|
805 |
From Greek onµeia. |
806 |
For sadr, cf. 1:373,
and p. 53 (n. 361),
above. |
807 |
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. |
808 |
Cf. pp. 183
and
225,
below. |
809 |
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. |
810 |
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. |
811 |
Cf. pp. 268 f.,
below. |
812 |
Cf. p. 166, above,
and (Pseudo-) Majriti, Ghayah,
p. 39.
|
813 |
For this paragraph, cf.
ibid.,
pp. 7 f. |
814 |
Cf. Bombaci, p. 460. |
815 |
Cf. Bombaci, pp. 460 f. |
816 |
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: |
817 |
Al-kawkab,
as in C. |
818 |
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. |
819 |
Cf. p. 88, above. |
820 |
Bulaq has "that relationship." |
821 |
Cf. Bombaci, p. 461. |
822 |
Cf.
(Pseudo-) Majriti, Ghayah, pp.
195 ff.,
225. |
823 |
Qur'an17.85 (87). |
824 |
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. |
825 |
Cf. p. 167, above. |
826 |
Sic
C and D.
The earlier texts have "nature." |
827 |
Cf. P. 102, above. "And consider it a temptation" appears
in C and D. |
828 |
"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. |
829 |
Mutahaffizan?
or
munhafizan,
as in A,
and apparently also in B, C, and D? |
830 |
Wa kayfiyatiha. |
831 |
The upper
text is that of C and D, the lower that of A and B. |
832 |
Cf. p. 178, above. |
833 |
Bi-khalq. |
834 |
Cf. the discussion of
as-Sabti's
Za'irajah of the World,
1:238
ff., above. |
835 |
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. |
836 |
This sentence is not found
in Bulaq. |
836a |
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. |
837 |
Cf. p. 172,
above, and p.
225,
below. This sentence is
not in Bulaq. |
838 |
And its attribution to as-Sabti" is found in the margin
of C and in the text
of D. |
839 |
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. |
840 |
I.e., as-Sabti. |
841 |
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. |
842 |
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.
|
843 |
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. |
844 |
Masculine plural, according to
Bulaq and the MSS. |
845 |
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. |
846 |
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. |
847 |
Sic A, C, and D. B: "in the horizons." |
848 |
Or "d," although the MSS seem to have
dhaka "that." |
849 |
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. |
850 |
The MSS have li faqihim [?]. |
851 |
Yushiffuhu
seems a
possible reading of the MSS. |
852 |
Leg. wa yuqna
bi-hasriha [?]. |
853 |
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. |
854 |
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. |
855 |
Cf. p. 228,
below. |
856 |
Or: "and you will hit." Cf. p. 191,
1.
4, below. |
857 |
Helios, the sun. |
858 |
Bahram is Mars, and Birjis Jupiter. |
859 |
The meter of the verse is in disorder. |
860 |
Ka-dhaka: C and
D. |
861 |
Mu'assalan. |
862 |
The famous Sufi, d. 246 [861]. Cf. GAL, I,198
f.; Suppl., I,
353. |
863 |
Cf.
2:187, above. |
864 |
The reference is to Abu Yazid al-Bistami. Cf.
p. 102,
above. |
865 |
Cf. Qur'an 15.87 (87).
The first surah is meant. |
866 |
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." |
867 |
Cf. p. 102, above. |
868 |
Abu Bakr ash-Shibli, d. 834 or 335 [946].
Cf. GAL, I,199 f.; suppl., I, 357. |
869 |
Khullah [?]. |
870 |
I.e.,
Jupiter. Cf. p. 189, above. |
871 |
Leg. ghala [?]. |
872 |
Or: "your making (it ready) to accept its sun." |
873 |
Leg. wa-na'i bihim ila [?]. |
874 |
Referring to the surah? "Houses,"
of course, could be "fields." |
875 |
The MSS seem to read something
like: bytr wa-tartili haqiqatin . . . |
876 |
Or Bahlul. Cf. GAL, Suppl., I,
350. |
877 |
That is, al-Hasan al-Basri. Cf. 2:184, above. |
878 |
The meter is corrupted. |
879 |
Wa-buqhum. |
880 |
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.
