Numerology and text in Anatolios of Laodikaia

KEYSER DI. Philos 7 Lic 20ab O LIT anali C 43 (pp. $6.8-22 H.) The body and its activities (Varro, Hebdomades in Gellius 3.19.7-15: Philon, Allez. 1.11-14 and Creation 117-126; Nikomakhos, Arithmetic 2 (Theol, Arith. pp. 45-53 Ast = pp. 62-71 deFalco]) PAUL T KEYSER Cl o C.2 seven soul parts NUMEROLOGY AND TEXT IN ANATOLIOS OF LAODIKAIA, ON THE DECADE L Disorder vabuls C.3 seven body parts, seven gut parts, and seven openings of head C.4 seven perceptibles C.5 seven voice modulations C.6 seven bodily movements C.7 seven vowels C.8 seven strings on lyre The sequence of thought on the heptad seems disturbed, placing material on astronomy amidst material on arithmetic and material on medicine amidst material on astronomy. Although the epitome in Theol. Arith. (pp. 41-42 Ast = pp. 54-56 de Falco) follows the order of the MS of Anatolios’ Decade ( p. 35.6-36.2), $ A.1-7 in the table below, it is not a reliable witness, omitting all of$ pe B.I. and reporting $ C in che order C.4, C.6, C.7, C.5 (omitting C.2, C.3, and C.$ altogether). Parallels from other authors confirm the dislocation (misplaced passages of Anatolios are bracketed): A (pp. 35.6-36.2 H.) Arithmetic (Philon, Alleg. 1.15 and Creation 91-100; Nikomakhos, Arithmetic2 (Theol. Arith. p. 44 Ast = pp. 58.7-59.1 de Falco]) A.1 seven is neither generative nor generating A.2 aseries of seven additions from one gives the perfect 28 [28-day lunar month composed of heptads] A.3 aseries of seven doublings from one gives a number both square and cube ... A.4 ... as does a series of seven triplings, etc. À.5 the three dimensions plus the four limits make seven A.6 seven is the first harmony (4/3) and the first geometric proportion (1, 2, 4) [seven is significant in human reproduction and disease] A.7 seven is the first right triangle (3 + 4) B (pp. 36.2-8 H.) Astronomy (Varro, Hebdomades in Gellius 3.19.2-6; Philon, Alleg. 1.8 and Creation 191-2, 113-116; Nikomakhos, Arithmetic 2 (Theol. Arith. pp. 44-45 Ast = pp. 59.5-60.18 deFalco]) B.1 seven planets B.2 -------------------- B.3 seven lunar phases B.4 seven stars in the bear and in the Pleiades B.5 seven-month interval of solstices and of equinoxes Anatolios begins with arithmetic, moves to astronomy (the makrokosmos), and then to biology and medicine (the mikrokosmos) - a natural development, seen also in most of the extant parallels and likely sources. The mid-first-century-BCE work Hebdomads (atcributed by the manuscripts to Hippokrates), which was probably an influence on Anatolios and Philon (Mansfeld, 1971. 229), begins with cosmology (1-2), descends to earth (3-4), and then treats the ages of human life (5), the connection between the mikrokosmos and the makrokosmos (6), then the body and its powers (7-9), and the seven parts of the soul (19). Gellius’ report of Varro’s Hebdomades suggests that he treated astronomy (B) before the body (C), and included the bracketed passages thereunder (3.10.6 and 3.10.7 respectively). The three topics are also separated in Philon of Alexandria, Creation 90-127 (in the same order A. B, C). and more briefly in Allegorical Interpretation 1.8-15 (in the order B, C, A). (In Creation 106-110. Philon finds seven in musical proportions.) Philon places the first bracketed passage in a position corresponding to B (Alleg. 1.8 and Creation 101), and places the second passage in a position corresponding to C (Alleg. 1.9. 1.13 and Creation 124-5). Anatolios and Philon adhere to the same branch of the hebdomad-tradition, usually standing somewhat apart from Theon and Nikomakhos (Robbins, 1921, 99-100: Mansteld. 