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Select index of Greek words and phrases discussed in the text

ˆdelf»v/ˆdelfž, 64, 123, 125, 154 galžnh, 66, 75, 491, 494–500, 504–05, 515 Škanqa, 341 g†r, 122–23 ˆll»triov, 194–95 gewmetr”w, 567 ˆnagka©wv, 396 gewmetrikž, 232–33, 244 ˆn†docov, 39–40 gewmetrik»v, 244 ˆna©sqhtov, 449 ˆnak†mptw, 538 de»menoi, 217–18 ˆnakl†w, 476–77 di‡cr»nou , 291 ˆnakÅptw, 322 diagignÛskw, 58–59, 149–51 ˆnalog©a, 179–81, 503, 529–37, 538; toÓ ­sou, diagnÛmen, xiv, 149 529–37 di†gnwsiv, 58–59, 149–51 ˆn†logon, 179 di†gramma, 396, 566 ˆnamonž, 291 d©aita, par‡tŸn d©aitan , 300–01 ˆnastrofž, 123, 155 diall†ttw, 215 ˆnepist†mwn, 193–94 di†sthma, 166–67, 169, 181, 458 ˆn»moiov, t‡ˆn»moia , 436, 441–43 diatribž, 228–32 ˆntere©dw, 561 dun†menoi, 217–18 ˆnt”reisma, 297 dÅnamiv, 446 ˆnt©lhyiv, 451 dusmžcanov, 79, 348, 375, 379 ˆnÛmalov, 513–15 ˆnwmal»thv, 513 –gg©gnomai, 539 ˆ»ristov, 511 e²dov, 93, 123, 226, 238, 250–51, 567; ˆp†qeia, 600, 603 (prÛtiston), 122 ˆpanti†zw, 113, 156 e«kÛn, 601 ˆplanžv, 542–43 –kle©pw, 247 ˆpodeiktikäv, 375, 379 –mp»diov, 335 ˆp»deixiv, 71, 232, 237–38, –mfus†w, 113, 160 248–49 –n aÉt
, 222 ˆpod”comai, 503–04 –nant©ov, 445 Šporov, 195 –nargžv, 71, 233, 236–37, 238, 246–47 ˆpofr†ssw, 160 –narm»zw, 351 ˆriqmhtikž, 240–44 –xeur©skw, 193, 195, 196–200, 202 ‰rmon©a, t‡perª tŸn ‰rmon©an , 565 –peiskwm†zw, 314, 322 ˆrcž, 358, 500, 502, 598 –piqumhtik»v, 93 ˆrcŸ kaª mhtr»poliv, 69 –p©stamai, 196–200 %rcÅtav, 619 –pist†mwn, 193–94 ˆstronomik»v, 244 –pist†thv, 389 aÎxh, 80, 386 –pitel”w, 72, 237–38, 247, 249 aÉt¼v ›fa, 55 –pit”mnw, 587 –stÛ, 96 banausourg©a, 380 ›scatov oÉran»v, 87

638

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Select index of Greek words and phrases 639

—ta±rov, 37 Melita±on kun©dion, 301 eÉekt©a, 599 m”rov, –n m”rei, 59; kat‡m”rov , 59 eÉqÅv, 115 m”sh, 177 eÎporov, 195 mes»thv, 178 eËr©skw, 193, 386–87, 389 met”cw, 93 eÎstocov, 492 m”tron, 204, 219 mhcanikž, 77 zht”w, 195, 196–200 mhcanik»v, 14, 379 zwƒof»rov, 606 mhcanopoi»v, 81 mon†v, 500; mon‡v q”sin ›cousa, 501 ¡dupaqžv, 316, 318 monoeidžv, 524 rem©a, 497, 504, 603, 605 morfž, 93 ¡suc©a, 491, 497 mousik»v, 244 §cov, 113, 140, 159, 161 nenožsqw, 351 qerapeutžr, 321 nhnem©a, 490–91, 494–500, 504–05, 603 qewr”w, 153 nwqräv, 474 qumoeidžv, 93 xen©a, 36 «d”a, 601 x”nov, 37 ­diov, 194–95 xugg”neia, 64 «diwtikäv, 370 «s»koilov, 475–76 o³† –sti, 152 «sonom©a, 211–12 o«ke±ov, 64 «sopacžv, 475–76 ½lbi»tufov, 24 ­sov, 567; t¼ ­son, 204, 211–15, 217, 529–37 Âlov, 89, 125 «s»thv, 204, 211–15, 503 ¾mal©zw, 317, 321–22, 513, 515 ¾mal»thv, 497, 504–05, 513, 515 kaq©zw, 578–79 ¾moiomeržv, 523 kaq»lou, 59–60, 125, 598 Âmoiov, 499; t‡Âmoia , 436, 441–43 k†lamov, 160, 476 ¾moiÛmata, 492 kanÛn, 204, 218–21 ¾m»noia, 73, 200–02, 204, 235, 322 kataskeuž, 80, 379 ¾mäv, 250 kaul»v, 525 ½rganik»v, 14, 80, 379, 523–24 k©nhsiv, 141, 538 oÉran»v, ˆplanžv, 542–43, 550; ›scatov, 542, knžmh, 525 548, 550; t¼ ›xw, 545 koinwn©a, 64, 314, 322 Àyiv, 557; t‡perª tŸn Àyin maqžmata , krŽsiv, 447 568 kr»talon, 305 kÅbov, 80 paradÅomai, 157 kwlutžr, 218–21 pedart†w, 290–91 p”nhtev, 217–18 l”getai, 376 per©, o¬ per©, 450–51, 477 l”xiv, 117–19 perikatalamb†nw, 113, 157 log©zomai, 75, 187, 199–200, 224 periferžv, 522–23, 532 logism»v, 72–73, 75, 189, 191, 199–200, 202–06, platagž, 304–07 214, 215, 218–21, 235–36, 243, 332 pl†tov, 137 logistikž, 69, 72, 204, 227, 232–33, 235–36, pleonex©a, 73, 204, 206–11, 212, 214, 240–44, 332 314–16 logistik»v, 93, 203, 244 plhgž, 60, 130–32, 141, 474 l»gov, 166–67, 181, 458, 567; d©ca l»gou, 391; ploÅsioi, 217–18 –n l»gwƒ, 532 polueidžv, 524 pragmate©a, 251 m†lista, 112 pragmateÅomai, 247 manq†nw, 56, 193 prŽtov, 124, 179

