From Greek onµeia.


For sadr, cf. 1:373, and p. 53 (n. 361), above.


Ahmad b. 'Ali. Cf. GAL, I, 497 f.; Suppl., I, 910 f. For the date of death indicated in GAL, 622 [1225], there seems to be no better authority than Hajji Khalifah, Kashf az-zunun, IV, 75. The printed edition of al­Buni's Shams al-ma'arif (Cairo, 1921/1903), apparently a reproduction of the edition of 1291/1874, seems to refer to later dates such as 670 (I, 42), and to Ibn Sab'in, d. 669 (1, 51). The mystical pedigree of al-Buni (IV, 103) would also suggest a late seventh [thirteenth] century date for him. However, there is a MS of one of his works in Berlin, No. 4126, dated 669. Thus, he probably lived ca. A.D. 1200. The apparent lack of influence on al-Buni by Ibn 'Arabi would not, however, rule out his flourishing at a later period.


Cf. pp. 183 and 225, below.


The order of the alphabet is according to the numerical values of the letters as employed in the West, which is:

alif 1   y 10   q 100
b 2   k 20   r 200
j 3   l 30   s 300
d 4   m 40   t 400
h 5   n 50   th 500
w 6   s 60   kh 600
z 7   ayn 70   dh 700
h 8   f 80   z 800
t 9   d 90   gh 900
            sh 1000

In the East, 60 is s; 90 is f; 300 sh; 800 d; 900 x; and 1000 gh. Cf. also 1:236, 2:190, 194, above, and p. 220, below, as well as P. Kraus, Jabir Ibn Hayyan, II, 223 ff.


Possibly Ibn Khaldun is thinking of squares designed so that the total of the numbers in the whole figure represents the numerical value of some word such as Allah; cf. below, p. 177 (n. 816). Or, perhaps the word 'adad in 'adad ash-shakl is superfluous and a mistake, and shakl "figure" refers to entire words as they were used in constructing magic squares.


Cf. pp. 268 f., below.


Cf. p. 166, above, and (Pseudo-) Majriti, Ghayah, p. 39.


For this paragraph, cf. ibid., pp. 7 f.


Cf. Bombaci, p. 460.


Cf. Bombaci, pp. 460 f.


Such magic squares, for instance, as the baduh type, where letters take the place of numerals; cf. T. Canaan in Berytus, IV (1937), 100 H: Or, the Allah type, in which the squares may be filled with numerals equivalent in their total to the numerical value of the letters of the word Allah (sixty-six). Cf. Canaan, op. cit., p. 79:

There is also a type of magic square consisting of phrases so arranged; cf., for instance, al-Buni, Lum'ah (Cairo, n.d.), where Qur'an 2.37 (35) is thus distributed:


Al-kawkab, as in C.


GAL, I, 497 f.; Suppl., I, 910, knows no such title, but it may be noted that the Shams al-ma'arif has ten chapters (xxi-xxx) dealing with the beautiful names of God, arranged in anmat.


Cf. p. 88, above.


Bulaq has "that relationship."


Cf. Bombaci, p. 461.


Cf. (Pseudo-) Majriti, Ghayah, pp. 195 ff., 225.


Qur'an17.85 (87).


The following remarks, down through p. 182, are not found in Bulaq. A and C have them on a special inserted sheet. The handwriting on the special sheet in A is quite remarkable in that it seems similar to that used for additions to C.


Cf. p. 167, above.


Sic C and D. The earlier texts have "nature."


Cf. P. 102, above. "And consider it a temptation" appears in C and D.


"Al-Bistami" is added in C and D. Cf. p. 102, above. The story is told in the name of Abu Yazid in Ibn al-Jawzi, Sifat as-safwah (Hyderabad 1855-56/1986-87), IV, 91. In as-Sarraj, Luma', ed. Nicholson (E. J. W. Gibb Memorial Series, No. 22) (Leiden & London, 1914), pp. 324 f., Abu Yazid is repeatedly quoted as being against karamat, but the above story is told in the name of another famous Sufi, Abul-Husayn an-Nuri. For Abu Yazid's negative attitude toward karamat, cf. also al-Qushayri, Risalah, p. 164.


