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LIBER D - Book 500

Sepher Sephiroth

sub figurâ D ο αριθνοσ

Liber D

A.A.

A∴A∴ Publication in Class B

Imprimatur:
N. Fra. A∴ A∴

PREFACE

CAN any good thing come out of Palestine? is the broader anti-Semitic retort to the sneer cast by the Jews themselves against the harmless and natural Nazarene; one more example of the poetic justice of History. And no doubt such opponents of the modern Jew will acclaim this volume as an admirable disproof of that thesis which it purports to uphold.

The dissimilarities, amounting in some cases to sheer contradiction, which mark many numbers, will appear proof positive that there is nothing in the numerical Qabalah, especially as we may presume that by filling up this dictionary from the ordinary Hebrew Lexicon one would arrive at a mere hotch-pot.

Apart from this, there is a deeper-lying objection to the Qabalah; viz., that the theory is an example of the fallacy Post hoc propter hoc.

Are we to believe, asks the sceptic, that a number of learned men deliberately sat down and chose words for the sake of their numerical value? Language is a living thing, with many sources and diverse; can it be moulded in any such arbitrary fashion?

The only reply seems to be a mere assertion that to some extent it certainly is so. Examples of a word being spelt deliberately wrong do occur; and such a jugglery as the changing of the names of Abram and Sarai to Abraham and Sarah can hardly be purposeless. Once admit the end of such a wedge, and it is difficult to say whether it may not be driven home so far as to split asunder the Tree of Knowledge, if not the Tree of Life.

Another line of argument is the historical. We do not here refer to the alleged forgery of the Qabalah by Rabbi Moses ben Leon — was it not? — but to the general position of the ethnologist that the Jews were an entirely barbarous race, incapable of any spiritual pursuit. That they were polytheists is clear from the very first verse of Genesis; that Adonai Melekh is identical with “Moloch” is known to every Hebraist. The “Old Testament” is mainly the history of the struggle of the phallic Jehovah against the rest of the Elohim, and that his sacrifices were of blood, and human blood at that, is indisputable.

Human sacrifices are to-day still practised by the Jews of Eastern Europe, as is set forth at length by the late Sir Richard Burton in the MS. which the wealthy Jews of England have compassed heaven and earth to suppress, and evidenced by the ever-recurring Pogroms against which so senseless an outcry is made by those who live among those degenerate Jews who are at least not cannibals.[1]

Is it to such people, indeed, that we are to look for the highest and subtlest spiritual knowledge?

To this criticism there are but two answers. The first, that an esoteric tradition of great purity may co-exist with the most crass exoteric practice. Witness the Upanishads in the land of Jagganath, hook-swinging, and the stupidest forms of Hatha-Yoga.

Witness the Tipitaka (with such perfections as the Dhammapada) in the midst of peoples whose science of torture would seem to have sprung from no merely human imagination. The descriptions in the Tipitaka itself of the Buddhist Hells are merely descriptions of the actual tortures inflicted by the Buddhists on their enemies.

The second, that after all is said, I find it work very well. I do not care whether Sq.Rt. -1 is an impossible, an unimaginable thing, or whether de Moivre really invented it, and if so, whether de Moivre was an immortal man, and wore whiskers. It helps me to make certain calculations; and so long as that is so, it is useful, and I stick to it.

Other criticisms of the methods of the Qabalah itself have been made and disposed of in the article on the subject in “The Temple of Solomon the King” (Equinox V) and no further reference need be made to them in this place. It is only necessary to say that the article should be studied most thoroughly, and also the article “A Note on Genesis” in the second number of The Equinox.

With these two weapons, and the Sword of the Spirit, the Practicus, fully armed, may adventure himself in the great battle wherein victory is Truth.

PERDURABO.

EDITORIAL NOTE

THIS dictionary was begun by Allan Bennett (Fra∴ Iehi Aour, now Bhikkhu Ananda Metteya) in the last decade of the nineteenth century since Ψ-J.C. It was bequeathed to the present Editor, with many other magical MSS., on I.A.'s departure for Ceylon in 1899.

Frater Perdurabo used it, and largely added to it, in the course of his Qabalistic workings. With George Cecil Jones (Fra∴ Volo Noscere) he further added to it by making it a complete cross-correspondence to the Book DCCLXXVII.

It was further revised and checked, re-copied by a Jewish scribe, and again checked through, in the year V of the present Era.

The mathematical additions were continued by Fra∴ P. and Fra∴ Lampada Tradam; and the MS. finally copied on a specially constructed typewriter by Gerald Rae Fraser (Fra∴ Ψ) who added yet further mathematical data.