1971. 162-163. 173-182, and 197-199). and indeed the topics arithmetic, astronomy, and biology are confused in Theon, Muthematics 2.46 (pp. 103-4 H.). Anatolios (pp. 36.22-25 H.) does add two references, to Plato's Timaios and to straits. which are not in Philon, and which are separated in Theon, Math. 2.46 (pp. 103.15-16 and 194.18-19 H.). Nonetheless, Nikomakhos Arithmetic 2 (Theol. Arith. pp. 42-53 Ast = pp. 56-71 de Falco) also presents the material in the order À. B, C (note especially his transition from A to B + Car p. 44 Ast = p. 59.1-3 de Falco: Su 101% ouvterzdever Ev Tolg KocULKOTS olguvıols te Kal tegiyelorz, datodot Kal “bots KUL uroiz, Kat’ ulti dototeelovat), and includes the bracketed passages in sections corresponding to B and C respectively (pp. 44-45 Ast = pp. 59.5-60.2 de Falco and pp. 46-47 + 51-53 Ast = pp. 61.13-63.5 + 68.11-71.3 de Falco). Hermippos of Berutos (Montanari, 1998, 439). apud Clement of Alexandria, Stromata 6.16.143, includes the lunar heptads (first bracketed passage) among his astronomical

Pike. ages 25012000} 1 1. NavscH Numercioygy ano lest in Anarottos of Lavdinila filling che lacuna with YMEPOYE, yielding red RÉVOUS TOR iyeuuvinod, the word order of p. 31.5 H. (6 20voc 6 tv dvulovia) and p. 31.22 H. {td tetodywvov TO Ex’ arg). Then read tà for the initial 10, and péyn for che printed uéoous (probably a later scribal emendation), yielding tú dizu Tot pégous TOU ifjeuovixoî néon ..., and render “the parts of the soul, other than the hegemonic part, are dividedinto 7.” The passage is omitted by the epitome in Theol. Arith., andis lacking fromNikomakhos, Arithmetic 2 and the other parallels. nents. Anazolivs (pp. 36.25-58.5 H.) concludes with a passage, taken trom Hebdomads 5 and from Solon, on the stages ofa man’s life, found alsoin Philon, Creation 193-5, in Hermippos apud Clement, Stromata 6.16.144, andin Nikomakkos, Artthmetic 2 (Theol. Arith. pp. 48-50 Ast = pp. 65-67 de Falco), and in part in Varro, Hebdomades apud Gellius 3.19.12, and Theon, Mathematics 2.46 (p. 104.3-9 H.). The first bracketed passage in Anatolios is 41 greck letters, the second 64, which possibly represents two and three lines of about 21 letters: a not untypical line-length for Greek prose (Birt, 1882, 273-281). The two bracketed passages are separated by 525 letters, or exactly 25 lines of 21 letters. 1 suggest that a scribe, copying line by line, completed the line ending §uéoeouv Lootpevov (p. 35.13 H.),in $ A.2 in the table above, Hl. Haplography and then by mistake copied two lines (uéou oeAñvns ... our nomdeioaL) from one page or column below, before realizing his mistake and returning to the proper place. Then, 25 lines later, the scribe completed the fine ending with yewuetouKtic a’ $ à (p. 35.25-26 H.), in § A.6, and made the same mistake, this time copying three lines «cetro... ¿B00uás before he noticed. The two displaced passages find their natural position în the table above ar $ B.2 (36.3 H.) and $ C.! (36.8 H.) respectively, which are separated by 238 letters or 11 lines of about 21 letters (e.g., + lines of 21 letters and 7 lines of 22 letters). The first passage would then begin 100 letters (or 5 lines) after yewnetouxijc a’ B’ 6°. Thus we have: Lines Passage [21 (B.2) 28 days of moon 25 (A3-6) [3] 5 (C.1) Telesphoros (A.7 and B.1) ess restored B.2 Il B.3-3 4] At the beginning of the section on the decade itself, Heiberg prints (p. 39.4-5 H.): mevtaKis yao dto L’. KÜK2OS éoti TavTOS dorduod Kai