Mutahaffizan? or munhafizan, as in A, and apparently also in B, C, and D?


Wa kayfiyatiha.


The upper text is that of C and D, the lower that of A and B.


Cf. p. 178, above.




Cf. the discussion of as-Sabti's Za'irajah of the World, 1:238 ff., above.


Al-masa'il as-sayyalah. The last word may be derived from the root sa'ala "to ask," or rather be connected with the ordinary word sayyal "fluid, changeable" (cf. Ghayah, p. 3, 1. s), but the precise meaning, though clear from the context, is not known.


This sentence is not found in Bulaq.


The Arabic word used here, to be vocalized muhawwal, must have acquired this meaning from its original meaning "changed (over)." For the Za'irajah table, see folding chart in pocket, end of this vol.


Cf. p. 172, above, and p. 225, below. This sentence is not in Bulaq.


And its attribution to as-Sabti" is found in the margin of C and in the text of D.


As he says himself, Ibn Khaldun did not quite understand the following poem, and our understanding of it cannot be expected to be much better. Probably only its author fully understood it, and even that is not entirely certain. A thorough study of the related literature and some bold interpretations will, I am sure, greatly improve upon the translation given here. The obvious flaws, it is hoped, will challenge some specialist on the history of magic to work on it successfully. At least, I feel that E. Doutte, Magie et religion dans l'Afrique du Nord, p. 581, was unduly pessimistic with regard to Ibn Khaldun's section on the Za'irajah.


I.e., as-Sabti.


The "prayer for a guide" refers to the use of the formula salla llahu 'alayhi wa-sallama, and the "satisfaction" refers to the formula radiya Ilahu 'anhum.


Bulaq has another verse which may have been left out of the later texts by mistake:

Whoever knows how to apply (it) will know his (own) reality

And understand his soul and become a true saint.


Zir is the treble string in musical terminology. Bamm is the bass string, and mathna and mathlath, mentioned later on, are the second and third strings, respectively. For identification of the strings of the lute with the elements, the humors, the planets, etc., cf., for instance, H. G. Farmer, The Minstrelsy of "The Arabian Nights" (Bearsden [Scot.], 1945), p. 14.


Masculine plural, according to Bulaq and the MSS.


The reference seems to be to the Almohad ruler Ya'qub al-Man;ar [1184-1199],under whom as-Sabti is supposed to have lived.


A son to their (the Spanish) Had [?]" looks like a reference to the Hudites of Saragossa, but such a reference would be very difficult to explain chronologically. If, in the following line, the Bana Na$r, the Nagrids of Granada, should actually be meant, the poem would have originated some decades after Ya'qub al-Manlar. But the Na$rids scarcely fit in the context, as far as it can be made out. The meter also seems to be disturbed.


Sic A, C, and D. B: "in the horizons."


Or "d," although the MSS seem to have dhaka "that."


According to Yigat, Mu'jam al-buldan, IV, 307, Kinawah is a Berber tribe and country adjacent to the Ghanah Negroes, which is identical with Qanawah, Janawah = Gnawah "Sudan Negroes." Cf. G. Ferrand, "Le Tuhfat al-albdb de Abu Hamid al-Andalusi al-Garnati," Journal asiatique, CCVII (1925), 285.


The MSS have li faqihim [?].


Yushiffuhu seems a possible reading of the MSS.


Leg. wa yuqna bi-hasriha [?].


In this case, as also on the following pages, the "signs" are mainly zimam numerals. See n. 882 to this chapter, below. Occasionally there are other numerals, letters, and magic signs. As far as I can see, these "signs" do not ever occur in the same combinations in the table.