This copy has again been checked by Fra∴ P. and Soror∴ N.N. and the proofs further by three separate scholars.

The method of employing the dictionary has been fully indicated in The Temple of Solomon the King (Equinox V).

None of the editors claim to possess even the smallest degree of scholarship. The method of compilation has been to include all words given in Von Rosenroth's Qabalistic Dictionary, those specially commented on in S.D., I.R.Q., and I.Z.Q., those given in 777, and those found by Fratres I.A. and P. Some of them are found in texts of the Hebrew Scriptures which appeared to those adepts to be of magical importance. Owing to their carelessness, the meaning of some few words has been lost, and cannot now be traced.

ABBREVIATIONS, SIGNS, AND FIGURES:

K.D. L.C.K. p___ = KABBALA DENUDATA cuius Pars Prima continet Locos Communes Kabbalisticos.
Dec. = Decan.
S.P.M. = Sphere of the Primum Mobile.
S.S.F. = Sphere of the Fixed Stars.
L.T.N. = Lesser Angel governing Triplicity by Night.
L.T.D. = Lesser Angel governing Triplicity by Day.
K.Ch.B. = Kether — Chokmah — Binah.
(Ch.) = Chaldee.
S.D. = Siphra Dtzenioutha.
I.R.Q. = Idra Rabba Qadisha.
Tet. = Tetragrammaton.
L.A. Angel = Lesser Assistant Angel.
I.Z.Q. = Idra Zuta Qadisha.
M.T. = Magister Templi.
ש. = Shemhamphorasch.
W. = Wands.
C. = Cups.
S. = Swords.
P. = Pentacles.
K. of S. = Key of Solomon.
O.P.A.A. = Oriens — Paimon — Ariton — Amaimon

 

♈ = Aries. : ♄ = Saturn.
♉ = Taurus. : ☉ = Sun.
♊ = Gemini. : ☾ = Moon.
♋ = Cancer. : ♂ = Mars.
♌ = Leo. : ☿ = Mercury.
♍ = Virgo. : ♃ = Jupiter.
♎ = Libra. : ♀ = Venus.
♏ = Scorpio. :
♐ = Sagittarius. :
♑ = Capricornus. :
♒ = Aquarius. :
♓ = Pisces. :

 

□ (Square) after a number shows that the number is a perfect square.

√ (Square Root) before a number shows that the number is a perfect square.

3√ (Cube Root) before a number shows that the number is a perfect cube.

4√ (Fourth Root) before a number shows that the number is a squared square.

👑 (Crown) after a number shows that the number is a perfect number.

ƒ_ (Factorial) about a number shows that the number is factorial*. (*See special table following.)

ƒƒ_ (Sub-factorial) about a number shows that the number is sub-factorial.

π (Pi) before a number shows that the number is a prime number.

∑ (1—k) is an abbreviation for “the sum of the first k natural numbers.” [2]

TABLE OF FACTORS

ODD NUMBERS FROM 1 TO 3321 (5'S EXCLUDED);

SHOWING LOWEST FACTORS, AND PRIMES (P.).

“—” INDICATES THAT THE NUMBER IS DIVISIBLE BY 3.

{WEH NOTE: This table was originally published five columns to a page. It is here reproduced the same format.

Note also that Crowley gives “1” as the first odd number. This is not always used by mathematicians. More significantly, he takes “1” as the first Prime number, and hardly any mathematicians of his time or the present do that. The first prime number is considered to be “2” by mathematicians, with “1” being the multiplicative identity element.

The main structure of this table is that of a compressed factoralization reference, always yielding the lowest factor directly or implicitly. Once that is obtained, any remaining factors may be found after division by the first factor and recursion to the table. Even numbers and numbers divisible by five are omitted in view of the fact that the lowest factor of such numbers is obviously 2 or 5.}

