’l-Fatḥ K̲h̲ān Tēg̲h̲-Jang, died. He himself died on 10 April 1863. His Urdu work Sittah i S̲h̲amsīyah was published in six volumes in 1256/1840 (see Āṣafīyah i p. 826, under Riyāḍī i Urdū). His eldest son, ʿUmdat al-Mulk M. Rafīʿ al-Dīn K̲h̲ān, was the author of some astronomical works in Persian and of at least two scientific works in Urdu (see Āṣafīyah i p. 824 no. 60, p. 826 no. 61). [Gulzār i Āṣafīyah pp. 286–90; Beale Oriental biographical dictionary under Shams-ul-ʿUmra; Madḥīyah i S̲h̲amsīyah ¶ [in Urdu, 76 pp.], by M. G̲h̲ulām-Imām K̲h̲ān, Ḥaidarābād 1280/1863°; Niẓāmī Badāyūnī Qāmūs al-mas̲h̲āhīr (in Urdu) ii p. 24.]

(1)

Risālah dar bayān i aʿmāl i qaṭṭāʿ: Āṣafīyah i p. 810 no. 162.

(2)

S̲h̲ams al-handasah, composed in 1241/1825–6: Āṣafīyah i p. 818 nos. 19, 119.

Edition: 1251/1835–6 (Āṣafīyah i p. 818 no. 224. Cf. p. 816 no. 18).

§ 49. Artillery Lieutenant August Kržiž was one of the seven Austrians who went to Persia in 1851 as teachers in the Dār al-Funūn College and the Military College⁵⁰ in Tihrān. He returned to Europe in 1859 (see Browne Press and poetry p. 154). In addition to works on gunnery he wrote:

(1)

(Kitāb dar tas̲h̲rīḥ u tauḍīḥ i ʿilm i jarr al-t̲h̲aqīl u ʿilm i ḥikmat i ṭabīʿī), translated by M. Zakī Māzandarānī from the French of Lieut. A.K.: [Tihrān 1858°] (unpaginated).

(2)

(Kitāb i ḥisāb ba-ʿilm i handasah), on geometry, similarly translated by M. Zakī Māzandarānī: [Tihrān] 1274/ 1858° (unpaginated).

(3)

Mīzān al-ḥisāb, on algebra, similarly translated by M. Zakī Māzan­darānī: [Tihrān] 1274/1857° (375 pp.).

§ 50. Najm al-Daulah⁵¹ Mīrzā ʿAbd al-G̲h̲affār K̲h̲ān b. ʿAlī Muḥammad Iṣfahānī, Chief Astrologer (Munajjim-bās̲h̲ī) to Nāṣir al-Dīn S̲h̲āh and “Professor of all the exact sciences” in the Dār al-Funūn College, was born in 1255/1839–40 (so D̲h̲arīʿah vii p. 8¹⁵) and died on 14 Jumādā i 1326/14 June 1908 (so D̲h̲arīʿah iii p. 58¹³, vii p. 8¹⁵).⁵² Several of his mathematical and scientific works are mentioned in Browne’s Press and poetry pp. 157–8.

(1)

Bidāyat al-handasah: printed Tihrān (D̲h̲arīʿah iii p. 60).

(2)

Bidāyat al-ḥisāb: printed 1322/1904–5 (D̲h̲arīʿah iii p. 58).

(3)

Bidāyat al-jabr: printed Tihrān (D̲h̲arīʿah iii p. 58).

(4)

Ḥisāb i jadīd: printed Tihrān (D̲h̲arīʿah vii p. 8 no. 27).

(5)

Kifāyat al-handasah: see Uṣūl al-handasah below.

(6)

Kifāyat al-ḥisāb: Ṭihrān 1291/1874 (Āṣafīyah i p. 818 no. 76).

(7)

¶ Uṣūl al-handasah, or Kifāyat al-handasah, in eight maqālahs, dedicated to Muẓaffar al-Dīn S̲h̲āh: Tihrān 1318/ 1900–1 (D̲h̲arīʿah ii p. 213 no. 830).

(8)

Uṣūl i handasah: [Persia] 1292/1875 (Āṣafīyah i p. 806 no. 77).

§ 51. Muhandis al-Mulk Mīrzā Riḍā K̲h̲ān was one of the teachers at the Dār al-Funūn College (cf. Browne Press and poetry p. 158 (29)–(33)).