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640 Select index of Greek words and phrases

pt»rqov, 525 t”cnh, 527–28 puqmžn, 438–41, 442, 462 t»de ti e²nai, 93, 597 toª perª t‡maqžmata , 149 ç†bdov, 158 熁diov, 195–96 Ìlh, 96 ç»mbov, 159 Ëpenant©a, 170, 177, 178 Ëperocž, 166–67, 179 sof©a, 71, 226, 235, 245 Ëpoke©menon, 93, 597 sp†niov, 195–96 st†qmh, 219 fer»mena, 130–31, 133 st†siv, 200–02 fq»ggov, 130, 140, 161, 445, 447, 449 st”lecov, 525 fil©a, 36 stigmž, 500 f©lov, 37 stoice±a, 357 for†, 393, 395 sugcal†w, 113, 156–57 fron”w, 153 summe©gnumi, 435, 443 fusik»v, 526 sump©ptw, 156 fÅsiv, 314–15 sun†llagma, 215–17, 322, 503 fwnž, 131, 134, 140, 161 sustoic©a, 510, 590, 599 sÅstomov, 113, 157 yallhgenžv, 24 y»fov, 60, 130–31, 156, 161 t”ktwn, 29, 302–03 t”menov, 318–19 Þv ›oike, 292 teÓcov, 113, 157 Ýs©a, 96

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Index locorum

(Entries in bold refer to the page on which the Greek or Latin text is provided).

Aelian (B29), 156;(B44a), 200;(B44), 315;(B63), Varia Historia (iii. 17) = (A5c5), 34, 276, 200;(B67), 200 300;(vii. 14) = (A1d), 12, 258, Apollonius Rhodius 300;(x. 12) = (A11a), 19, 31, 100, 340; ii (1055), 260, 305 (xii. 15) = (A8), 298, 299;(xiii. 23), 292; Apostolius, Michael (xiv. 19) = (A11), 4, 19, 31, 73, 100, 337; xiv (37.1) = (Leutsch and Schneidewin i. (xiv. 20), 338 213) = (A10, Text A), 29, 302, 304 Aeschylus Apuleius Prometheus Bound (454–59), 228 Apologia (1), 553;(3), 553;(13), 553;(15), 554; Aetius¨ (15–16) = (A25), 31, 68, 77, 85, 86, 88, 99, (i. 18.6), 584;(i. 23.1), 514;(ii. 6.2), 592; 297, 528, 550;(16), 554 (ii. 31.2), 558;(iv. 13.9–10) = (A25, Text B), De Platone (i. 3) = (A5b7), 25, 33, 271 552;(iv. 14.3 ) = (A25, Text A), 551, 557–58, Arcadius 561 De Accentibus (28.17), 619 Aetius¨ Medicus Archelaus (DK) ii (103.3), 301 (A1), 134 pseudo-Albertus Magnus Archimedes The Marvels of the World (p. 91 Best and Spir. (2.8.3), 248 Brightman), 611;(94), 611 Arethas of Caesarea Alcmaeon (DK) Scholia on Porphyry’s Isagoge and Aristotle’s (A10), 451 Categories (136.14 Share), 596;(223.20), 596 Alexander of Aphrodisias Aristides, Aelius in Metaph. = CAG i (39.13–14), 484;(75.16), To Plato: In Defence of the Four (232) = 584;(550.37 ff.), 489;(798.23), 588 (A5a2), 269 Quaestiones (106.35–107.4), 544, 549 Rh.(1.10.1), 246 in Top. = CAG ii. 2 (118. 13–19), 503 Aristides Quintilianus Anaxagoras (DK) (iii. 20), 138 (A106), 134 Aristophanes (B1), 547 Birds (995), 567 Anaximenes (DK) Clouds (1061), 315;(1075–78), 315;(1400), 315 (A7), 547 Aristotle Anonymus Iamblichi APo. (73a39), 524;(75a38 ff.), 526;(75a39), 243; DK ii (402.21), 208 (75b13–14), 377;(75b16 ff.), 563, 566; Anonymous Prolegomena to Platonic (76a24), 81;(76a34), 393;(77b41 ff.), 534; Philosophy (78b34 ff.), 76, 232;(78b37), 81, 393, 566; (5. 15–24 = 11 Westerink), 370 (78b38), 391, 393;(79a7–8), 567;(88b11), Antiphanes 243;(99a13), 357;(100b7), 203 (PCG ii. 369), 535 APr.(24a16 ff.), 59;(28a), 249;(41a26–7), 234; Antiphon (DK) (68b36), 246