1. P. 83. P. 171. 259. 7 347. P.
2. P. 87. 173. P. 261. 349. P.
3. P. 89. P. 177. 263. P. 351.
5. P. 91. P. 179. P. 267. 353. P.
7. P. 93. 181. P. 269. P. 357.
9. 32 97. P. 183. 271. P. 359. P.
11. P. 99. 187. 11 273. 361. □ 192
13. P. 101. P. 189. 277. P. 363.
17. P. 103. P. 191. P. 279. P. 367. P.
19. P. 107. P. 193. P. 281. P. 369.
21. 109. P. 197. P. 283. P. 371. 7
23. P. 111. 199. P. 287. 7 373. P.
27. 33 113. P. 201. 289. □ 172 377. 13
29. P. 117. 203. P. 291. 379. P.
31. P. 119. 7 207. 293. P. 381.
33. 121. □ 112 209. 11 297. 383. P.
37. P. 123. 211. P. 299. 13 387.
39. P. 127. P. 213. 301. 7 389. P.
41. P. 129. 217. 7 303. 391. 17
43. P. 131. P. 219. 307. P. 393.
47. P. 133. 7 221. 13 309. 397. P.
49. □ 72 137. P. 223. P. 311. P. 399.
51. 139. P. 227. P. 313. P. 401. P.
53. P. 141. 229. P. 317. P. 403. 13
57. 143. 11 231. 319. 11 407. 11
59. P. 147. 233. P. 321. 409. P.
61. P. 149. P. 237. 323. P. 411.
63. 151. P. 239. P. 327. 413. P.
67. P. 153. 241. P. 329. 7 417.
69. 157. P. 243. 35 331. P. 419. P.
71. P. 159. 247. P. 333. 421. P.
73. P. 161. 7 249. 337. P. 423.
77. 7 163. P. 251. P. 339. 427. 7
79. P. 167. P. 253. 11 341. 11 429.
81. □ 34 = 92 169. 132 257. P. 343. 7 431. P.

433. P. 529. □ 232 623. 7 719. P. 813.
437. 19 531. 627. 721. 7 817. 19
439. P. 533. P. 629. 17 723. 819.
441. □ — 212 537. 631. P. 727. P. 821. P.
443. P. 539. 7 633. 729. □ 36 = 93 = 272 823. P
447. 541. P. 637. 7 731. 17 827. P.
449. P. 543. 639. 733. P. 829. P.
451. 11 547. P. 641. P. 737. 11 831.
453. 549. 643. P. 739. P. 833. 7
457. P. 551. 19 647. P. 741. 837.
459. 553. 7 649. 11 743. P. 839. P.
461. P. 557. P. 651. 747. 841. □ 292
463. P. 559. 13 653. P. 749. 7 843.
467. P. 561. 657. 751. P. 847. 7
469. 7 563. P. 659. P. 753. 849.
471. 567. 661. P. 757. P. 851. 23
473. 11 569. P. 663. 759. 853. P.
477. P. 571. P. 667. 23 761. □ P. 857. P.
479. P. 573. 669. 763. 7 859. P.
481. 13 577. P. 671. 11 767. 13 861.
483. 579. 673. P. 769. P. 863. P.
487. P. 581. 7 677. P. 771. 867.
489. 583. 11 679. 7 773. P. 869. 11
491. P. 587. P. 681. 777. 871. 13
493. 17 589. 17 683. P 779. 19 873.
497. 7 591. 687. 781. 11 877. P.
499. P. 593. P. 689. 13 783. 879.
501. 597. 691. P. 787. P. 881. P.
503. P. 599. P. 693. 789. 883. P.
507. 601. P. 697. 17 791. 7 887. P.
509. P. 603. 699. 793. 13 889. 7
511. 7 607. P. 701. P. 797. P. 891.
513. 609. 703. 19 799. 17 893. 19
517. 11 611. 13 707. 7 801. 897.
519. 613. P. 709. P. 803. 11 899. 29
521. P. 617. P. 711. 807. 901. 17
523. P. 619. P. 713. 23 809. P. 903.
527. 17 621. 717. 811. P. 907. P.

909. 1003. 17 1099. 7 1193. P. 1289. P.
911. P. 1007. 19 1101. 1197. 1291. P.
913. 11 1009. P. 1103. P. 1199. 11 1293.
917. 7 1011. 1107. 1201. P. 1297. P.
919. P. 1013. P. 1109. P. 1203. 1299.
921. 1017. 1111. 11 1207. 17 1301. P.
923. P. 1019. P. 1113. 1209. 1303. P.
927. 1021. P. 1117. P. 1211. 7 1307. P.
929. P. 1023. 1119. 1213. P. 1309. 7
931. 7 1027. 13 1121. 19 1217. P. 1311.
933. 1029. 1123. P. 1219. 23 1313. 13
937. P. 1031. P. 1127. 7 1221. 1317.
939. 1033. P. 1129. P. 1223. P. 1319. P.
941. P. 1037. 17 1131. 1227. 1321. P.
943. 23 1039. P. 1133. 11 1229. P. 1323.
947. P. 1041. 1137. 1231. P. 1327. P.
949. 13 1043. 7 1139. 17 1233. 1329.
951. 1047. 1141. 7 1237. P. 1331. 11
953. P. 1049. P. 1143. 1239. 1333. 31
957. 1051. P. 1147. 31 1241. 17 1337. 7
959. 7 1053. 1149. 1243. 11 1339. 13
961. □ 312 1057. 7 1151. P. 1247. 29 1341.
963. 1059. 1153. P. 1249. P. 1343. 17
967. P. 1061. P. 1157. 13 1251. 1347.
969. 1063. P. 1159. 19 1253. 7 1349. 19
971. P. 1067. 11 1161. 1257. 1351. 7
973. 7 1069. P. 1163. P. 1259. P. 1353.
977. P. 1071. 1167. 1261. 13 1357. 27
979. 11 1073. 29 1169. 7 1263. 1359.
981. 1077. 1171. P. 1267. 7 1361. P.
983. P. 1079. 13 1173. 1269. 1363. 29
987. 1081. 23 1177. 11 1271. 31 1367. P.
989. 23 1083. 1179. 1273. 19 1369. □ 372
991. P. 1087. P. 1181. P. 1277. P. 1371.
993. 1089. □ — 332 1183. 7 1279. P. 1373. P.
997. P. 1091. P. 1187. P. 1281. 1377.
999. 1093. P. 1189. 29 1283. P. 1379. 7
1001. 7 1097. P. 1191. 1287. 1381. P.