Hazār masʾalah i jabr u muqābalah: printed Tihrān (D̲h̲arīʿah v p. 87 no. 354).

§ 52. Mīrzā ʿAlī M. K̲h̲ān Mutarjim i Humāyūn is the author of Dastūr i dānis̲h̲, containing durūs wa-ḥikāyāt, printed in Tihrān (D̲h̲arīʿah viii p. 153).

(1)

Ḥisāb i ibtidāʾī, in two parts: printed (D̲h̲arīʿah vii p. 7 no. 24).

(2)

Ḥisāb i mufaṣṣal: Tihrān (D̲h̲arīʿah vii p. 11 no. 43).

(3)

Ḥisāb i muqaddamātī: Tihrān (D̲h̲arīʿah vii p. 11 no. 44).

(4)

Uṣūl i jabr u muqābalah: printed Tihrān 1331/1913 (D̲h̲arīʿah ii p. 179 no. 663; Mas̲h̲had iii, fṣl. 17, ptd. bks., no. 2).

§ 53. M. Ḥasan b. M. Ḥusain al-Qārī.

Tuḥfah i Muk̲h̲tārīyah, composed in 1293/1876 and dedicated to Nawwāb Muk̲h̲tār al-Mulk: Āṣafīyah i p. 808 no. 52 (ah 1293/1876, autograph).

§ 54. Ḥaidar-Qulī b. Ḥusain-Qulī Bayāt Muk̲h̲tārī Nis̲h̲ābūrī [so].

(1)

As̲h̲kāl i baiḍī (beg. Baiḍī i musaṭṭaḥ saṭḥī ast), composed in 1301/1883–4: D̲h̲arīʿah ii p. 112, Majlis 154 (ah 1301/1883–4).

(2)

Risālah i mak̲h̲rūṭ u usṭwānah (beg. Wa-ba‘d c̲h̲ūn rasm i mujassamāt), dedicated to Āṣaf al-Daulah, Governor of K̲h̲urāsān: Majlis 179 (ah 1302/1884–5).

(3)

Risālah i rasm i mujassamāt i mutas̲h̲ābih u qaṭʿ i zāʾid (beg. A. b. īn risālah īst dar maʿrifat i qaṭʿ i zāʾid), composed in 1294/1877: Majlis 176.

§ 55. Āqā K̲h̲ān b. Ḥusain-Qulī K̲h̲ān Muḥāsib al-Daulah was one of the teachers at the Dār al-Funūn College in Ṭihrān (cf. Browne The press and poetry of modern Persia p. 158).

Uṣūl i ʿilm i jabr u muqābalah: Tihrān 1305/1888° (216 pp.); 1310/1892–3 (D̲h̲arīʿah ii p. 179 no. 661).

§ 56. Mīrzā ʿAlī K̲h̲ān Nāẓim al-ʿUlūm, one of the teachers in the Dār al-Funūn College (cf. Browne Press and poetry p. 155¹), died circ. 1317/1899–1900.

(1)

Ḥisāb i jadīd, known as Ḥisāb i ʿAlī K̲h̲ān: printed (D̲h̲arīʿah vii p. 8 no. 29).

(2)

¶ Uṣūl i ʿilm i fizīk: printed (D̲h̲arīʿah ii p. 200).

(3)

Uṣūl i jabr u muqābalah: printed Tihrān (D̲h̲arīʿah p. 179 no. 662).

§ 57. Mīrzā Mūsā K̲h̲ān b. Maḥmūd K̲h̲ān Miftāḥ al-Mulk⁵³ died in 1335/1916–17.

Ḥisāb i jadīd: Tihrān 1300/1882–3 (D̲h̲arīʿah vii p. 8 no. 30).

§ 58. S̲h̲. Yūsuf b. M. Gīlānī.

(1)

Ḥall al-ʿuqūd fī s̲h̲arḥ ḥisāb al-jummal al-maʿhūd (beg. al-Ḥ. l. al-Wāḥid al-Aḥad), composed in 1322/1904 “dar taʿrīf i s̲h̲umārah bā angus̲h̲tān ‘ḥisāb i sar-angus̲h̲tī’ u s̲h̲ināsāʾī i asrār u maʿānī i abjad hawwaz ḥuṭṭī” (in Arabic or Persian?): Majlis 761 (1).