|
881 |
The verse is quoted above, 1:240, and below, pp. 211 and 214. |
882 |
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:
|
883 |
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. |
884 |
Sic! Cf. p. 211, below. |
885 |
The following words, which also introduce the term nash'ah,
translated
arbitrarily as "growth," are particularly obscure. Possibly the text is
in disorder. |
886 |
Cf. 1:238 (n. 364), above, and for the answer, p. 213,
below. |
887 |
Bulaq adds: "among the letters of the
chords, and then, the letters of the questions," which would seem to be
out of place.
|
888 |
One would
expect a multiple of twelve: seventy-two or eighty-four? |
889 |
That is, the sum of the letters of the chords and the
letters of the question. Cf. p. 211, below.
|
890 |
Sic Bulaq. |
891 |
Apparently, the quotient and remainder after being
divided by twelve. |
892 |
93
÷ 12 = 7, remainder 9. |
893 |
Cf. p. 163,
above. |
894 |
Sic C and D. The other texts have "is the ascendant." |
895 |
The
zimam
numeral for 940 looks like the ligature
lam-alif,
and the Arabic letter t ordinarily has
the numerical value of 400. |
896 |
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. |
897 |
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. |
898 |
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. |
899 |
The MSS have "twenty," which is corrected to "ten" in Bulaq. |
899a |
Cf. n. 896 to this chapter, above. |
900 |
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. |
901 |
The text is doubtful. Bulaq corrects it
to read: "one subtracts four from eight." |
902 |
Bulaq: "five." |
903 |
The
appearance of two letters at the same time is strange, but, as shown on
p. 219, this is what is needed. |
904 |
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. |
905 |
Bulaq:
"fourth." |
906 |
Leg. "twelfth"? |
907 |
Cf. p. 199 (n. 892), above. |
908 |
The MSS have nine, but apparently seven, as in Bulaq, is correct. |
909 |
Bulaq has
the required text. The other texts read: "one doubles it." |
910 |
Bulaq corrects: "One goes up five on the side of eight." |
911 |
It should be sixteen, unless the sum 6
+ 3 + 1 is intended. |
912 |
Bulaq corrects to "nine." |
913 |
For the following eight principles, cf.
p. 198, above. |
914 |
Cf. 1:244,
above, and pp.
214 and 224, below. |
915 |
C and D: k. |
915a |
The letter
alif,
which one would expect here, is not
mentioned. |
916 |
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
|
917 |
This letter is superfluous; cf. p. 206
(n.
900). |
918 |
The MSS
have a wrong j. |
919 |
A w is required instead of alif.
Cf. n.
904,
above. |
920 |
Cf. p. 201, above. |
921 |
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.
|
922 |
Bulaq:
"They think." |
923 |
Cf. 1:243, above. |
924 |
This is the title of a treatise (or a
section of a larger work). The author is not known. |
925 |
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. |
926 |
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).
|
927 |
The operation is described again below, pp. 224 f. |
927a |
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. |
929 |
For the following
discussion, cf. p. 226, below. |
930 |
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. |
931 |
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. |
932 |
The correct text is found in Bulaq. Cf. p. 226, below. |
933 |
Bulaq may be translated as "I have
observed ..." and this may be the correct text. |
934 |
According According to the MSS, Ibn
Khaldun pronounced the word al-qafitus. |
935 |
Ibn Khaldun apparently did not quote this
explanation. |
936 |
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. |
937 |
"Four," as in Bulaq, may be a necessary
correction. |
938 |
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. |
939 |
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). |
940 |
Aries is counted in. |
941 |
al Bulaq: al-qara'in. |
942 |
Lit., "largest
fraction," that is, the fraction with the largest denominator. |
943 |
A, C, and D have
eight. In B, eighty seems to result from a correction of eight. |
944 |
Again, according to the Eastern value. Forty as an aliquot part of sixty is
two-thirds; cf. p. 221, above. |
945 |
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. |
946 |
This might refer to the operation called base. |
947 |
Cf. p. 214,
above. |
948 |
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. |
949 |
Cf. pp. 214
f., above. |
950 |
Cf. pp. 172
and 183,
above. |
951 |
For the following
operation, cf. pp. 217 f., above. 226 |
951a |
Hukmi,
rather than
hikmi "philosophical." |
952 |
This paragraph is not in Bulaq. C has it
in the margin. |
953 |
The reference appears to be to 1:248 f., above. |
|
|