239a

Cf. 2:423, below.

240

Cf. al-Bukhari, Sahih, ed. Krehl (Leiden, 1862-1908), I, 4.

241

Cf. ibid., 1, 6; IV, 490. Cf. also Concordance, III, 78b. Cf. p. 201, below.

242

Cf. al-Bukhari, Sahih, I, 4.

243

Qur'an 73.5 (5).

244

Qur'an 13.33 (33); 39.23 (24), 36 (37); 40.33 (35).

245

This does not refer to Muhammad's decision in the quarrel over the honor of replacing the Black Stone. Legend tells that he had it placed upon a garment and lifted into position by several rival groups. It refers to Mubam­mad's carrying ordinary stones to help with the restoration. Cf. al-Bukhari, Sahih, I, 400. For variations in the story, see, for instance, Ibn Kathir, Bidayah, II, 287 f., or Ibn Sayyid-an-nas,' Uyun al-athar (Cairo, 1356/1937­58), I, 44 f., where we also find the story of the wedding. Cf. also T. Andrae, Die Person Muhammeds . . . , pp. 124 ff.; 1. Goldziher in EI, s.v. '-Isma.'

246

Cf. al-Bukhari, Sahih, I, 219; IV, 444 f. Cf. also Handbook, p. 155b.

247

al-Bukhari, Sahih, I, 7 f., and, for further references, Handbook, p. 97. Cf. also below, 3:42.

248

Cf. also pp. 322 and 414, below.

249

Cf Concordance, I, 291a. Since the reference to "wealth" was inappropriate in the case of Muhammad, "wealth" has been explained to mean "great number," or "protection, power, influence."

250

Abu 'Abdallah Muhammad b. 'Abdallah, al-Hikim an-Nisiburi, 321­405 [933-1014]. Cf. GAL, I, 166; Suppl., I, 276 f. Cf. his Mustadrak 'ala 1-Sahihayn [of al-Bukhari and Muslim] (Hyderabad, 1334-42/1915-29), II, 561.

251

The term ahsdb is used in this story in al-Bukhari, Sahih, III, 215; Concordance, I, 464b, II, 32 f.

252

 The text from here to p. 192, 1. 22, is found in C on an inserted slip.

253

Khawariq are things that "break through" the ordinary course of affairs. Mu'jazah is "miracle" in the sense of something done by a prophet in confirmation of his mission. The terms may be used as synonyms, but, in general, "wonders" are considered inferior to "miracles," where both terms occur together.

254

Cf. 2:372, below, and Rasa'il Ikhwan as-safa', III, 319 f.

255

Tahaddi, literally, means that the prophet seeks the people out, that he "goes to them and challenges them (tahaddahum)," by announcing his impending miracle and daring them to perform something similar. Ibn Khaldun explains the term as "the claim made in advance that the miracle will happen in agreement with the prophetic announcement"; cf. 3:100 and 170, below. Instead of "advance challenge," another suitable translation would be "advance information." Already in his Lubab al-Muhassal (Tetuan, 1952), p. 111, Ibn Khaldun used the same definition of "miracle" he repeats here at greater length.

For the problem of tahaddi in Muslim theology, see, for instance, al­Bagillani, Tamhid, pp. 114, 121 f., 126-29; idem, I'jdz al-Qur'an (Cairo, 1315/1898), pp. 116 f.; Imam al-Haramayn, Irshad (Cairo, 1369/1950), p. 313; Ibn lIazm, Faf (Cairo, 1317-21), V, 2 and 7 f.

255a

Following de Slane's doubtful suggestions, we might translate the very difficult passage as follows: "Therefore, the latter constitutes part of the miracle, or, to use the expression of speculative theologians, is its specific quality. It is one, for (speculative theologians) hold that (oneness) is the meaning of essential." There are, however, more objections to this transla­tion than to the one given in the text.