(2)

Muk̲h̲taṣar al-jummal (beg. Baʿd az ḥ. u t̲h̲. bar K̲h̲āliq i Maʿbūd), on the same subject: Majlis 761 (2).

§ 59. S. Ḥusain Quds-al-S̲h̲arīfī, entitled Fahīm al-Sulṭān, b. S. Taqī known as Mustaufī was born on 12 D̲h̲ū ’l-Qaʿdah 1308/19 June 1891.

Ḥisāb i 128 [128 = Ḥusain]: printed (100 pp. D̲h̲arīʿah vii p. 7 no. 23).

§ 60. Appendix

(1)

Alqāb al-rubʿ: D̲h̲arīʿah ii p. 300 no. 1207 (ms. at Najaf in K̲h̲wānsārī’s library).

(2)

Aʿmāl Abī Bakr al-K̲h̲alīl al-tājir al-raṣadī (beg. Faṣl fī qismat al-mut̲h̲allat̲h̲āt al-qāʾim al-zāwiyah wa-hiya mut̲h̲allat̲h̲āt al-uṣūl ʿalā nisbat al-arit̲h̲mātīqī), on dividing right-angled triangles, measuring arcs, pulleys, the laws of reflexion, measuring the heights of inaccessible objects, etc.: Blochet ii 772 (18) (early 17th cent.).

(3)

Arbaʿīn (beg. (in Mas̲h̲had ms. without ḥamdalah) Īn risālah mus̲h̲tamil ast bar c̲h̲ihil suʾāl), answers to forty questions relating to arithmetic: Mas̲h̲had iii, fṣl. 17, mss., no. 9 (not later than 1166/1753).

(4)

Badīʿ al-ḥisāb, a manual of arithmetic and geometry, by Mīrzā Rajab ʿAlī Bēg b. Fāḍil Bēg: Lucknow 1263/1847* (91 pp.); Cawnpore 1267/1851* (78 pp.); place? 1270/1853–4 (Āṣafīyah i p. 806 no. 265).

(5)

Baḥr al-jawāhir (beg. Yagānah K̲h̲udāy rā sitāyis̲h̲), on mathematics and accountancy,⁵⁴ by ʿAbd al-Wahhāb b. M. Amīn S̲h̲āhs̲h̲ahānī ¶ Ḥasanī Ḥusainī Iṣfahānī: D̲h̲arīʿah iii p. 32 no. 63, Maʿārif ii 239 (76 foll. ah 1270/1853–4), Chanykov 125 (ah 1272/1856). Editions: Tihrān 1271/1854–5 (D̲h̲arīʿah, loc. cit.); 1297/1880 (ibid.).

(6)

Basīṭ al-ḥisāb (beg. Sp. u st. i bī-ḥadd wa-lā ʿadd ba-Yazdān i jahān), in a muqaddamah, two bābs and some faṣls, by ʿUbaid Allāh b. S̲h̲. ʿĪsā Ṣiddīqī Suhrawardī Gōpāmawī:⁵⁵ Rāmpūr (Nad̲h̲īr Aḥmad 246).

(7)

Bīkat C̲h̲intāmanī a Persian version:⁵⁶ Browne Suppt. 210 (King’s 66. Palmer p. 25).

(8)

Bisāṭ i g̲h̲arīb, by M. Naṣīr al-Dīn Ḥaidarābādī. Edition: 1291/1874 (Āṣafīyah i p. 806 no. 34, under Riyāḍī, but without mention of the precise subject).

(9)

C̲h̲ihil suʾāl: D̲h̲arīʿah v p. 315 no. 1505 (ms. presented in 1166/1753 to the Imām Riḍā Library at Mas̲h̲had: see no. (3) above.

(10)

Ḍarb i sittīn: Āṣafīyah i p. 818 nos. 143, 111. Edition: 1299/1882 (Āṣafīyah i p. 818 no. 230).

(11)

Dastūr i taʿlīm i ḥisāb i muqaddamātī, by Ḥabīb Allāh Ṣaḥīḥī: printed (D̲h̲arīʿah viii p. 152).