Awzan "weights" refers to mizdn "scale," which appears in the following verses and for which one may compare the chapter on the "Theorie de la balance" in P. Kraus, Jabir Ibn Hayyan, II, 187 ff.


Cf. p. 228, below.


Or: "and you will hit." Cf. p. 191, 1. 4, below.


Helios, the sun.


Bahram is Mars, and Birjis Jupiter.


The meter of the verse is in disorder.


Ka-dhaka: C and D.




The famous Sufi, d. 246 [861]. Cf. GAL, I,198 f.; Suppl., I, 353.


Cf. 2:187, above.


The reference is to Abu Yazid al-Bistami. Cf. p. 102, above.


Cf. Qur'an 15.87 (87). The first surah is meant.


The famous Sufis, Ma'ruf al-Karkhi, d. 200 or 204 [815/16 or 819/201, and as-Sari as-Saqati, d. 253 18671. Cf. al-Khatib al-Baghdidi, Ta'rikh Baghdad, XII, 199-209; IX, 187-92.

Bulaq corrects "after" to "before."


Cf. p. 102, above.


Abu Bakr ash-Shibli, d. 834 or 335 [946]. Cf. GAL, I,199 f.; suppl., I, 357.


Khullah [?].


I.e., Jupiter. Cf. p. 189, above.


Leg. ghala [?].


Or: "your making (it ready) to accept its sun."


Leg. wa-na'i bihim ila [?].


Referring to the surah? "Houses," of course, could be "fields."


The MSS seem to read something like: bytr wa-tartili haqiqatin . . .


Or Bahlul. Cf. GAL, Suppl., I, 350.


That is, al-Hasan al-Basri. Cf. 2:184, above.


The meter is corrupted.




Bulaq adds: "derived from people who work with the za'irajah and whom we have met." This seems quite a proper statement, in view of the fact that Ibn Khaldun derived his knowledge of the problem discussed in the following pages from Jamal-ad-din al-Marjani, whom he had met in Biskra in 1370/71. Cf. i:xliii and 238 f., above. He mentions the question below, p. 199, and the answer is given below, p. 213.

The table constituting the za'irajah is not reproduced in all MSS and printed texts. It is found in A, E, and MS. Ragib Pala (but not in B, C, and D), in the Turkish translation (Istanbul, 1277), and in the second Bulaq edition of 1284. Since the table requires a special sheet, it can, of course, easily become detached from the copy to which it originally belonged.

The letters evolved in the procedure described by Ibn Khaldun are marked in this translation by boldface type. However, the rationale of their determination and the relationship of the description to the table are by no means clear to me. As in the case of the za'irajah poem, a translation - one might rather call it a transposition of Arabic into English words - is offered here in the hope that it may serve as a basis, however shaky, for future improvement.


The verse is quoted above, 1:240, and below, pp. 211 and 214.


Ghubar means "dust," or rather, in this connection, "abacus," according to S. Gandz, "The Origin of the ghubar Numerals, or The Arabian Abacus and the Articuli," Isis, XVI (1931), 393-424. The ghubar letters are the numerals from one to nine, in a form practically identical with that in which the Arabic numerals are written in the West to this day. This is how they look in MS. B, fol. 224a:











The zimam letters are twenty-seven signs that have the numerical values from one to nine in the units, tens, and hundreds. They are supposed to be of Greek-Coptic origin. Cf. G. S. Colin, "De l'origine grecque des 'chitfres de Fis' et de nos 'chiffres arabes,' " Journal asiatique, CCXXII (1933), 193­215; G. Levi Della Vida, "Numerali Greci in documenti arabo-spagnoli," Rivista degli studi orientali, XIV (1934), 281-83; J. A. Sanehez Perez, "Sobre las cifras RGmies," al-Andalus, III (19,95), 97-125.