1383. 1479. 1573. 11 1669. P. 1763. 41
1387. 19 1481. P. 1577. 19 1671. 1767.
1389. 1483. P. 1579. P. 1673. 7 1769. 29
1391. 13 1487. P. 1581. 1677. 1771. 7
1393. 7 1489. P. 1583. P. 1679. 23 1773.
1397. 11 1491. 1587. 1681. □ 412 1777. P.
1399. P. 1493. P. 1589. 7 1683. 1779.
1401. 1497. 1591. 37 1687. 7 1781. 13
1403. 23 1499. P. 1593. 1689. 1783. P.
1407. 1501. 19 1597. P. 1691. 19 1787. P.
1409. P. 1503. 1599. 1693. P. 1789. P.
1411. 17 1507. 11 1601. P. 1697. P. 1791.
1413. 1509. 1603. 7 1699. P. 1793. 11
1417. 13 1511. P. 1607. P. 1701. 1797.
1419. 1513. 17 1609. P. 1703. 13 1799. 7
1421. 7 1517. 37 1611. 1707. 1801. P.
1423. P. 1519. 7 1613. P. 1709. P. 1803.
1427. P. 1521. □ — 392 1617. 1711. 29 1807. 13
1429. P. 1523. P. 1619. P. 1713. 1809.
1431. 1527. 1621. P. 1717. 17 1811. P.
1433. P. 1529. 11 1623. 1719. 1813. 7
1437. 1531. P. 1627. P. 1721. P. 1817. 23
1439. P. 1533. 1629. 1723. P. 1819. 17
1441. 11 1537. 29 1631. 7 1727. 11 1821.
1443. 1539. 1633. 23 1729. 7 1823. P.
1447. P. 1541. 23 1637. P. 1731. 1827.
1449. 1543. P. 1639. 11 1733. P. 1829. 31
1451. P. 1547. 7 1641. 1737. 1831. P.
1453. P. 1549. P. 1643. 31 1739. 37 1833.
1457. 31 1551. 1647. 1741. P. 1837. 11
1459. P. 1553. P. 1649. 17 1743. 1839.
1461. 1557. 1651. 13 1747. P. 1841. 7
1463. 7 1559. P. 1653. 1749. 1843. 19
1467. 1561. 7 1657. P. 1751. 17 1847. P.
1469. 13 1563. 1659. 1753. P. 1849. □ 432
1471. P. 1567. P. 1661. 11 1757. 7 1851.
1473. 1569. 1663. P. 1759. P. 1853. 17
1477. 7 1571. P. 1667. P. 1761. 1857.