(12)

Durj al-jawāhir wa-burj al-zawāhir (beg. Wa-baʿd īn muk̲h̲taṣarī-st dar ʿilm i misāḥat nām i ū D. al-j … kih az bahr i k̲h̲izānah i … K̲h̲udāwand Amīr i kabīr Isfahsālār i ʿālam … Fak̲h̲r al-Daulah wa-’l-Dīn … Qāmiʿ al-kafarah wa-’l-mus̲h̲rikīn Malik mulūk al-umarāʾ fī ’l-ʿālamīn Pahlawān i Jahān Ṣāḥib-qirān i āfāq … Aʿẓam Tāzīk Abū Bakr Ẓahīr Amīr al-muʾminīn⁵⁷), a short anonymous treatise in three sections dealing with “la métrologie des surfaces, des solides, des mesures sur le terrain, du jaugeage des fleuves, etc.”: Blochet ii 772 (6) (early 17th cent.).

(13)

¶ Fawāʾid al-afkār fī ʿilm al-firkār, by Farīd al-Dīn Aḥmad: Āṣafīyah i p. 818 no. 166.

(14)

Ḥisāb i ʿilmī u ʿamalī, for secondary schools, by Abū ’l-Ḥasan Arjmand Sāwajī (cf. pl. i § 1668 (22)): Lahore a.h.s. 1306/1927* (264 pp.).

(15)

Ḥisāb-nāmah, in seven bābs, by Anand Kāhan b. Hēm Rāj Kāyat’h Guwāliyārī: Lahore Panjāb Univ. (four bābs only, acephalous. N.d. See ocm. x/3 (May 1934) p. 100).

(16)

al-Irs̲h̲ād, by ʿAbd al-Raḥīm b. Aḥmad Ḥusain: Āṣafīyah i p. 818 no. 157 (under Riyāḍī, but without mention of the precise subject).

(17)

Irs̲h̲ād al-ḥussāb, by Abū ’l-Qāsim surnamed (al-mulaqqab bi-) Fuyūḍāt: printed Tabriz (D̲h̲arīʿah i p. 513 no. 2514).

(18)

al-Jabr, by Abū ’l-Ḥasan Arjmand Sāwajī (cf. no. (14) above): Lahore a.h.s. 1306/1927* (194 pp. Mufīd i ʿĀmm Pr.).

(19)

Jabr u muqābalah i qadīm: Āṣafīyah i p. 808 no. 124 (ah 1088/1677).

(20)

al-Jaʿfarīyah fī ’l-masāʾil al-ḥisābīyah (beg. Ḥ. u t̲h̲. K̲h̲udāwandī-rā kih wujūd i har maujūd), in a muqaddamah, five maqālahs and a k̲h̲ātimah, dedicated to S̲h̲āh Sulṭān Jaʿfar by Qawām al-Dīn Ḥusain b. S̲h̲ams al-Dīn M. al-K̲h̲afarī [vocalisation?]: D̲h̲arīʿah v p. 109 no. 455 (where a ms. at Najaf is mentioned).

(21)

K̲h̲ulāṣah i Hās̲h̲imī, by Āqā Hās̲h̲im S̲h̲āh. Edition: 1313/1895–6 (Āṣafīyah i p. 810 no. 263, under Riyāḍī, but without mention of the precise subject or the place of publication).

(22)

K̲h̲ulāṣah i riyāḍīyāt i mutawassiṭah, by Bī-ras̲h̲k Anwārī: printed Tihrān a.h.s. 1326/1947–8 (D̲h̲arīʿah vii p. 227).

(23)

Maʿdin al-ḥisāb, by Bīm [Bhīm?] Rāj: Cambridge 2nd Suppt. 90 (1) (136 foll.).

(24)

Majmūʿah i riyāḍī: printed Persia (Āṣafīyah i p. 820).

(25)

Mak̲h̲zan al-asrār: Āṣafīyah i p. 820 no. 118 (under Riyāḍī, but without mention of the precise subject).

(26)

Mirʾāt al-ḥisāb, by M. Māh [doubtless identical with K̲h̲wājah M. Māh, who wrote a commentary on the K̲h̲ulāṣat al-ḥisāb, for which see pl. ii p. 11 (h)]: Āṣafīyah i p. 820 no. 96.

(27)

Miṣbāḥ al-ḥisāb: Āṣafīyah i p. 820 no. 134.

(28)

Mīzān al-ḥisāb, by Qādir ʿAlī K̲h̲ān. Edition: 1265/1849 (Āṣafīyah i p. 820 no. 59).