256

Ibrahim b. Muhammad al-Isfarayini, d. 418 (10271. Cf. GAL, Suppl., 1, 667; Abu I-Muzaffar al-Isfarayini, at-Tabcir fi d-din (Cairo, 1359/1,940), p. 119. Cf. also pp. 223, 393, and 3:100, below.

257

Cf., for instance, al-Isfarayin , p. 104.

258

Cf. 3:167, below.

259

Cf. 3:279, below.

259a

Cf. al-Bukhari, Sahih, III, 391; IV, 419.

260

The text from here to p. 194,1. 3, below, appears (to my knowledge) only in MS. Ragib Pala 978, fol. 47a (and in the Paris edition). In the MS. Ragib Pala, the text is contained in a marginal note accompanied by the remark: "I found it this way in the manuscript written in the handwriting of the excellent Qatari, following the autograph ('ala khatt) of the author." Cf. p. xcix, above, and p. 230, below.

261

Matluw "recited"; cf. pp. 260, 437, and 3:113, 284, below.

262

It should not be forgotten that i'jax "inimitability" is formed from the same root as mu jixah "miracle." Both convey the idea of something that ordinary mortals are too weak to achieve, and by which they are confounded.

263

The hadith qudsi "holy traditions." Cf. S. M. Zwemer in Der Islam, X11I (1923), 53-65, and L. Massignon, Essai sur les origines du lexique technique de la mystique musulmane (2d ed.; Paris, 1954), pp. 135 f. Cf. also 3:88, below.

264

Qur'an 75.16 f. (16 f.).

265

Qur'an 15.9 (9).

266

Qur'an 8.63 (64).

267

Cf. Issawi, pp. 164 f. For the discussion that follows here, see below, 2:419 ff. and 3:70 ff.

268

For the use of such formulas to introduce the communication of esoteric knowledge, cf. n. 925 to Ch. vi.

269

Lit., "horizon."

270

Cf. Issawi, pp. 170-74. 195

271

Cf. P. 215, below.

272

A1-Hiss al-mushtarik: koinh aisqesiz. Cf. A.-M. Goichon, Vocabulaires compares d'Aristote et d'Ibn Sina (Paris, 1939), p. 7; S. van den Bergh (tr.), Averroes' Tahafut al-Tahafut (E. J. W. Gibb Memorial Series, N.S. No.19) (London, 1954), I, 333 ff.

273

Cf. A.-M. Goichon, p. 40, and F. Rahman, Avicenna's Psychology (Oxford & London, 1952), pp. 79 ff.

274

That is, the lower human powers.

275

Tasawwur and tasdiq. Cf. A.-M. Goichon, Lexique de la langue philosophique d'Ibn Sina, pp. 191 ff., 179 f.

276

Cf. Bombaci, p. 444.

277

The term wijdan, with the adjective wijdani, is used repeatedly by Ibn Khaldun; see below, pp. 207, 230, 2:48, 3:71 f., 83, 85, 89, 101, 155, 252, 295, and 360. Basically, Ibn Khaldun's understanding of it corresponds to the one commonly found in philosophical literature. For instance, al-Iji in his commentary on the Mukhtasar of Ibn al-Hajib, one of the legal works that ibn Khaldun studied in his boyhood, distinguishes five types of perceptions: (1) Internal observations, called wijdaniyat, i.e., those not requiring the services of the intellect, such as hunger, thirst, and pain; animals also possess this type of perception. (2) Primary (intellectual) observations. (3) Observations by means of the senses. (4) Observations by experience. And (5) continuous (traditional) knowledge. Cf. al-Iji, Sharh `ala Mukhtasaral-Muntaha li-Ibn al-Hajib (Constantinople, 1307/1889-90), p. 19.

Ibn Khaldun thus uses the term for "intuition, observation by means of inner, emotional feeling." It should be noted, however, that he also uses wijdan parallel with wujud "existence" in 'Ibar, V, 437; VI, 7. The meaning of "existing" for wijduni may, for instance, apply below, n. 1027 to Ch. vi. Cf. also 2:340, below.