641

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642 Index locorum

Aristotle (cont.) 520;(990b30), 562;(992a20), 502; Ath. (lxii. 3), 12 (993b1–2), 57;(996b21), 178;(997b20), 566; Aud. (803a), 140 (1003a ff.), 227;(1003a24), 598;(1003a26), Cael. (268a), 493;(273b30), 89; 598;(1004a10), 599;(1004b28), 599; (273b30–274a3), 537;(286b11 ff.), 526; (1015a29), 479;(1024b22), 152;(1043a12), (290b), 131, 135;(290b12 ff.), 137;(290b28), 497;(1043a14–26) = (A22), 31, 51, 66, 67, 150;(298a7), 524;(300a23), 526;(302b5), 74–75, 84, 92, 99, 189, 489, 490, 492, 526;(304b20), 526;(306a5), 526 506–07, 515, 603;(1043b31), 492;(1060b32), Cat. (11b17–24), 596;(15b1), 504 59;(1061b18 ff.), 227, 599;(1068b24), 504; de An. (405a30), 527;(407a28), 538;(412b1), (1073b19), 550;(1077a5), 566;(1078a14), 523;(413a19), 177;(419b4 ff.), 131, 141; 566;(1078b20 ff.), 491;(1078b21), 491, 492; (420a18), 194;(420a–b), 140;(420b33), (1078b22), 493;(1078b22–23), 492; 156 (1084a36), 487;(1085a33), 500;(1087b5–6), EE (vii. 7), 201;(1215b23), 538;(1235b), 196 589;(1087b14), 589;(1087b26), 588–89, 590; EN (ix. 6), 200;(1094b12 ff.), 192, 321; (1087b27), 589;(1092b8–14) = (A13, Text (1094b23 ff.), 504;(1101b10 ff.), 599; I), 55, 583, 585, 593;(1093a29), 178 (1101b32), 599;(1103b14), 216;(1103b26), Mete.(342b36 ff.), 557;(364b12), 538;(367b15), 251;(1104b24), 603;(1106a36), 180; 504 (1107a2), 178;(1109a29), 196;(1113a33), 219; MM (i. 9), 196;(ii. 12), 201;(1182a11), 590; (1116b8), 152;(1126a28), 215;(1130b28), 530; (1182a14), 493;(1194a28–b3), 493;(1194a29), (1130b30), 192;(1131a9), 213;(1131a29 ff.), 590 192;(1131a31), 180, 529;(1131b13), 180; Mu.(392a11), 606;(400b1), 157 (1131b32 ff.), 192;(1132a22), 604;(1132b21), PA (646b13), 523;(662a24), 157;(642a14), 491; 223;(1132b23 ff.), 493;(1139a11 ff.), 203; (687a2), 525 (1141a12), 245;(1141a16), 235;(1152a31), 479; Ph.(194a7), 232;(194a11), 563; (1152b16–18), 333, 335, 336;(1153a20–23), 333; (200b12–201b15), 509;(201b5), 514; (1156a26 ff.), 37;(1156a30), 37; (201b16), 520;(201b16–202a2), 509, 589; (1167a22–28), 200;(1167a24), 192; (201b26), 510, 590;(203b15–203b29), 541; (1167a25), 201;(1168b8), 212;(1169b18), 295; (203b22 ff.), 545;(203b23), 85, 548;(204b2), (1172a2), 295;(1172b9–10), 7, 316;(1177a27), 543;(215a24), 89;(249b27 ff.), 537; 294;(1177a35), 296 (249b29), 89;(260a22 ff.), 527;(262b), Fr. (47), 178;(192), 536;(201), 584;(202), 584; 538 (203), 484, 492–93;(205), 584;(208), 451 Po.(1457b21), 535;(1459a7), 506 GA (724b23), 522;(734b28), 522;(741b37), Pol.(1265b35), 602;(1266a1), 602;(1266a38), 525;(786b ff.), 143 217;(1266b3), 322;(1266b16), 505; HA (486b17), 180;(486b20), 341;(491a25), (1280a7–25), 213;(1286a37), 247;(1291b14 523;(494a5), 525;(501b11), 59;(527a7), 476; ff.), 17;(1295b2 ff.), 602;(1297a10 ff.), 208; (612b10), 301;(613a16), 59;(614a34–35), 578; (1301a9 ff.), 213;(1301b26–27), 205; (619b5), 578 (1301b27–1302a8), 205;(1301b30 ff.), 213; Int. (17a39), 59 (1302b7), 208;(1303a), 9, 17;(1307b32), 157; Mech. (847a ff.), 527;(847a–b), 393;(847b16 (1314b25), 450;(1318b1), 218;(1320a24), 217; ff.), 528;(848b10), 532;(848b31), 532; (1320b), 17, 184;(1320b9–14), 214; (849a15 ff.), 528;(849b ff.), 532;(852b), 131; (1320b10), 206;(1320b12), 217, 317;(1322b), (857b22), 525 203;(1336b3–8), 339;(1340b25–31) = Metaph.(980b28), 203;(982a ff.), 227; (A10), 19, 30, 82, 298, 302;(1342b23), 149 (982a2), 598;(982a4 ff.), 235;(982a28), 227, Pr.(870a10), 160;(883a30), 525;(883b14), 525; 233;(982b9), 598;(985b19), 520;(985b23 (892a20), 301;(899a9 ff.), 140;(899a22 ff.), ff.), 45, 489;(985b27 ff.), 492, 521;(985b31), 143;(910b36), 131, 529;(915a25–32) = 564;(986a10), 131;(986a12), 585;(986a22), (A23a), 28, 31, 66, 68, 74, 78, 85, 88, 99, 510, 590;(986a23 ff.), 599;(986a25), 590; 516, 592–93, 594;(915a33), 524;(915a35), (987a20 ff.), 492;(987a21), 492, 493; 527;(915b18), 131;(916a24), 527;(919b1 (987a23), 493;(987a25), 493;(987a29 ff.), ff. = Prob. xix. 23), 145, 477;(920a27 ff.), 42, 484;(987b24), 489;(987b26), 484, 513; 432;(946b39), 157 (987b28), 496;(988a12), 321;(989b30), 68, Rh.(1371b4), 247;(1407a17), 535; 247;(989b34), 424;(990a4), 237;(990a8), (1412a11–18) = (A12), 31, 75, 92, 99, 492,