(29)

(Muk̲h̲taṣar dar ʿilm i misāḥat) (beg. Sp. i bī-q. u ḥ. i bī-ʿadad i Ḥakīmī kih āsmān i mudawwar bah pargār i qudrat), in eight bābs: Blochet ii 772 (9) (early 17th cent.).

(30)

Muntak̲h̲ab al-ʿajāʾib, on arithmetic, by Gōpāl Sing’h: Siyālkōt [18?*] (C̲h̲as̲h̲mah i Faiḍ Pr. 34 pp.).

(31)

¶ Nādirīyah, apparently⁵⁸ a prose work on arithmetic by M. Jalāl b. Mullā Ḥusain: Rehatsek p. 20 no. 34 (2).

(32)

Nāṣir al-ḥisāb: Āṣafīyah i p. 820 no. 184.

(33)

Qāʿidah i kullīyah, by M. Faiyāḍ al-Dīn K̲h̲ān. Edition: 1285/1868–9 (Āṣafīyah i p. 818 no. 273, under Riyāḍī, but without mention of the precise subject or the place of publication).

(34)

al-Qisṭās al-mustaqīm, on arithmetic, in two rukns each subdivided into maqālahs, defective at both ends in the Mas̲h̲had ms. and therefore lacking the author’s name, but doubtless identical with the work of this title by “Dailamī”, which is one of the sources of the anonymous arithmetical tract preserved in Bānkīpūr xi 1040: Mas̲h̲had iii, fṣl. 17, mss., no. 146.

(35)

(Risālah dar ʿilm i handasah) (beg. al-Ḥ. l. R. al-ʿā.), in a muqaddamah, two maqālahs and a k̲h̲ātimah: Cairo p. 520.

(36)

Risālah dar ʿilm i handasah, in a muqaddamah and two maqālahs: Lahore Panjāb Univ. (62 foll. See ocm. x/3 (May 1934) p. 101).

(37)

(Risālah dar ʿilm i handasah): Lindesiana p. 142 no. 717a (circ. ad 1760).

(38)

Risālah dar ʿilm i ḥisāb, by Ḥasan Tūnī: Kapūrt’halah (ah 1160/1747. See M. S̲h̲afīʿ in ocm. iii/4 (Aug. 1927) p. 5).

(39)

Risālah dar ʿilm i ḥisāb: Leningrad Univ. no. 406 (Salemann-Rosen p. 15).

(40)

Risālah dar ʿilm i ḥisāb (beg. Jamʿ [read Jamīʿ?] i maujūdāt dū qism ast wājib al-wujūd u mumkin al-wujūd): Madrās 502 (ah 1351/1932–3).

(41)

(Risālah dar ʿilm i ḥisāb) (beg…. (at end of muqaddamah) az kutub i mutaqaddimān hīc̲h̲ kitābī muhad̲h̲d̲h̲ab u muk̲h̲taṣar u āsān ba-Pārsī na-yāftam wājib dīdam kih dar-īn bāb risālaʾī bi-pardāzam), in twenty-four bābs: Majlis 640 (9).

(42)

(Risālah dar ʿilm i misāḥat) (beg…. a. b. bi-dān-kih īn kitāb uṣūl i ū bar sih nauʿ ast awwal maʿrifat i ālāt i misāḥat u t̲h̲ānī maʿrifat i as̲h̲kāl u t̲h̲ālit̲h̲ maʿrifat i ṭuruq i misāḥat ammā ālāt i misāḥat sih ast d̲h̲irāʿ …): Blochet ii 772 (10) (early 17th cent.).

(43)

Risālah dar ʿilm i misāḥat (beg. A. b. īn risālah īst dar ʿi. i m. u ān mus̲h̲tamil bar c̲h̲and faṣl ast Faṣl i awwal dar d̲h̲arʿī kih Banī Hās̲h̲im qarār dādah and mas̲h̲hūr ba-gaz i s̲h̲arʿ kih maʿmūl i K̲h̲urāsān-ast): Rieu Suppt. 421 (1) (ah 1233/1818).

(44)

(Risālah dar ʿilm i misāḥat) (beg. al-Ḥ. l. R. al-ʿā. wa-’l-ṣ…. a. b. īn risālah īst dar iṣlāḥ [read iṣṭilāḥ?] i ahl i misāḥat Faṣl dar ān-kih īn sawād u Baṣrah u kuwar i Ahwāz u nawāḥī i Fārs): Blochet ii 772 (11) (early 17th cent.).