278

Cf. M. Schreck in EI, s.v. "Barzakh," and 3:69 ff., below.

279

 Cf. 3:39, below.

280

Etymology is known to be one of the weakest spots in ancient and medieval scholarship. Actually, why appears to be related to Aramaic hwy "to show, inform" and to Palmyrenian words such as mwh' and twhyt.

281

Cf. Ibn Hajar, Tahdhib, II, 161 f. Cf. also p. 185, above.

282

Comprehension, in this case, was an action of the past that happened but once, hence the perfect. Whereas in the other case it was a continuous and repeated action in the past, hence the present. This distinction is, of course, based upon the supposed meaning of Arabic tenses, which do not correspond exactly with English tenses. The Arabic "perfect" is a completed action; the Arabic present/future, for which Arabists use the more correct term "imperfect," may refer to repeated action.

283

For this quotation from the Qur'an and the following two traditions, seep. 185, above. Cf. also 3:73, below.

284

Cf. 3:39, below.

285

Cf. also p. 261, below.

286

Cf. 3:73, below.

287

The term al-mufassal used by Ibn Khaldun refers to the surahs near the end of the Qur'an, beginning with surah 49 (or, according to certain other scholars, with some surah close to it). Cf. as-Suyuti, Itqan (Cairo, 1317/1899), 1, 65 (Ch. 18).

288

Qur'an 5.3 (4-5).

289

Surahs 55, 51, 74, 93, and 96, respectively.

290

The MSS add "not." Bulaq applies the necessary correction.

291

Cf. (Pseudo-) Majriti, Ghayah, ed. H. Ritter (Leipzig & Berlin, 1933), p. 84.

292

For muwazanah, a term of literary criticism, seen. 1576 to Ch. vi.

293

Ibn Khaldun seems to be thinking of Muhammad' s statement about someone belonging to the brotherhood (ikhwan) of the soothsayers. Cf. Concordance, I, 35b. Since Muhammad himself used saj' "rhymed prose" in the Qur'an, there was a tendency among Muslim scholars not to regard it as the exclusive property of soothsayers. See, for example, Majd-ad-din Ibn al-Athir, Nihayah, IV, 43.

294

The story of Ibn Sayyid is found in al-Bukhari, Sahih, II, 261 f.; IV, 153. Cf. also Concordance, II, 61a, 11. 12 f. Nothing definite is known about Ibn Sayyid who is said to have become a Muslim and to have died in 63 [682]. Cf. Lisan al-'Arab, IV, 251, and G. Lev_,i Della Vida, Annales de I'Institut d'Etudes Orientates, XII (Algiers, 1954) p. 27 (n. 60).

295

Cf. Qur'an 15.17 ff. (17 ff.); 37.7 ff. (7 ff.).

296

Cf. also p. 224, below.

297

Cf. Bombaci, p. 445.

298

Cf. n. 277 to this chapter, above.

299

For Umayyah b. Abi s-Salt, a famous poet of Muhammad's time, cf. GAL, I, 27 f.; Suppl., 1, 55 f. For Ibn Sayyad, cf. n. 294, above. For the pseudo-prophet Musaylimah, cf. F. Buhl in EI, s.v. "Musailima."

300

For the pseudo-prophet Tulayhah, cf. V. Vacca in El, s.v "Tulaihah." For Qarib, cf. Ibn Hajar, Isabah (Calcutta, 1856-73), III, 434 H:, No. 1164.

301

Ta'bir specifically is the interpretation of dreams, to which a special discussion is devoted, 3:103 ff., below.

302

Cf. al-Bukhari, Sabih, IV, 348 ff.; Concordance, II, 409b, 11. 21 f.; I, 296b, last line. Cf. also, for instance, Ibn Abi Zayd, Risalah, pp. 322, 326. Fractions mentioned by Ibn Hazm, Fasl, V, 20, are one twenty-sixth, one forty-sixth, and one-seventieth. Cf. also 3:103 and 107, below.