1859. 11 1953. 2049. 2143. P. 2239. P.
1861. P. 1957. 19 2051. 7 2147. 19 2241.
1863. 1959. P. 2053. P. 2149. 7 2243. P.
1867. P. 1961. 37 2057. 11 2151. 2247.
1869. 1963. 13 259. 29 2153. P. 2249. 13
1871. P. 1967. 7 2061. 2157. 2251. P.
1873. P. 1969. 11 2063. P. 2159. 17 2253.
1877. P. 1971. 2067. 2161. P. 2257. 37
1879. P. 1973. P. 2069. P. 2163. 2259.
1881. 1977. 2071. 19 2167. 11 2261. 7
1883. 7 1979. P. 2073. 2169. 2263. 31
1887. 1981. 7 2077. 31 2171. 13 2267. P.
1889. P. 1983. 2079. 2173. 41 2269. P.
1891. 31 1987. 11 2081. P. 2177. 7 2171.
1893. 1989. P. 2083. P. 2179. P. 2273. P.
1897. 7 1991. P. 2087. P. 2181. 2277.
1899. 1993. P. 2089. P. 2183. 37 2279. 43
1901. P. 1997. 2091. 2187. 37 2281. P.
1903. 11 1999. P. 2093. 7 2189. 11 2283.
1907. P. 2001. P. 2097. 2191. 7 2287. P.
1909. 23 2003. P. 2099. P. 2193. 2289.
1911. 2007. 2101. 11 2197. 13 2291. 29
1913. P. 2009. 7 2103. 2199. 2293. P.
1917. 2011. P. 2107. 7 2201. 31 2297. P.
1919. 19 2013. 2109. 2203. P. 2299. 11
1921. 17 2017. P. 2111. P. 2207. P. 2301.
1923. 2019. 2113. P. 2209. □ 472 2303. 7
1927. 41 2021. 43 2117. 29 2211. 2307.
1929. 2023. 7 2119. 13 2213. P. 2309. P.
1931. P. 2027. P. 2121. 2217. 2311. P.
1933. P. 2029. P. 2123. 11 2219. 7 2313.
1937. 13 2031. 2127. 2221. P. 2317. 7
1939. 7 2033. 19 2129. P. 2223. 2319.
1941. 2037. P. 2131. P. 2227. 17 2321. 11
1943. 29 2039. P. 2133. 2229. 2323. 23
1947. 2041. 13 2137. P. 2231. 23 2327. 13
1949. P. 2043. 2139. 2233. 11 2329. 17
1951. P. 2047. 23 2141. P. 2237. P. 2331.

2333. P. 2429. 7 2523. 2619. 2713. P.
2337. 2431. 11 2527. 7 2621. P. 2717. 11
2339. P. 2433. 2529. 2623. 43 2719. P.
2341. P. 2437. P. 2531. P. 2627. 37 2721.
2343. 2439. 2533. 17 2629. 11 2723. 7
447. P. 2441. P. 2537. 43 2631. 2727. P.
2349. 2443. 7 2539. P. 2633. P. 2729. P.
2351. P. 2447. P. 2541. 2637. 2731. P.
2353. 13 2449. 31 2543. P. 2639. 7 2733.
2357. P. 2451. 2547. 2641. 19 2737. 7
2359. 7 2453. 11 2549. P. 2643. 2739.
2361. 2457. 2551. P. 2647. P. 2741. P.
2363. 17 2459. P. 2553. 2649. 2743. 13
2367. 2461. 23 2557. P. 2651. 11 2747. 41
2369. 23 2463. 2559. 2653. 7 2749. P.
2371. P. 2467. P. 2561. 13 2657. P. 2751.
2373. 2469. 2563. 11 2659. P. 2753. P.
2377. P. 2471. 7 2567. 17 2661. 2757.
2379. 2473. P. 2569. 7 2663. P. 2759. 31
2381. P. 2477. P. 2571. 2667. P. 2761. 11
2383. P. 2479. 37 2573. 31 2669. 17 2763.
2387. 7 2481. 2577. 2671. P. 2767. P.
2389. P. 2483. 13 2579. P. 2673. 2769.
2391. 2487. 2581. 29 2677. P. 2771. 17
2393. P. 2489. 19 2583. 2679. 2773. 47
2397. 2491. 47 2587. 13 2681. 7 2777. P.
2399. P. 2493. 2589. 2683. P. 2779. 7
2401. □ 74 = 492 2497. 11 2591. P. 2687. P. 2781.
2403. 2499. 2593. P. 2689. P. 2783. 11
2407. 29 2501. 41 2597. 7 2691. 2787.
2409. 2503. P. 2599. 23 2693. P. 2789. P.
2411. P. 2507. 23 2601. □ — 512 2697. 2791. P.
2413. 19 2509. 13 2603. 19 2699. P. 2793.
2417. P. 2511. 2607. 2701. 37 2797. P.
2419. 41 2513. 7 2609. P. 2703. 2799.
2421. 2517. 2611. 7 2707. P. 2801. P.
2423. P. 2519. 11 2613. 2709. 2803. P.
2427. 2521. P. 2617. P. 2711. P. 2807. 7