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Index locorum 643

494, 500, 505;(1412a12), 507;(1412a14–15), De Institutione Musica (Praef. 4.27–5.4), 454; 497;(1413a1), 535 (i–iii), 455;(i–iv), 433;(i. 2), 138;(i. 3), 142, Sens.(437b25), 557;(443a23), 150;(448a ff.), 147;(i. 16), 455;(i. 30), 448;(i. 31), 448, 447, 448, 450;(448a22), 449 449;(i. 32), 433;(ii. 8), 462;(ii. 18–20), 433; Top.(100a27), 248;(105b12), 585;(108a7), 491, (ii. 18), 433;(ii. 19), 433;(ii. 20), 433;(iii), 496, 503;(108a11), 505;(108a12), 494, 499; 455;(iii. 1–4), 456;(iii. 5–8), 456;(iii. 6), (100a18), 251;(108b), 504;(108b7), 506; 456;(iii. 9–10), 456;(iii. 10), 456;(iii. (108b23), 491, 496;(108b24), 75, 499, 501; 11) = (A19), 30, 46, 47–48, 49, 50, 55, 56, (108b25), 487, 499, 505;(108b26), 497; 60, 62, 99, 130, 169, 415–16, 419, 451, 456, (128b), 504;(142a19), 504 564;(iii. 12), 456;(iv. 2), 466;(iv. 3), 460; Aristoxenus (v), 455;(v. 4), 455;(v. 8–10), 433; Fr. (16 Wehrli), 327;(43), 536;(54a), 288;(72), (v. 17–18), 402, 409 479 pseudo–Boethius Harm.(i. 3.21), 137;(i. 8.13 ff.), 146;(i. 23), Ars geometriae (line 379 Folkerts), 610;(380), 412;(i. 27), 413;(i. 28), 412;(ii. 52), 413 610;(645), 610;(723), 610;(741), 610; Arius Didymus (926), 610 Stobaeus, Eclogae (ii. 7.20.93), 219 Arnobius Christopher of Mytilene Adversus Nationes (ii. 9) = (A21a), 66, 67, 85, (122. 86–90) = (A3e), 264 488 Cicero Asclepius of Tralles Amic.(13), 329;(87), 295;(88) = (A7a), 19, in Nic.(28 Taran)´ = (Fr. 1 Text H), 111, 115, 24, 31, 74, 100, 293, 327, 568 125;(49), 567;(61), 370 Att. (viii. 4.1), 326;(xiii. 32), 327 Athenaeus Dom.(75.4), 297 Deipnosophistae Fin. (ii. 14), 609;(iii. 60–61), 606;(v. 16–23), i (4e), 318;(5f), 26 606;(v. 18.49), 326;(v. 29.87) = (A5b2), iii (82a), 26 33, 270 iv (184e) = (B6), 27, 31, 281 Hort.(Fr.84), 327 x (433c), 535 N.D. (ii. 15), 297;(ii. 24), 578;(ii. 47.20), 297; xii (509d), 311;(509e), 298;(511c), 316;(512a), (ii. 58), 297;(ii. 84), 297;(ii. 120), 568 316;(516c), 26;(518f), 298;(519b) = (A8), Off.(i. 7), 609 19, 31, 74, 100, 297, 620;(526d), 318;(527c), de Orat. (iii. 33.132), 326;(iii. 34.138–39.14) = 312;(527d–e), 312;(528e), 311;(541f), 312; (A5c2), 7, 34, 275, 495 (544a), 311;(545a) = (A9), 3, 4, 8, 19, 26, Rep. (i. 10.16) = (A5b1), 33, 270, 330;(i. 31, 36, 73, 92, 97, 100, 184, 190, 211, 216, 15.22), 23;(i. 16), 329;(i. 38.59) = 220, 232, 300, 307, 332–33, 451, 479, 515, (A7, Text E), 24, 285, 327;(ii. 28), 327; 605;(546b), 211 (vi. 18–19), 138 xiii (600f), 27 Sen.(3), 328;(15), 331;(39–41) = (A9a), 7, 19, xiv (624a), 292 21, 24, 31, 56, 73, 100, 211, 293, 295, 323, xv (700d), 36 605;(42), 331;(44), 331 Athenaeus Mechanicus Tusc.(i. 10.19), 326;(i. 11.24), 326;(i. 18.41), (5.1) = (A1a), 29, 78, 256 326;(i. 22.51), 326;(iv. 2–3), 329;(iv. 36.78) = (A7, Text D), 24, 285, 327;(v. Ban¯uM¯us¯a 23.64) = (A5b3), 270;(v. 35.100), 42;(v. Verba filiorum (334–41 Clagett), 342 64), 327 Bion Claudianus Mamertus (Fr. 1.4), 304 De statu animae (2.7), 607 (Fr. 227) = (A3d), 24, 619 Codex Ambrosianus D27 sup. Biton (f. 81–115r – see Catalogus Codicum (62), 15, 16;(65), 15, 16 Astrologorum Graecorum iii. 11), 614 Boethius Columella in Cat.(1), 595 De Re Rustica (i. 1.7) = (B8a), 27, 281; De Institutione Arithmetica (i. 20), 462; (ii. 10.35), 577 (ii. 41), 595;(ii. 42), 455;(ii. 45), 599; Constantius Porphyrogenitus (ii. 50), 455 De Sententiis (294) = (A7, Text A), 284

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644 Index locorum

Corpus Paroemiographorum Graecorum (281b1), 489;(318b30), 514;(404. 3–13 = A25, (Leutsch and Schneidewin i. 213) = (A10, Text B), 552, 558;(405. 15–22 = A25, Text A), 29, 302, 304;(ii. 667), 607 Text A), 551, 557–58, 561