303

Cf. al-Bukhari, Sahih, IV, 346. Cf. also 3:103, below.

304

  For the following discussion, cf. 3:104 ff., below.

305

Cf. also p. 74, above.

306

Cf. p. 196, above.

307

Leg. alladhi.

308

Adghath al-ahlam. Qur'an 12.44 (44); 21.5 (5). Cf. also 2:420 and 3:105, below.

309

The references in the Sahih of al-Bukhari seem to mention only a twofold division of dreams, those from God and those from Satan. But Cf. Concordance, I, 296b, last line.

Polydore Virgil, who was born in the century in which Ibn Khaldun died, distinguished in his De prodigiis three varieties of dreams: divine, human, and daemonic. Cf. D. Hay, Polydore Virgil (Oxford, 1952), p. 41.

310

The Ghayat al-hakim ascribed to the famous tenth-century Spanish scientist Maslamah b. Ahmad al-Majriti. Cf. GAL, I, 243; Suppl., I, 431 f. Modern scholarship has shown that the Ghayah (on sorcery) and the Rutbat al-hakim (on alchemy) are pseudepigraphical. Ibn Khaldun makes much use of these works later on in his discussion of the two sciences mentioned. The reference here is to Ghayah, ed. H. Ritter (Studien der Bibliothek Warburg) (Berlin, 1933), pp. 187 ff. The term halumah "dream word" as such is not mentioned there. It is derived from Aramaic halomd "dream" (rather than from the Hebrew form haloma). Cf. also M. Plessner in Der Islam, XVI (1927), 95.

311

These magical words seem to be Aramaic and may have sounded some­thing like this: Tmaggesh b'eddan swadh (?) waghdhash nawmtha ghadhesh, "You say your incantations at the time of conversation (?), and the accident of sleep happens." The "perfect nature" is also discussed at length by Fakhr-ad-din ar-Razi, as-Sirr al-maktzum; cf. 3:164, below. Cf. also H. Ritter, in Vortrage der Bibliothek Warburg 1921-1922, pp. 121 f.

312

Cf. n. 471 to Ch. vi, below.

312a

Unless one reads kanat, instead of kana, the only possible antecedent would be "preparedness," but it ought to be "soul," as indicated above.

313

Qur'an 6.18 (18), 73 (73); 34.1 (1).

314

Cf. also 2:201, below.

315

Arabic kashf, a common term of mysticism (and metaphysics), for Ibn Khaldun a crucial concept in the discussion of these subjects.

316

Lit., "veiled." Cf. preceding note.

317

Cf, p. 196, above.

318

The reference appears to be to pp. 203 f., above.

318a

For takhabbata "to become possessed," cf. Qur'an 2.275 (276), and A. Spitaler, Orientalistische Literaturzeitung, XLVIII (1953), 535.

319

III, 347 ff.

320

For Shiqq and Satib, cf. G. Levi Della Vida in EI, sm. "Satih." The strange tribal connections of these mythological figures, which make Mazin a "son" of Ghassin, were found by Ibn Khaldun in al-Mas`udi, op. cit., III, 364. For the dubious tribal genealogy of Shiqq, cf. also Ibn Hazm, Jamharat ansab al-'Arab, pp. 365 f.

321

Cf. Ibn Hisham, Sirah, pp. 9 ff: Cf. also 2:202, below.

322

Cf. al-Mas`udi, op. cit., 1:217; 11, 228. For the Mobedhan, see n. 25 to p. 80, above.

323

The verse is by 'Urwah b. Hizam al-'Udhri (GAL, Suppl., I, 81 f.), who is also the author of the following two verses. Cf. al-Mas'udi, op. cit., III, 353, where the name of the poet is not given; Ibn Qutaybah, Kitab ash­shi'r wa-sh-shu'ara', ed. M. J. de Goeje (Leiden, 1904), pp. 396 f.; Abul-Faraj al-Isfahani, Kitab al-Aghani (Bulaq, 1285/1868), XX, 154 f.; Lisan al-'Arab, XI, 142; * Ibn al-Jawzi, Dhamm al-hawa (Cairo, 1962), pp. 408 fr.