The zimam letters have the following forms in MS. B, fol. 225a:


Dawr, one of the technical terms of the Za'irajah, was introduced, though not explained, above, 1:242. It seems obvious that the term somehow refers to the circles of the Zd'irajah, but the usual meaning of dawr is "cycle," not "circle."

Another frequently used technical term, "side of eight," is easily ex­plained by reference to the reproduction of the Zd'irajah.


Sic! Cf. p. 211, below.


The following words, which also introduce the term nash'ah, translated arbitrarily as "growth," are particularly obscure. Possibly the text is in disorder.


Cf. 1:238 (n. 364), above, and for the answer, p. 213, below.


Bulaq adds: "among the letters of the chords, and then, the letters of the questions," which would seem to be out of place.


One would expect a multiple of twelve: seventy-two or eighty-four?


That is, the sum of the letters of the chords and the letters of the question. Cf. p. 211, below.


Sic Bulaq.


Apparently, the quotient and remainder after being divided by twelve.


93 ÷ 12 = 7, remainder 9.


Cf. p. 163, above.


Sic C and D. The other texts have "is the ascendant."


The zimam numeral for 940 looks like the ligature lam-alif, and the Arabic letter t ordinarily has the numerical value of 400.


What is translated here and on the following pages as "indicating that it belongs to," or "belonging to," is the preposition min. It may mean that the mark is taken from the verse of the poem (by Malik b. Wuhayb; see p. 211, below), but this would not seem to make much sense. Without any connection with a letter belonging to the solution of the problem, this min occurs only p. 205 (n. 899a), below, and there it is doubtful whether the poem is meant and whether bayt means "verse" or something else.


This refers to the method according to which the letters evolved by the procedure (and here marked in boldface) are later shuffled so as to produce the rhymed answer to the question. Cf. p. 213, below.


Since "exponent" is one of the meanings of uss in algebra (cf. n. 627 to this chapter, above), it might here be supposed that the relationship is 25 = 32. However, here and on the following pages uss is also a special technical term in the Zd'irajah procedure, and as such was mentioned above, 1:241. Possibly the two here is obtained by subtracting the full number of degrees in the preceding sign from thirty-two. However, this is merely a guess. The original meaning of uss "base" has been retained in the transla­tion, here and on the following pages.


The MSS have "twenty," which is corrected to "ten" in Bulaq.


Cf. n. 896 to this chapter, above.


The listing of the letters on p. 413 shows an m between the r and the following h. That m, however, is superfluous. Cf. also n. 904 to this chapter, below.


 The text is doubtful. Bulaq corrects it to read: "one subtracts four from eight."


Bulaq: "five."


The appearance of two letters at the same time is strange, but, as shown on p. 219, this is what is needed.


Bulaq has "six" and omits "with five" at the end of the next sentence. There is something wrong here. The listing on p. 213 shows an alif after the h. However, not an alif but a w is needed (unless the w has to be sought earlier in the discussion, p. 206 [n. 900], which seems unlikely). The "six" that appears in Bulaq may have something to do with the expected w.


Bulaq: "fourth."


Leg. "twelfth"?


Cf. p. 199 (n. 892), above.


The MSS have nine, but apparently seven, as in Bulaq, is correct.


Bulaq has the required text. The other texts read: "one doubles it."


Bulaq corrects: "One goes up five on the side of eight."


It should be sixteen, unless the sum 6 + 3 + 1 is intended.


Bulaq corrects to "nine."


For the following eight principles, cf. p. 198, above.


Cf. 1:244, above, and pp. 214 and 224, below.


C and D: k.


The letter alif, which one would expect here, is not mentioned.


To the left, the letters of the verse are listed with consecutive number­ing. At the end it seems that there was not enough room for the last four letters on the original table, so they were written to one side. Of course, it should be:

m               38

th               39

l                 40

alif             41


This letter is superfluous; cf. p. 206 (n. 900).


The MSS have a wrong j.


A w is required instead of alif. Cf. n. 904, above.