2809. □ 532 2903. P. 2999. P. 3093. 3189.
2811. 2907. 3001. P. 3097. 19 3191. P.
2813. 29 2909. P. 3003. 3099. 3193. 31
2817. 2911. 41 3007. 31 3101. 7 3197. 23
2819. P. 2913. 3009. 3103. 29 3199. 7
2821. 7 2917. P. 3011. P. 3107. 13 3201.
2823. 2919. 3013. 23 3109. P. 3203. P.
2827. 11 2921. 23 3017. 7 3111. 3207.
2829. 2923. 37 3019. P. 3113. 11 3209. P.
2831. 19 2927. P. 3021. 3117. 3211. 13
2833. P. 2929. 29 3023. P. 3119. P. 3213.
2837. P. 2931. 3027. 3121. P. 3217. P.
2839. 17 2933. 7 3029. 13 3123. 3219.
2841. 2937. 3031. 7 3127. 53 3221. P.
2843. P. 2939. P. 3033. 3129. 3223. 11
2847. 2941. 17 3037. P. 3131. 31 3227. 7
2849. 7 2943. 3039. 3133. 13 3229. P.
2851. P. 2947. 7 3041. P. 3137. P. 3231.
2853. 2949. 3043. 17 3139. 43 3233. 53
2857. P. 2951. 13 3047. 11 3141. 3237.
2859. 2953. P. 3049. P. 3143. 7 3239. 41
2861. P. 2957. P. 3051. 3147. 3241. 7
2863. 7 2959. 11 3053. 43 3149. 47 3243.
2867. 47 2961. 3057. 3151. 23 3247. 17
2869. 19 2963. P. 3059. 7 3153. 3249. □ — 572
2871. P. 2967. 3061. P. 3157. 7 3251. P.
2873. 13 2969. P. 3063. 3159. 3253. P.
2877. 2971. P. 3067. P. 3161. 29 3257. P.
2879. P. 2973. 3069. 3163. P. 3259. P.
2881. 43 2977. 13 3071. 37 3167. P. 3261.
2883. 2979. 3073. 7 3169. P. 3263. 13
2887. P. 2981. 11 3077. 17 3171. 3267.
2889. 2983. 19 3079. P. 3173. 19 3269. 7
2891. 7 2987. 29 3081. 3177. 3271. P.
2893. 11 2989. 7 3083. P. 3179. 11 3273.
2897. P. 2991. 3087. 3181. P. 3277. 29
2899. 13 2993. 41 3089. P. 3183. 3279.
2901. 2997. 3091. 11 3187. P. 3281. 17

The first dozen factorials, and sub-factorials; and the ratios they bear to one another;
note that ƒ_n / ƒƒ_n = e

N ƒ_N ƒƒ_N ƒ_N ÷ ƒƒ_N ƒƒ_N ÷ ƒ_N
1 1
0 0.000000
2 2 1 2.000000 0.500000
3 6 2 3.000000 0.333333
4 24 9 2.666666 0.375000
5 120 44 2.727272 0.366666
6 720 265 2.716981 0.368055
7 5040 1854 2.718446 0.367857
8 40320 14833 2.718262 0.367881
9 362880 133496 2.718283 0.367879
10 2628800 1334961 2.718281 0.367879
11 39916800 14684570 2.718281 0.367879
12 479001600 176214841 2.718281 0.367879

 

Factorial n, or ƒ_n is the continued product of all the whole numbers from 1 to n inclusive and is the number of ways in which n different things can be arranged.

Sub-factorial n, or ƒƒ_n, is the nearest whole number to n ÷ e, and is the number of ways in which a row of n elements may be so deranged, that no element may have its original position.

Thus ƒ_n = 1 × 2 × 3 × ... × n,
and ƒƒ_n = (1 × 2 × 3 × ... × n ) ÷ 2.71828188 ± h,

where h is the smaller decimal fraction less than unity by which the fraction (1 × 2 × 3 × ... × n ) ÷ 2.71828188 differs from a whole number, and is to be added or subtracted as the case may be. — The most useful expression for ƒƒ_n is:

ƒƒ_n ≡ n! - [(n÷1) x (n-1)!] + {[(n(n-1)) ÷ (1*2)] x (n-2)!} - {[n(n-1)(n-2)] ÷ (1*2*3)] x (n-3)!} + etc.

to (n+1) terms.

e ≡ 1 + (1÷1!) + (1÷2!) + (1÷3!) ... + to ∞

≡ 2.71828188 ... .[3]

 