324

Cf. the preceding note and T. Noldeke, Delectus veterum carminum arabicorum (Berlin, 1890), p. 8. Cf. further al-Mas'udi, op. cit., VII, 353 f.; Rasa'il lkhwan as-Safa', III, 261; as-Sarraj, Masari' al-'ushshaq (Constantinople, 1301), p. 209 f.; al-Kutubi, Fawat al-Wafayat (Cairo, 1961-53), II, 72 f.

325

This is the vocalization of MSS. B, C, and D. Ibn Khaldun derived the names from al-Mas'udi, op. cit., III, 353.

326

Cf. (Pseudo-) Majriti, Ghayah, pp. 139 f. (See n. 310 to this chapter, above.) A similar magical practice is ascribed to the Sabians of Harran. Cf. Ibn an-Nadim, Fihrist, p. 321 (of the Flugel ed.); pp. 446 f. (of the Cairo ed.); A. Mez, Abulkasim, ein bagdader Sittenbild (Heidelberg, 1902), p. tvn; C. G. Jung, in Papers from the Eranos Yearbooks (Bollingen Series XXX), Vol. 2: The Mysteries (New York, 1955), pp. 306 f.

327

Cf. n. 1509 to Ch. vi, below.

328

Mujahadah "exertion."

329

Bulaq adds: "and nourish the soul with dhikr exercises, so that it may grow stronger." Ibn Khaldun probably omitted this statement, because it belonged rather to Sufism, mentioned below.

330

Lit., "taste." Cf. n. 463 to Ch. vi, below.

331

Cf. n. 471 to Ch. vi, below.

332

Cf. 8:102 and 179 f., below.

333

Abdallah ('Ubaydallah) b. Abi Zayd, 316-386 1928-9961. Cf. GAL, I, 177 f.; Snppl., I, 301 f., one of Ibn Khaldun's famous and oft-quoted school authorities. Cf. p. 189, above.

334

Cf. the references in Handbook, p. 234b, where muhaddath "spoken to" is translated "inspired." Cf. also 2:203, below.

This tradition, as well as the stories of Sariyah and 'A'ishah, were also mentioned by al-Ghazzali, Ihya', p. 21.

335

Cf. at-Tabari, Annales, I, 2701. Ibn Khaldun refers to the story again in the Autobiography, p. 165.

336

Cf. Malik, Muwatta', in the Kittb al-aqdiyah (Tunis, 1280/1863-64), p. 299. It is interesting to note how frankly Ibn Khaldun expresses himself in paraphrasing the case. In the text of the Muwatta', Abu Bakr makes the suggestion in a very guarded form, and 'A'ishah, of course, refuses to take advantage of it.

337

Qur'an 5.54 (59); 57.21 (21); 62.4 (4).

338

Cf. 3:259, below.

339

Cf. 3:258 fl., below.

340

Arabic khatt ar-raml. Cf. E. Doutte, Magie et religion dans l',Afrique du Nord (Algiers, 1908), pp. 377 ff.; O. Rescher in Der Islam, IX (1919), 37; P. Tannery, "Le Rabolion," in his Memoires scientifiques (Toulouse & Paris, 1920), IV, 297-411. The section dealing with Arabic geomancy in Tannery's posthumous paper was compiled by B. Carra de Vaux.

341

It follows that these are the figures used in geomancy:

Instead of the two dots, a line may be used. For the names of the figures in Arabic and the various European languages, see the comparative table in Tannery, op. cit., IV, 410 f.