TÉQUS. CnR7.T Before KÜKAOG a second L' appears to have been omitted, which is the subject of its sentence, The epitome in Theol. Arith. (p. 63 Ast = p. 86 de Falco) has che numerals written out and only one déku; as tor the dislocation (above, $ 1), this haplography may be early. nm MUSTER IV. Garble Further on, after some arithmetic and some epithets, Anatolios (p. 39.16-19 H.) says: ywolay te lon aegipetgog EBAOMAAQN ebyiuxetut TOD LF" tetoapovou Kai Tob IN Too KOUS” Ahevyal de Tobtwv è’ Kai Fr terpúxis yao SF’, Kai Écékic y in’, th dè d' Kal F’ motel tov 0’. restored C.1 The dislocation may have occurred early, and found its way into the epitome (Theol. Arith.). Y. Lacuna Heiberg records that the MS Monac. Gr. 384 marks a lacuna of 6 or 7 letters, at the beginning of $ C.2 in the table above, and prints (p. 36.8-9 H.): TO dizu TO ------- TOU NYEROVIKON pévous THs puis els E” dLargettat TmrN Heiberg remarks quae sequuntur obscura, and the text as printed is indeed nonsense; Tannery translates che Latin (arearum ipsarum) of G. Valla, but banishes ywotwy te ... ESúxac y” un’ to the margin as otiose. The epitome in Theol. Arith. (pp. 63-64 Ast = pp. 86-87 de Falco) breaks off before this passage, which is also omitted by Nikomachos and Philon. I suggest that EBAOMAAQN is wrong and arose as follows: EMBAAQ was miscopied as EBMAAQ, and then ‘corrected’ to EB[AOJMAAQIN]. For Eußuö-"area” cp. Heron, Meer. I. pr, 1.1. 1.8, 1.31, 1.35, etc., Geom. 21, 24, etc.; Theon, Math. 3,3 (p. 126 H.); Diophantos, Arith. 6.17, ete and especially Anat. p. 32.9 H. More to the point, the same idea, similarly expressed, occurs in Anat. p. 31.22-23 H. (of the number 4): He suggests tà dizu (and no lacuna) for 16 dizu T6: “the soul's things, other than the hegemonic part, are dividedinto 7” (similar to Philon, Creation 117). I suggest TO TETDÜYWVOV TO EX’ GTS, TOUTÉOE TO Eupaddy, th meoutétow toov KTH.

Baus ns Nutuetolupy sei Cons lia of li So tar trom vtiose and marginal, the emended text fits Anatotios’ thought, and explains the otherwise dangling 16.08 d' Kai F’ toi rèv 1°. Render “perimeter equal to area of figures is found in the case of the square 16 and the rectangle 18”, and the rest is no longer obscure, but clear. Anatolios correctly gives the sole quadrangular figures in integer side whose area is numerically equal to their perimeter. Bibliography Th. Birt. Das antike Buchwesen, Berlin 1882, J. L. Huiberg, Anatolius sur les dix premiers nombres, in: Annales internationales d'histoire, Congrès de Paris 1909. 5° section, Histoire des sciences, Paris 1904, 27-57. Jaap Mansteld, The pseudu-Hippucracic tract MEPL EBAOMAAQN, Assen 1971. Fr. Montanari, Hermippos, in: Der Neue Pauly 5, 1998, 439. E E. Robbins, The tradition of Greek arithmology, CP 16, 1921, 97-123. 18M Watson Research Center | Hawthorne, USA - 10532 NY Abstract Anatolios’ Decade is rarely read despite its interest as a document of the transition from late paganism to early Christianity. Dating probably from his tenure as professor in Alexandria, it is the earliest extant work devoted to neo-pythagorean arithmology: the earlier Mathematics of Theon of Smurna only includes a little such material, while merely fragments of the earlier Arithmetic of Nikomakhos of Gerasa are preserved, in the summary by Photios of what may be Iamblikhos’ work. Here I want to offer four emendations to the text of Anatolios as printed by Heiberg (1900); the text is disordered and has a lacuna in the section on 7, while in the material on 10 there is a haplography and a garble.