Damascius Empedocles (DK) De Principiis (ii. 172.16–22 – Ruelle) = (A13, (A86), 134 Text F), 45, 581, 585, 588–91 (B17), 215;(B35), 215;(B59), 156 Democritus (DK) Epicurus (A1), 547;(A37), 451;(A43), 156;(A47), 132; (Fr. 250), 451 (A57), 156, 250 Epistolographi Graeci (B6), 220, 250;(B10), 152;(B14), 53;(B86), (626 Hercher), 609;(635), 609 206;(B106), 195;(B145), 339;(B167), 250; Etymologicum Magnum (B187), 203;(B226), 150;(B232), 195; (674.37), 305 (B249), 200;(B250), 200;(B255), 200, Euclid 218 Elements Demosthenes i (Post. 1), 350, 357; (Post. 2), 351, 357; (Post. 3), De Corona (72.6), 220 351, 357;(27), 355, 357;(31), 350, 351, Erotic oration (44) = (A5c1), 5, 33, 34, 274 357 in Tim.(213.3), 216 iii (31), 355, 357;(35), 354, 357 Diodorus Siculus iv (1), 351 iv (13.2), 305; x (7.4) = (A7, Text A), 284, v (Def. 6), 179;(17), 459 289, 292, 293; xi (25), 312;(52), 9; xii (28.3), vi (Def. 1), 200, 355;(4), 355, 357;(6), 354, 357; 15, 82; xiv (41.3), 15;(50.4), 15; xv (7.1), 33; (8), 355, 357;(13), 177 xix (91), 9;(100), 10;(100–06), 9 vii (Def. 1), 460;(Def.2), 460;(Def.3), Diogenes of Apollonia (DK) 459;(Def.11), 464;(Def.20), 179;(3), (A21), 134 464;(22), 461, 463, 464–65, 468;(33), 458, Diogenes Laertius 468 i (30.3), 450;(38), 28 viii (7), 469;(8), 457, 465–66, 469 ii (77), 228, 229, 230;(77.4), 450;(84), 229; x (7), 233;(App.27), 234 (85), 229;(105.12), 450 xi (Def. 3), 354, 357;(Def.14), 395;(Def.18), iii (6), 32, 33, 39;(8), 229;(21–22), 608;(58.7), 352, 395;(Def.21), 351, 395;(11), 353, 357; 598;(61), 42;(62), 42;(91.3), 216 (19), 354 iv (2), 535;(13.9), 8;(40.8), 450;(41.8), 450; xii (14, line 9), 351;(15, line 23), 351 (52) = (A3d), 263 Sectio Canonis (Jan 148–49), 147;(148.49), v (25) = (A13, Text A), 8, 31, 45, 68, 84, 86, 140;(149), 148;(149.17), 130;(149.18–20), 92, 128, 563, 579, 583;(26), 563 435;(152.1 ff. = Prop. 3), 457–66, 468–69; vii (32.5), 450;(34), 229, 230;(36), 229;(64.2), (158.19 ff. = Prop. 11), 468 450;(68.8), 450;(84.5), 450;(163), 229–30; Eudemus (175), 229–30, 231;(178), 229–30 History of Astronomy (Fr. 149 Wehrli), 349 viii (15), 536;(20), 288, 290;(29), 557;(34 ff.), History of Geometry (Fr. 135 Wehrli), 349; 526;(46), 7, 8;(46–7), 28;(79–80), 607; (Fr. 139), 346;(Fr.140), 346, 348, 349 (79–83) = (A1), 4, 6, 12, 13, 18, 24, 26, 31, Physics (Fr. 60 Wehrli) = (A23), 31, 68, 85, 32, 82, 255, 303, 384, 492, 571;(80–81), 608; 86, 88, 92, 99, 508, 510–12, 522, 537; (82), 611, 619;(83), 80;(86) = (A6c), 6, 7, (Fr. 65) = (A24), 23, 31, 56, 68, 85, 92, 99, 278 295, 496, 540, 562;(Fr.88), 138–58 ix (31), 132;(38), 133;(46–7), 53;(47), 220; Eunapius (48), 53;(51), 598;(54), 439 Vitae Sophistarum (23. 1.8) = (A6d), 25, 278 Diogenianus Euripides ii (98.1) = (Leutsch and Schneidewin i. Electra (52), 219; Hecuba (602), 219; Helen 213) = (A10, Text A), 29, 302, 304 (1362), 159; Hippolytus (926), 58; Orestes Dionysius of Halicarnassus (889), 217; Phoenissae (531 ff.), 212 xx (7), 10 Eusebius Dioscorides Contra Hieroclem (xi) = (A6e), 25, 278 Mat. Med. iv (173.3.2), 301 Eutocius Doxographi Graeci in Archim. dim. circ.(228 Heiberg), 346

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Index locorum 645

in Archim. sphaer. et cyl. ii (iii. 56.13 Regimen (i); (i. 2), 57, 151 Heiberg/Stamatis), 381;(iii. 66.8 ff.), 345;(iii Regimen in Acute Diseases (11.66), 150;(11.84), 84.12–88.2) = (A14), 31, 44, 46, 49, 50, 52, 150 55, 56, 92, 98, 342, 396;(iii 88.3–96.27) = Wounds of the Head (19.13), 151 (A15), 29, 31, 57, 84, 100, 361, 372–76, Hippolytus 377–78, 379, 397, 619 Refutation of all Heresies (iv. 13 ff.), 440; (vi. 24), 596 Florus Homer i (13. 2–3) = (A4a), 11, 265 Iliad (iii. 182), 24;(xx. 131), 246;(xxiii. 416), 157 Gellius, Aulus Odyssey (ii. 354), 158;(v. 392), 504;(v. 452), Noctes Atticae (x. 12), 571;(x12.8–10) = 504;(x. 238), 158;(xii. 168–69), 504; (A10a), 30, 82, 384, 570;(xvii. 21), 330 (xvi. 374), 193 Greek Anthology Horace vi (165), 159;(309), 160 Carmina (i. 28) = (A3), 19, 20, 21, 22, 260, Gregory of Corinth 293, 297, 610;(iii. 2. 21–22), 22;(iii. 4. De Dialectis (praefatio) = (A6g), 31, 279 29–31), 22 H. unayn ibn Ish. ¯aq Hellanicus, FGrH 4 Maxims of the Philosophers (20 = Loewenthal (Fr. 104), 305 83), 615 Heraclides of Pontus (Fr. 44), 311 Iamblichus Heraclitus (DK) Comm. Math. (17.15 Festa), 484;(31.4 ff.), 110; (B7), 58, 150;(B40), 56;(B45), 195;(B129), 56 (43.13), 187, 194;(44.10–17) = (Fr. 3), 182; Herodian (45.2–3), 195;(45.7–8), 186;(78.8–18) = Hdn. Gr. (57. 9–10 Lentz), 619;(77.12), 619; (A25, Text C), 77, 552, 557, 563–68; (654.27–28), 619;(656.15), 619;(851.33), (78.27–36), 52 619 in Nic. (6.16–7.2 Pistelli), 109;(9.1–7) = Herodotus (Fr. 1 Text F), 110, 124;(52.17), 220;(82 ff.), i (13), 249;(115), 249;(126), 249;(138), 338; 442;(101), 477;(100.19–101.11) = (Fr. 2, (207), 248 Text A), 164, 170, 171;(110.17 ff.), 178; iii (80.2–82), 211;(117.9), 566;(136), 9 (113.12–113.21) = (Fr. 2, Text B), 164, 171; vii (149.3), 201, 206;(170), 9, 291 (116.1–7) = (Fr. 2, Text C), 165, 171; viii (112.1), 206 (118.19–119.3) = (Fr. 2, Text D), 165, 176 ix (62), 193 VP (31), 536;(88), 20;(96), 319;(101), 291; Hero (104) = (A6b), 26, 277;(113), 290;(115.8), Definitiones (135.5), 241;(136.1) = (A6a), 277; 565;(126), 292;(127) = (A6b), 37, 277, (138.5), 241 296, 301, 609;(132.11–23), 52;(138.5), 250; Geometrica (8,p.218 Heiberg), 610 (138.11), 250;(160) = (Fr. 1 Text D), 109, Pneumatics (9), 575;(14–15), 575;(15), 575; 115, 125;(196), 288;(197–8) = (A7), 4, 14, (28–30), 575;(37), 575;(37–38), 575;(42), 18, 19, 31, 73, 92, 100, 283, 288;(198), 609; 575;(54), 575 (216), 292;(229–40), 296;(231), 291;(233), Hesychius 296, 301;(234), 288;(239), 292, 609; (4823), 220 (250) = (A6b), 6, 277;(266) = (A6b), Hesychius of Miletus 277;(267) = (A6b), 6, 15, 277;(267), 95, Life of Aristotle (Aristotelis...Fragmenta 608, 609 14 = A13, Text B), 580, 583 Ibn Ab¯iUs.aybi aë Hippasus (DK) Sources of Information on the Classes of (A12), 54, 135 Physicians, 616 Hippocratic Corpus Isocrates AWP (10.1), 150 Arch.(67.6), 217; Areop. (21), 213;(39 ff.), 604; Epidemics (i. 23), 151 (60.3), 207, 212; Busiris (28–29), 536; Helen Fleshes (9.14), 248 (42.3), 150; Letters (viii. 3.1), 215; Nicocles Physician (1), 216 (14 ff.), 213;(33.6), 215; To Nicocles (38), Places in Man (24), 157 249