342

The following discussion, down to p. 132, 1. 19, appears in B in the margin and on an inserted slip. It is inserted in the texts of C and D. The older texts, Bulaq, A, and E, and the original text of B, have the following sentence in place of the above sentence: "They are based upon arbitrary conventions and wishful thinking. Nothing about them is proven." Then the text found below, p. 229, II, 10-22, is given, followed by an explanation of the tradition which reads: " `And whoever concurs with the writing of that prophet-this is it.' He is right in view of the fact that the writing was supported by the revelation that came to that prophet whose custom it was to have the revelation come to him while he was writing. Were he to take it from the writing without the concurrence of revelation, he would not be right. This is the meaning of the tradition. And God knows better."

342a

Dama'ir "the unconscious."

343

The same argument is referred to below, 2:320 and 3:267.

344

Abu 'Abdallah Muhammad (b.'Uthman?) az-Zanati, whose dates appear to be uncertain. Cf. Tannery, op. cit., IV, 300; GAL, Suppl., II, 1037 (No. 5), and 1041 (No. 40). He is the great authority on geomancy now as he was in the past, and his works are often reprinted under titles such as al-Aqwal al-mardiyah fi l-ahkam ar-ramliyah (Cairo, 1326/1908-9) and Kitab al-Fasl fi usul'iim ar-raml (Cairo, 1280/1863-64), etc. Their genuine­ness remains to be investigated.

345

Like the Biblical Daniel, the Quranic Idris is among the most favored names for attributing authorship of magical works. He is probably correctly identified with the Biblical Enoch, and, incorrectly, with Hermes; cf. 2:367 f., below. Cf., for instance, 3:213 (n. 921), below. The following tradition is referred to Idris in Ibn Kathir, Bidayah, I, 99. The sequence "Daniel or Idris" is that found in C and D.

346

It may be possible to translate, "and whose writing agrees with (the writing of that prophet) But the above translation seems preferable, and the difference in meaning is not great. A variant of the tradition is quoted in Majd-ad-din Ibn al-Athir, Nihayah, I, 338. It reads: "and whoever agrees with his writing knows as much as he does."

347

Qur'an 2.253 (254).

348

Cf. also the tradition quoted below, 2:401. For the "Israelite Stories," see n. 47 to Ibn Khaldun's Introduction, above.

349

The rest of the paragraph is found only in the MS. Ragib Pasa 978, fol. 56b (as well as in the Paris edition). The scribe of the MS again states that he derived the note from the MS of al-Qatari. Cf. p. 192, above, and n. 260 to this chapter. Though it did not enter the mainstream of the Muqaddimah tradition, it is undoubtedly by Ibn Khaldun.

350

Qur'an 37.164 (164).

351

Cf. nn. 342 and 346 to this chapter, above.

352

That is, heaps of grains.

353

That is, one or two dots.

354

The rules governing this procedure vary. If there is one dot next to either one or two dots, it may result in one dot for the new combination, and so on, as explained by de Slane, Les Prolegomenes d'Ibn Khaldoun, (n. 1).

355

The procedure described leads to a figure such as we find reproduced (from Western texts) in Tannery, Memoires scientifiques, IV, 345 f. For instance:

	.	..	..	.	..	..	..	.
	.	..	.	..	..	.	.	..
	..	.	..	..	.	..	..	..
	..	.	..	..	..	..	.	.
	.		.		..		.
	.		.		..		.
	.		..		..		..
	.		..		..		..
	.				.
	.				.
	..				..
	..				.
				.
				.
				.		..
				.		.
						.
						..

Ibn Khaldun, however, does not say anything about triangular houses for the last two combinations.

356

Cf. p. 216, above.

357

Cf. Bombaci, p. 446.

358

Qur'an 2.142 (136), 213 (209), etc.

359

The meaning of the word nim (or whatever the consonants n y-m may signify) is not clear. There are many possibilities, none of them convincing. The MSS of the Muqaddimah practically never vocalize it (except D, in the passage below, p. 238). Ibn Khaldun was probably not sure of the pro­nunciation himself.