THE LETTERS

Letter Number

  Name of Letter Hebrew Figures of Letter Hebrew Name of Letter English Equivalents Numerical values of the Letters
1. (M) {Aleph} א אלף A 1
2. (D) {Beth} ת בית B 2
3. (D) {Gimel} ל גמל C 3
4. (D) {Daleth} ת דלת D 4
5. (S) {Hé} ה הה H (E) 5
6. (S) {Vav} ו וו V (U) 6
7. (S) {Zayin} ן זין Z 7
8. (S) {Chet} ת חית Ch 8
9. (S) {Tet} ט טית T 9
10. (S) {Yod} י יוד. Y (I or J) 10
11. (D) {Kaf} כ / ך כף K 20, 500
12. (S) {Lamed} ד למד L 30
13. (M) {Mem} מ / ם מים M 40, 600
14. (S) {Nun} נ / ן נון N 50, 700
15. (S) {Samech} ס סמך S 60
16. (S) {Ayin} ע עין O (A'a or Ng) 70
17. (D) {Peh} פּ / ף פּה P 80, 800
18. (S) {Tsadeh} צ / ץ צדי Tz 90, 900
19. (S) {Qof} ק קוף Q 100
20. (D) {Resh} ר ריש R 200
21. (M) {Shin} ש שין S (Sh) 300
22. (D) {Tav} ת תו T (Th) 400

When written large, the Value of a Hebrew letter is increased to one thousand times its ordinary value. A large Aleph is counted 1000: a large Beth, 2000: and so on.

Note that A, I, O, U, H, are really consonants, mere bases for the vowels. These vowels are not here given, as they have no importance in Gematria[4].

(M), (D) and (S) before the names of the letters shew their division into Mothers, Double and Single letters, referred respectively to active Elements, Air, Water, Fire, Planets, and Signs. But ש {Shin} and ת {Tav} also serve to signify the Elements of Spirit and of Earth. See Liber 777.

THE NUMBERS

{WEH NOTE : Note that in the 1st edition, the following pages of Sepher Sephiroth are printed and numbered on one side only. In the Weiser edition, the pages are printed on both sides. In the following, for considerations of space and monitor display, this format has been changed to three columns.

All text within curly brackets for the remainder of this transcript is added, not part of the original. “Liber 777” references have been checked and errors noted in the same fashion. References to page numbers in Liber 777 have been changed to refer to column numbers. In this version, finals and medials of Hebrew letters are not distinguished by symbols. All instances of final letters are noted in the associated text. Hebrew words are not prefaced by “HB:” unless circumstances require it.

Some curiosity will undoubtedly be evoked by the many Latin meanings of Hebrew words given below. Most of these are directly from the glossary in “Kabbalah Denudata”, but others are euphemisms for sexual terms. “Kabbalah Denudata” is available on microfilm, but no translation of the Latin or checking of the entries from that source or “Kabbalah Unveiled” by Mathers has been attempted yet.}

— Under Construction —

π √ 1 👑     1.
ƒ_1
ƒƒ_2
The Mystic Number of Kether. S.P.M.    
π  2     2.
ƒ_2
ƒƒ_3
S.S.F.
[Abbreviation for 422, אנפין אריך, q.v.] א׃א׃ A:A:
π 3     3.
∑ (1—2)
The Mystic Number of Chokmah.    
Father אב AB
To come, go בא BA
√ 4     4.

22
The Number of Abra-Melin Princes.    
Father אבא ABA
Hollow; a vein בב BB
Proud גא GA
π  5     5.
Mist, vapour אר AD
Back בג BG
6 👑     6.
∑ (1—3)
ƒ_3
The Mystic Number of Binah.    
To gather, collect גבא GBA
Gog, the giant whose partner is Magog גג GG
A bear דב DB
A window הא HA
π 7     7.
Lost, ruined אבד ABD
A name of GOD attributed to Venus. Initials of Adonai haAretz. אהא AHA
Desire; either, or או AV
Gad, a Tribe of Israel; good fortune גד GD
Was weary דאב DAB
Riches, power דבא DBA
Fish דג DG
3 √ 8     8.
23
☿ 
The number of Abra-Melin Sub-Princes, and of the Servitors of Oriens.    
To will, intend אבה ABH
Desired, beloved בהא AHB
  אוא AVA
Then אז AZ
The entrance, threshold באה BAH
To be anxious, grieve דאג DAG
Love; beloved, breast; pleasures of love. דד DD
Nqn. Zauir Anpin 478 q.v. זא ZA
√ 9     9.
ƒƒ_4
34

Ventriloquus: the special ‘fire’ of black magic, whence Obi, Obeah. Cf. 11 and 207. אוב AVB
He kindled אזא AZA
Brother אח ACh
A garment בגד BGD
Became powerful, grew high גאה GAH
Middle גו GV
Spendour; cf. 15 הד HD
     

to be continued...

[A pendant to this work, on the properties of pure number, is in preparation under the supervision of Fraters P. and y. Also a companion volume on the Greek Qabalah by them and Frater J.M.]