Cf. p. 201, above.


These letters, then, form the following verse, indicating that the Zd'irajah was invented by Idris, the Qur'inic sage who is identified with the Biblical Enoch. It reads:

Tamhanna ruhu l-qudsi ubriza sirruha
Li-Idrisa fa-starqa bi-ha murtaqa l-'ula.

The Holy Spirit will depart, its secret having been brough forth
To Idris, and through it, he ascended the highest summit.


Bulaq: "They think."


Cf. 1:243, above.


This is the title of a treatise (or a section of a larger work). The author is not known.


This formula, and even more so the one used below, p. 218, is characteristic of esoteric literature. Cf., for instance, the Rasd'il ikhwdn as­safd' and Ibn 'Arabi's Futdbdt. Cf. also 1:194, above.


The text appears to be: bi-tajzi'atin bi-l-kulliyah.

The following listing of the letters contains forty-four letters, and this is the number required, even though Ibn Khaldun refers again to forty­three letters, p. 225, below. Instead of one of the r's, an n should be read .(for the last letter of idhan).


The operation is described again below, pp. 224 f.


Cf. p. 222, below, for an explanation.

928 The numerals appearing in the following table are all zimam numerals. The letters appearing in the right-hand column represent the numerical values from one to seven.


For the following discussion, cf. p. 226, below.


I.e., the seven letters (th, j, kh, z, sh, z, and f) that do not occur in the first surah of the Qur'an.


Sarayan, which in Avicenna's terminology might be translated as diffusion, infiltration, circulation, according to A.-M. Goichon, Lexique de la langue philosophique d'Ibn Sina, p. 150.


The correct text is found in Bulaq. Cf. p. 226, below.


Bulaq may be translated as "I have observed ..." and this may be the correct text.


According According to the MSS, Ibn Khaldun pronounced the word al-qafitus.


Ibn Khaldun apparently did not quote this explanation.


Cf. pp. 172 f., above. Here, however, the sequence of the letters is that used in the East. Furthermore, according to the above-mentioned distribution of the letters among the elements, the letters mentioned here would indicate the combinations fiery-watery, earthy-airy, watery-earthy, and fiery-airy.


"Four," as in Bulaq, may be a necessary correction.


As explained by at-Tahanawi, Kashshaf istilahat al funun, pp. 127 f., s.v. "bast," istintaq means the retransformation of the numerical value of a word into letters. For instance, the numerical value of M (u) h (a) m (ma) d is ninety-two. Thus, its istintaq is s-b. Here, istintaq may refer to the method of the "great calculation," described hereafter.


The "great calculation" consists of counting the numerical values of the letters of the names of the letters of a given word, disregarding the letters of the word as such. For instance, in the name Mubammad, the numerical values of mim ( m-y-m), ha' (h--'), etc., are added up. Cf. C. A. Nallino, Raccolta di scritti editi e inediti, V, 968 (n. s).


Aries is counted in.


al Bulaq: al-qara'in.


Lit., "largest fraction," that is, the fraction with the largest denominator.


A, C, and D have eight. In B, eighty seems to result from a correction of eight.


Again, according to the Eastern value. Forty as an aliquot part of sixty is two-thirds; cf. p. 221, above.


This sentence is not found in B. A "perfect number" is one that is equal to the sum of its aliquot parts (including one). Six, thus, is the sum of one, two, and three.


This might refer to the operation called base.


Cf. p. 214, above.


He might be identical with the mathematician Muhammad b. Ibrahim, d. 715 [1315]. Cf. GAL, Suppl., II, 378, though proof is needed for this identification.


Cf. pp. 214 f., above.


Cf. pp. 172 and 183, above.


For the following operation, cf. pp. 217 f., above. 226


Hukmi, rather than hikmi "philosophical."


This paragraph is not in Bulaq. C has it in the margin.


The reference appears to be to 1:248 f., above.