The pseudo-Aristotelian Politics, or Secretum secretorum, contains something quite similar. Cf. the edition of the Arabic text by 'Abd-ar-Rahman Badawi, pp. 152 ff., and the English tr. in Roger Bacon, Opera, ed. R. Steele, V, pp. LX f. and 250 f. However, no mention whatever is made in the Secretum of hisab an-nim. A description not identical with Ibn Khaldun's, but which comes rather close to it, appears after the Secretum in the Istanbul MS, Suleymaniye, 782, fols. 44b and 45b. There are two sets of letter arrangements in that MS. One, on fol. 45b, corresponds to that mentioned by Ibn Khaldun as going back to Ibn al-Banni' (p. 238, below). The other is different from that mentioned by Ibn Khaldun below, pp. 236 f. (De Slane states that he found a reference to the hisab an-nim in the margin of one of the Paris MSS of the Secretum.)

Greek texts dealing with the procedure are ascribed, not to Aristotle but to Pythagoras. Cf. P. Tannery, "Notices sur des fragments d'onomato­mancie arithmetique," Notices et Extraits des Manuscrits de la Bibliothique Nationale, XXXI 2 (1886), 231-60, esp. pp. 248 fl. In Arabic tradition, Ptolemy is credited with a book on "Which of two adversaries will be successful"; cf. Ibn an-Nadim, al-Fihrist, p. 268 (of the Flugel ed.); p. 375 (Cairo ed.).

For fifteenth-century Arabic monographs on the "Calculation of Victor and Vanquished," cf. GAL, Suppl., I, 536 (n. 2), and the Durr al-matlub fi sirr al-ghalib wa-l-maghlub by Yusuf b. Qorqmas Amir al-hajj al-Halabi, which deals with the Aq-Qoyunlu and Qara-Qoyunlu, MS. Nuru Osmaniye, 4901. On fol. 10b of the MS, the verses quoted by Ibn Khaldun are found. They are not found in the MS of the Secretum mentioned above. Numerous other manuscripts on the subject are listed, for instance, by G. Vajda, Index general des manuscrits arabes musulmans de la Bibliotheque Nationale de Paris (Paris, 1953), p. 359.

360

The use of sh for 1,000 is characteristic of the Muslim West. In the East, gh is used. Cf. n. 809 to Ch. vi, below.

B says at the end of the sentence that "gh is the last letter of the numerical alphabet."

361

The fractional remainder of 20, 200, or 2,000 divided by 9 is always two; of 30, 300, or 3,000 always three, and so on. Two is also the "(unit) number" of 20, 200, etc.; three of 30, 300, etc.

362

The editor of Bulaq, Natr al-Huruni, calls attention to the fact that Ibn Khaldun had just said that there are no letters expressing numerals higher than 1,000.

363

Ahmad b. Muhammad [ca. 1285-1321]. Cf. GAL, 11, 255; Suppl., II, 363 f. As a mathematician he is quoted later on by Ibn Khaldun; cf. 3:121, 123, 137, below. His role as a magician was a legend developed after his death; cf. H. P. J. Renaud in Hesperis, XXV (1938), 21.

364

Cf. 3:182 ff., below. Ibn Khaldun was initiated into the use of the za'irajah during his stay in Biskra in 1370/71, at least as far as the question that he discusses 3:197 ff., below, is concerned. He discussed it with Jamal-ad-din 'Abd-al-Malik b. `Abdallah al-Marjani. Al-Marjini himself informs us of this in his work on the za'irajah which was discovered and discussed by H. P. J. Renaud, "Divination et histoire nord-africaine au temps d'Ibn Khaldun," Hesperis, XXX (1943), 213-21.

The origin of the word za'irajah has not yet been satisfactorily explained. It has been suggested correctly that it is related to Persian zd'icha "horo­scope, astronomical tables," (cf. zij, 3:135 below), but the r seems to be an arbitrary addition, possibly by combination with da'irah "circle"?