(45)

Risālah dar ʿilm i misāḥat: Browne Suppt. 676 (ah 1245).

(46)

¶ (Risālah dar ʿilm i riyāḍī), by ʿAbd al-Wāḥid b. M. Būbakānī: Āṣafīyah iii p. 750.

(47)

Risālah i ʿaqd i anāmil (beg. Baʿd az ḥ. i Parwardgārī kih aṣnāf i alṭāf), a short tract “dar ḥisāb i ʿuqūd i aṣābiʿ ”, probably (ʿalā ’l-iḥtimāl) by S̲h̲araf al-Dīn Yazdī⁵⁹ (for whom see pl. i § 356): Mas̲h̲had iii, fṣl. 17, mss., no. 67, Blochet ii 772 (24) (early 17th cent.).

(48)

(Risālah i ʿaqd i anāmil), on “the manner of counting from 1 up to 10,000 on the fingers, which is not unknown and may be found recorded in the Farhang-i-Jehangyri; a method like this is practised in the bazárs when people wish to strike secret bargains”: Rehatsek p. 220 no. 17 [(5)].

(49)

Risālah i arit̲h̲maṭīqī: Lindesiana p. 114 no. 704 (M. S̲h̲āh’s 18th regnal year [ah 1148–9/1735–6]).

(50)

Risālah i handasah: Āṣafīyah i p. 812 no. 218.

(51)

Risālah i Rafīʿīyah (beg. Īn lauḥ i mustaṭīl kih pargār i nisbat ast … pargār i mutanāsibah a j f a k l ālatī ast mus̲h̲tamil bar dū sitārah), on pargār-s̲h̲ināsī and handasah, by M. Rafīʿ (?): Majlis 177 (defective. 41 foll.).

(52)

Risālah i S̲h̲ihābīyah (beg. al-Ḥ. l. ’l. ʿaṭāʾuhu lā yuʿaddu wa-lā yuḥṣā), dedicated by Maḥmūd b. Badr al-Dīn al-Īrāns̲h̲āhī to a courtier (muqarrab al-mulūk wa-’l—salāṭīn) entitled S̲h̲ihāb al-Daulah wa-’l-Dīn and divided into two bābs, of which the first, in thirty-five faṣls, deals with whole numbers (ṣiḥāḥ) and the second, in twenty faṣls, with fractions (kusūr): Gotha 37 (26 foll.).

(53)

Risālah i tasṭīḥ: Āṣafīyah i p. 810 no. 14.

(54)

S̲h̲abīkah [Risālah i s̲h̲abīkah, sic?], apparently⁶⁰ a metrical work on arithmetic and geometry: Rehatsek p. 20 no. 34 (1).

(55)

S̲h̲ihābīyah: see Risālah i S̲h̲ihābīyah.

(56)

Tabṣirat al-ḥisāb: Lindesiana p. 222 no. 699b (“selections”. ah 1142/1729–30).

(57)

Tabṣirat ūlī ’l-albāb fī ʿilm al-ḥisāb (beg. al-Ḥ. l. al-munazzah ʿan idrāk al-anām [read al-afhām?]): Chanykov 128 (c).

(58)

Taisīr al-maṭlūb fī aʿmāl al-juyūb, by Ḥāfiz Aḥmad: Āṣafīyah i p. 808 no. 158.

(59)

Tas̲h̲rīḥ fī ʿilm al-tasṭīḥ by Ṭāhir al-Ḥusainī: ʿAlīgaṛh Subḥ. mss. p. 22 no. 5.

(60)

Tuḥfat al-majālis: Āṣafīyah i p. 808 no. 212 (under Riyāḍī, but without mention of the precise subject).

(61)

¶ Tuḥfat al-ras̲h̲ād (beg. Maujūdī kih kunhas̲h̲), dedicated by an anonymous author to Bālā-pras̲h̲ād, son of C̲h̲andū La‘l, and divided into six muqaddamahs and six faṣls: Ivanow Curzon 582 (20 foll. 19th cent.).

(62)

Wiṣālīyah, by Ḥamīd al-Wiṣālī: Āṣafīyah i p. 820 no. 172 (ah 1233/1818. Under Riyāḍī, but without specification of the precise subject).

(63)

Zubdat al-ḥisāb, by M. Ṣāliḥ: Lindesiana p. 195 no. 699a (ah 1142/1729).

next chapter: 2 Weights and Measures