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646 Index locorum

Jerome In Gorg. (31.4 Norvin), 241 Contra Rufinum (iii. 40) = (A5b8), 272 Pr.inCat. = CAG xii. 1 (13), 94 Ep. (xlix. 19.4–5) = (B5a), 31, 32, 280; Vit. Pl. (61), 320 (liii. 1.2) = (A5b8), 272;(lxxix. 9) = Origen (A7, Text H), 287 Cels. (4.89.4), 246 De Viris Illustribus (Praef.), 327 John the Geometer Pappus (J. P. Migne, Patrologiae Cursus, series Graeca, Comm. on Euclid x (1.1), 176;(2.17), 176 Vol. 106: 919) = (A3f), 264 Mathematical Collection (681.7), 178; Justin (1022.7–9), 393;(1022.13–15), 77; xx (5), 10 (1024.12–1025.4), 78;(1028.18–21), 81, 384 Parmenides (DK) Lactantius (B8. 42–49), 547 On the Anger of God (18.4) = (A7, Text G), Pausanias 286, 288 i (18.2.2), 319;(37.2.2), 319; vi (20.12), 576; vii Leonidas of Tarentum (30.2), 319; viii (34.1), 319; ix (34.1), 319; AP (vi. 309), 305 x (9.3.1), 319;(10.6), 9;(13.10), 9 Livy Pherecydes of Athens, FGrH 9 ix (1), 329; xxiv (3), 10;(34.10), 577 (Fr. 72), 305 Lucian Philo of Byzantium Apol. (11.23), 301 Pneumatics (40), 575;(42), 575 Lucretius Philodemus i (968–83), 546; ii (216 ff.), 132;(225), 132; Acad. Ind. (v. 32–vi. 12) = (A5c3), 34, 275; v (1069), 577 (x. 5–11) = (A5b4), 33, 34, 271 Lumen Animae Philolaus (Huffman) (ii Aa, Farinator [see subject index]), 612;(ii (A7a), 69, 72 Da), 612;(iii V), 612;(vii R), 612;(xxi G), (Fr. 1), 70, 481, 495;(Fr.4), 424, 495, 564; 612;(xxxi Aa), 612; (xxxxix B), 612; (xlix (Fr. 5), 152, 250, 424, 486;(Fr.6), 70, Cg), 612; (xlix Ec), 612; (xxxxix O), 612 177, 435–36, 443, 481;(Fr.6a), 66, 174, Lydus, Joannes 176, 177, 412, 415, 417–18, 436, 481, 534; De mensibus, 607 (Fr. 7), 70, 526;(Fr.13), 66;(Fr.17), 177, 178 Michael of Ephesus Pseudo-Philolaus in Eth. Nic. = CAG xxii. 3 (16.10), 530 (Fr. 11), 228;(Fr.12), 591 Philoponus Nepos De Aeternitate Mundi (522.16–23 Rabe) = Dion (2.1–2) = (A5b5), 40, 271 (A13, Text G), 582;(527.6), 591 Nicomachus in APo. = CAG xiii. 3 (102.12–22), 369, 377; Ar.(i. 2.4–5), 116;(i. 3), 391, 454;(i. 3.1–2), (159.46), 534;(160.3), 534 116;(i. 3.2), 121;(i. 3.3) = (Fr. 1, Text C), in Nic. (7 Hoche) = (Fr. 1, Text G), 110, 115, 108, 115;(i. 3.4), 448;(i. 3.5), 116;(i. 3.7), 125 116, 121;(i. 5.2), 121;(i. 6.4), 122;(i. 8–13), Philostratus 241;(i. 11.2), 122;(i. 18.1), 122;(i. 19), 439, VA (vi. 31), 341, 606 458;(i. 21), 439, 462;(ii. 7), 501;(ii. 19), Photius 439;(ii. 21 ff.), 241;(ii. 21.3), 443;(ii. 22), Bibliotheca (167) = (A5b11), 273;(249) = 170, 455;(ii. 23.4), 530;(ii. 23.6), 178; (A5b10), 25, 33, 273 (ii. 24.2), 534;(ii. 24.4), 534;(ii. 25.2), 178; Pindar (ii. 26.2), 173–75;(ii. 27), 455;(ii. 29), 176 O. (10.84), 160 Harm.(3), 138;(4), 147, 148;(6), 142, 476, 565; Plato (12,Jan262.1), 447 Alc. i (126c), 191, 201 Ap. (19a), 152;(20b), 479 Oinopides (DK) Ax. (367a), 138–58 (A9), 53 Chrm. (166a), 241 Olympiodorus Cra. (436a), 195;(438b1–3), 193 In Alcibiadem (2.86–93) = (A5b9), 33, 272 Epin. (984e), 592;(990d), 388;(991d ff.), 116