365

His name was Muhammad (Ahmad) b. Masud. Cf. GAL, Suppl., I, 909. He is a rather shadowy figure, and GAL puts him in the late thirteenth century, whereas according to Ibn Khaldun he lived at the end of the twelfth. Ibn Khaldun is possibly closer to the truth; cf. nn. 845, 846, to Ch. vi, below. Bulaq adds "Sidi Ahmad" to his name, thus confusing him with a famous saint, Ahmad b. Jafar, who lived from 540 to 601 [1145/46 to 1204/5]. Cf. M. Ben Cheneb in EI, s.v. "al-Sabti." (Cf. also GAL, 2d ed., I, 655.)

366

He ruled from 1184 to 1199. Cf. also nn. 845 and 846 to Ch. vi, below.

367

The table was reproduced by Ibn Khaldun below in connection with his extensive discussion of the za'irajah. See pls. i and n and chart in end pocket, Vol. 3.

368

Cf. n. 882 to Ch. vi, below.

369

This difficult expression seems to refer to the innermost circle, which contains references to such subjects as horses and warfare.

370

The tables published in the first volume of the 'Ibar and in the Turkish translation of the Muqaddimah, as well as those in A and E, have only 128.

371

The verses do not appear on the table, but they are quoted by Ibn Khaldun below, 3:183 ff.

372

He lived in the early twelfth century (453-525) [1061-1131]. Cf. 'Ibar, VI, 228; de Slane (tr.), II, 169. He was a friend of Ibn Bajjah (Avempace); cf. Ibn Abi Usaybi'ah,' Uyan al-anba', II, 63. Cf. also at-Safadi, Wafi, ed. S. Dedering (Damascus, 1953), III, 325 f., and D. M. Dunlop, in The Islamic Quarterly, II(1955), 101-4.

B has a marginal note in this place by a Maghribi scholar, Abul-Fadl b. al-Imam, who calls attention to the fact that Malik lived before as-Sabti, the reputed inventor of the za'irajah. (There seems to be some confusion of za'irajahs in general, that existed long before, and the particular Za'irajah of the World discussed here.) The time interval between the two men makes it unlikely that as-Sabti was the inventor, and its invention should rather be ascribed to Idris. (Cf. n. 921 to Ch. vi, below.) The teacher of the writer of the note, a certain Abu l-Qasim b. Dawud as-Salawi (?), maintained this.

The verse is quoted again, 3:211, 214, and 224, below. It occurs also in a za'irajah ascribed to Ibn 'Arabi; cf. the Princeton MS, 5472 H, fol. 7b.

373

The word discussed here is uss "base." It has a specific meaning in algebra-cf. n. 627 to Ch. vi, below-but still it is difficult to assume that instead of to "astrologers," Ibn Khaldun refers here to "arithmeticians," even though the word he uses (hussab) might mean the latter rather than the former. For the use of uss in the za'irajah, cf. 3:203 ff., below. The only meaning the above definition of the term would seem to suggest is that, in the za'irajah, uss refers to the number of degrees counting back to the beginning of the sign of the ascendant (or to some earlier sign), whereas in astronomy uss means the number of degrees to the end of the sign. This, however, is so far mere speculation.

374

Cf. p. 233, above.

375

It seems doubtful which passages Ibn Khaldun has in mind here.

376

At-Tustari, a Sufi of the ninth century. Cf. GAL, Suppl., I, 333.

377

Cf. 3:213 f., below.

378

In modern symbols, x being the number of fowls, y the number of dirhams:

y•1/8 = 1

y + y•1/8 = x

x = 8 + 1.

379

Mutabaqah "conformity, agreement," is an important concept in Ibn Khaldun's epistemology. Cf. also, for instance, 3:251, below.

In another application, the term also plays an important role in Ibn Khaldun's definition of rhetoric. Cf., for instance, 3:335, below.

380

Qur'an 2.216 (213), 232 (232); 3.66 (59); 24.19 (19).