 


Footnotes:

This hypertext version of Liber D was completely re-entered and edited by myself, and I take full responsibility for any errors in it which do not occur in the printed version or in the ASCII edition. I have corrected a number of errors which could be dealt with within the entry for a given number: many words are mis-spelt, and placed at the correct numeration for the mis-spelling. Both B.H.'s and T.S.'s versions were considered to create this final version. —D.M.T.

An extensive study of these entries will be included in the Gematria project now in process of compilation by Bill Heidrick. This project is expected to ultimately extend to several times the number of entries here, including notes of source, discussions of differences between Crowley's approach and that of traditional Qabalah and into new areas.

[1] Crowley's irony at times has led to his detriment. Elsewhere, and much later, he denies the validity of the “Blood Libel”. Here he writes in somewhat dubious humor an anti-Semitic seeming introduction to a book on Jewish mysticism! —B.H.

[2] I have made alterations to the page of abbreviations, signs and figures to reflect actual use. The notation of a box around a number to indicate a perfect square is used only in the table of factors; in the main table a root symbol was used. Similarly, we were informed that “R (n) before [a number shows that the number is] a reciprocal (or ‘amicable’) number” which is nowhere defined and nowhere used. The printed edition did not explain that π (Pi) was used in the main table to denote prime numbers. A “perfect” number is one which is the sum of its factors (including 1), e.g. 6 = 1+2+3; 28 = 1+2+4+7+14; 496 = 1+2+4+8+16+31+62+124+248. —T.S.

[3] I here append a note to the material following the “Table of Factor” in the preface. The software I used to set up mathematical expressions cannot cope with the notation Crowley used to represent factorials. In the expressions for ƒƒ_n and e I have therefore substituted the modern use of n! for n factorial. 0! is conventionally defined as 1; for a positive integer n, n! is thus equal to (n-1)! × n. e is defined as the sum from n=0 to infinity of 1/(n!), otherwise written: e ≡ i=0 i!

While I am not familiar with the notation of sub-factorials used here, I will observe that if we similarly define sub-factorial 0 as 1 (again, simply as a convenience) then for any positive integer n, ƒƒ_n = n × ƒƒ(n-1) + (-1)n. [(-1)n = 1 if n be even, -1 if n be odd.] Or we could have a computer do it thus (using the conventional notation of the C programming language):

int subfact (int n) { if (n < 1) return 1;
/* strictly speaking should be undefined for negative numbers
*/ else return (n*subfact(n-1) + 1 – 2*(n%2));
/* 1- 2*(n%2) is 1 if n be even, -1 if n be odd */ }

Similarly, the rather ugly expression for ƒƒ_n given in the preface simplifies to:

(n!÷0!) - (n!÷1!) + (n!÷2!) - (n!÷3!) + ... to n+1 terms; or, in sigma notation, n(∑)i=0 [(-1)i n!] ÷ i!

[4] There is a limited use in Gematria for the vowel points. All dots are counted as 10 and all linears, whether vertical or horizontal, are counted as six. On this method see the collections at Oxford: HUNT. 41. —B.H.

[5] This word actually means “Bride groom” or “Lord of the Bride”. It is Syriac, not Hebrew in origin. The meaning “Lord of the Flies” is an ubiquitous error through-out much of Christian and European magical history, so general as to have its own standing. —B.H.

[6] SIC, should be Angel of 3 Taurus if the Shemhametphorash is properly constructed from Ex. —B.H.

[7] The citations of “S.D. ii. 467” in the entries for 157 and 227 refer not to the Sepher Dtzenouthia but to Blavatsky’s Secret Doctrine. My thanks to Tim Maroney for this information. —T.S.

[8] In the entries for 704 : Pietro di Abano was neither the actual nor the imputed author of the “Arbatel of Magick” (de magia veterum), in fact “Arbatel” may well have been meant as the author’s name. The first and only known book of the “Arbatel” (an outline description of the work lists nine volumes) was printed as Basle in 1575 and bound up in vol. i of the Lyons edition (ca. 1600) of Cornelius Agrippa’s Opera which included the Heptameron, a short Grimoire of planetary magick spuriously attributed to d’Abano. —T.S.

 


Text © Ordo Templi Orientis.

Proof read and edited by Frater D.M.T - Bahlasti Ompehda Camp, Budapest. (Anno iX)

[ » SEE ALSO : Liber LVIII - Qabalah ]

[ » SEE ALSO : Liber MCCLXIV - The Greek Qabalah ]

[ » Primary Source: Liber D - Sepher Sephiroth - English version « ]

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