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Index locorum 647

Epistulae (527d), 116;(528a–d), 385, 391–92;(528a), vii (324a) = (A5), 35, 266;(326b ff.), 312; 57, 391, 559;(528a6–7), 385;(528a9–b1), 385; (326b–d) = (A5), 35, 36, 266;(338c–d) (528b), 80;(528b2–3), 386;(528b3), 377; = (A5), 35, 36, 266;(339a–b) = (A5), 8, (528b4–7), 386–87, 389;(528b6), 390; 37, 266;(339d–e) = (A5), 34, 35, 36, 37, (528b7–8), 388;(528c), 41, 57, 398;(528c1), 266;(350a) = (A5), 35, 37, 40, 267 388;(528c2–4), 390;(528c4–5), 390; xiii, 255 (528c5–6), 390;(528c7), 388;(528c7–d1), Euthd. (290c), 244, 390, 396 389;(528d), 251;(528d9), 387, 389;(529a ff.), Euthphr.(2a), 229;(7b ff.), 191, 221;(7b10), 387;(529d), 57, 322, 395;(529e), 566;(530), 202 155;(530c), 424;(530d), 8, 41, 64, 84, 92, Grg. (451b), 69, 240, 241;(451c), 69, 240, 241; 109, 114, 395, 414;(531a), 398;(531c), 41, 49, (453e2), 240;(453e7), 240;(464d), 222; 57, 63, 237, 414, 423;(531d), 64;(531e), 504; (465b7), 209, 210;(483c), 207, 314, 315; (536d), 69;(545d ff.), 89;(545e), 437;(546a (483d), 314;(484c), 315;(491b), 249;(507e ff.), 436;(546b), 236;(546b14), 442;(546c), ff.), 191;(508a), 73, 205, 208, 210;(512b), 82 430, 439, 442;(546d), 191;(558c5–6), 213; Hp. Ma. (304c), 247 (562c), 245;(581b), 558;(587e), 236;(598a), Hp. Mi. (366c), 241 152;(610a), 194 Ion (538c5), 150 Smp. (188b), 206;(204b7), 195;(213d), 215 Lg. (653d–e), 304;(700c), 158;(712d), 602; Sph. (221a), 158;(256d), 510, 513 (729b), 339;(746e), 239;(747a–b), 227, Tht. (145a), 69, 226, 244;(150b2), 150;(153c), 228, 239;(757a6), 212;(757b), 213;(757e), 500, 504;(161e), 251;(162e), 249;(171d), 205;(817e), 391;(875b6), 207;(889b), 131, 322;(173e), 567;(184a), 322;(198a), 240 156;(893b), 78;(893e), 133;(898a), 527; Ti. (17a), 86;(20a), 85;(27a), 85;(27d), 116; (906c), 206;(918c3), 505 (28c–d), 587;(29e–47e), 86;(31c–32c), 180; Meno (82b9–85b7), 360 (32c), 87;(33b), 527;(33c), 87, 548; Mx. (244a), 215 (33d–34a), 87;(35a ff.), 64;(36a), 178, 180; Phd. (60d), 479;(64a), 334;(64c ff.), 329; (36a–b), 167;(36e), 87, 542, 548;(40a), 527; (65a), 335;(66b ff.), 326;(66c), 334;(67a), (40b4), 550;(44d), 524;(45b ff.), 88, 556, 334;(69c8), 149;(77c), 504;(83b), 589; 560;(45c), 556, 561;(45d), 556;(46a), 556; (85c7), 193;(92d), 249;(99c), 193;(108b), (48b–68d), 86;(49b ff.), 590;(51b), 292; 154;(109d–e), 322 (52e), 513, 537;(56c), 537;(57e), 505, 511, Phdr. (261d), 131;(267a), 479;(270b ff.), 89; 513–14;(58a), 514;(67a), 140;(67b), 130, 135, (270c), 89;(274c), 202;(274c8), 202; 141;(67c), 143;(80a), 140, 436, 448;(80b), (276d), 154 447;(91c), 160 Phlb. (16c–17a), 89;(17b), 90;(17c11), 181; Plethon, Georgius Gemistus (17d), 90;(21a), 334;(54a), 504;(55c–59b), E Diodoro et Plutarcho (19–20) = (A5a2), 269 232;(56d), 242;(56e), 242;(63c), 335;(63d), Pliny 335 Naturalis Historia i (8c) = (B8b), 27, 282; Plt. (257a ff.), 205;(257b), 205, 210;(258d), (10c) = (B8b), 27, 282;(14c) = (B8b), 27, 243;(259e), 242, 243 282;(15c) = (B8b), 27, 282;(17c) = Prm. (147b), 589 (B8b), 27, 282;(18c) = (B8b), 27, 282; x Prt. (314e), 319;(334b2), 525;(346b), 215; (137), 572; xxxiv (40), 577;(75), 576; xxxvi (356d), 191;(356e), 201;(361d), 247 (117), 577 Rep. (343c), 194, 314;(344a), 207;(351d), 235; Plutarch (359c), 207;(367e), 245;(376a), 318;(376e), Advice about Keeping Well (131a–b), 341; 480;(397a), 156;(404d), 312;(422e9), 217; (132b), 301 (424d), 157;(428b), 235;(428d), 71, 245; Cato the Elder (ii. 3), 329 (432a), 235;(439d1), 203;(441a9), 203; Common Conceptions (1069e), 606; (442b), 249;(443d–e), 235;(458d), 210; (1070f–1071e), 606 (472c), 152;(475), 513;(484c), 246;(500b), Dion (xviii. 5.4) = (A5a1), 8, 36, 39, 268;(xx. 322;(509d), 597;(509d–511e), 598;(511a), 1.1) = (A5a1), 39, 268;(xx. 2), 39 246;(518c), 503;(521c), 59;(521d), 57, 242, The Divine Vengeance (551a) = (A7, Text C), 424;(525a), 69;(525a–b), 243;(525b), 69; 285 (525c), 69, 243;(526b), 243;(526c), 242; The E at Delphi (386d–f) = (A15, Text B), (527a), 395;(527a–b), 385;(527c), 385; 367–68, 371, 372, 375, 378, 391

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648 Index locorum

Plutarch (cont.) 167;(92.28 ff.), 167;(93.5), 167;(94.24–26), The Education of Children (8b) = (A5c4), 167;(94.29), 167;(96.7), 117;(104.4–16) = 34, 276;(9f), 339;(10d) = (A7, Text B), (A18), 60, 62, 99, 133, 152, 443;(104.6–7), 284 446;(104.14), 445;(107.15–108.21) = The Face on the Moon (930a), 347 (A17), 48, 49, 51–52, 54–55, 60, 62, 99, 428; The Generation of the Soul in the Timaeus (108.28–29), 432;(109.3), 439;(112.12), 439; (1021a), 475 (115.1), 439;(119.13), 476;(119.14–15), 476; Greek Questions (295a), 26 (130.9), 439;(136.13), 402;(138–42), 402, Lycurgus (xii. 1.7), 301 410;(139.27), 427;(141.7), 409;(144.5), 439; Lysander (xix), 36 (144.15), 441;(145.13), 441;(148.5), 439, 441; Marcellus (xiv), 14;(xiv. 5–6) = (A15b), 79, (149.6), 441 80, 365, 378–80, 392–93, 394 VP (19), 527;(32), 319;(56), 6 On Music (1147a) = (A19c), 100, 481 Proclus Nicias,(xi. 1.3), 291 in Euc. (38.1), 241;(39 ff.), 391;(65.16–21), 52; Pericles (xvi. 3), 12;(xxvii), 15, 82 (66), 357;(66.4–18) = (A6), 5, 46, 50, 51, Pompey (viii), 13 52, 69, 276, 359, 400;(66.18 ff.), 5;(66–67), Precepts of Statecraft (821b–c) = (A1c), 12, 258 359;(72–3), 358;(95.21), 501;(213), 350; The Sign of Socrates (579b–d) = (A15, Text (250), 349;(419.15–18), 52;(428.10), 610 C), 368, 371, 372, 378 in Plat. Tim. (32a–b, Diehl ii. 33.29–34.4) = Solon (v), 36 (A14a), 344, 345;(ii. 76.22), 345 Table Talk (714e), 304, 305;(718e) = (A15a), De Prov. (54), 287 14, 79, 80, 364, 378–80, 391, 392–93, 394, Procopius 398, 451;(745e), 138 de Bellis (vii. 13.16.3), 156 Polyaenus Propertius vi (11), 9 iv (1. 75–78) = (A3c), 21, 22, 263 Polybius Psellus, Michael ii (39), 9 Chronographia (v. 31.10), 156 iii (86.7), 13;(88.4), 9 Historia Brevis (100.5–11) = (A6f), 25, 279 x (1), 9 Opuscula (7.130), 596 Polyclitus (DK) Ptolemy (B2), 72, 238 Harmonics (i. 1–2), 565;(i. 1–16), 407–09; Porphyry (i. 2), 427;(i. 3), 146, 147, 148;(i. 4), 166; In Cat. = CAG iv. 1 (59.10), 450;(131.17), (i. 5), 166, 351, 426;(i. 5–6), 426;(i. 6), 428, 566 431, 433, 434, 443, 444, 446, 451;(i. 7), 432; Fr. (60) = (A13, Text G), 582, 585, 591–93 (i. 8), 142, 476;(i. 13–14) = (A16), 24, 41, Isagoge,(3.17–18), 597 44, 46–47, 49, 54, 55, 60, 63, 74, 87, 98–99, Philosophy from Oracles (121.8), 220 130, 169, 175, 402;(A16, lines 24–26), In Ptolemaei Harmonica (During¨ 3.18 ff.), 432; 417–18, 421;(i. 14), 434;(ii. 5), 446;(ii. 14), (5.7), 116–17, 445;(5.8 ff.), 432, 437; 402, 409, 416 (5.13–14), 437;(6.23), 146;(9.34–10.1), 146; Ptolemy (10.23 ff.), 166;(11.24), 489;(25.7), 117; Life of Aristotle (Aristotelis...Fragmenta (31.6–12), 449;(31.27–28), 118;(33.16 ff.), 20 = A13, Text C), 581, 583 147;(33.17), 118;(33.18), 118;(35.27), 447; (37.15), 445;(39.10), 118;(41.13), 118;(42.30), Quintilian 118;(46.4), 118;(47.14), 118;(48.32), 118; Institutio Oratoria (i. 4–17), 479;(i. 10.9), 480; (49.15), 118;(49.22), 118;(51.15), 118; (i. 10.12–13), 480;(i. 10.17) = (A19b), 100, (55.27–58.4) = (Fr. 1), 24, 25, 27, 30, 51–52, 478;(ii. 6.5), 568 54, 58–60, 62, 68, 69, 74, 76, 96, 97, 98–99, 103, 115, 167–68, 187, 473–75, 481, 562; Scholia in Clem. Al. Protr. (56.2), 620;(56.5), 119;(61.16–65.19), 118; (2.17.2), 159 (61.19), 118;(62.31), 140;(80.28–81.16) = Scholia in Dem. (Fr. 1 Text B), 107, 115, 119, 137;(90.3–5), xxiv (114), 319 166;(92.9–94.28) = (Fr. 2), 30, 51–52, Scholia in Euc. 54–55, 60, 69, 74, 98–99, 156, 162, 188, 244, (p. 654 Heiberg), 389 418, 529, 530–31, 604;(92.9), 166;(92.22), Scholia in Horatium

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Index locorum 649

(ps.-Acron, Keller 1902: 105) = (A3a), 19, Strabo 262 vi (2.11), 301;(3.4) = (A4), 5, 9, 10, 11, 13, 17, (Porphyrio, Holder 1894: 36) = (A3b), 19, 19, 265 262 Suda Scholia in Plat. (4121) = (A2), 4, 6, 7, 10, 13, 18, 26, 31, 32, Charm. (165e), 241 259 Phaed. (108d4), 135 Synesius R. (509d = Hermann vi. 350), 597 Sermo de dono astrolabii (ii. 5 ff.) = (A1f),259 Seneca Syrianus De Ira (1.15), 287 in Metaph. = CAG vi.1 (151), 597;(166), 597; De Tranq. (17.4), 299 (175), 95 Sextus Empiricus Adversus Mathematicos (vii. 137), 251;(vii. Themistius 138), 220;(viii. 327), 220;(x. 278 ff.), 502; Orationes (17) = (A1e), 258 (x. 316), 592 Theocritus Simplicius (2.30), 159;(8.88), 304 in Cael. = CAG vii (58.36), 550;(83.18), 550; Theognostus (285.21–27), 544;(296.16–18 = A13, Text Canones (244.2), 619;(249.5), 619 E), 581, 584, 585, 587;(379.14–17 = A13, Theologumena Arithmeticae Text D), 581, 584, 585, 587, 588;(392.16), (52.9 De Falco), 433 584;(408.3), 550;(444.28), 550 Theon of Smyrna in Cat. = CAG viii (2.9–25), 95, 596; Life of Plato = (A5c3), 275 (128.18–20), 78, 81;(206.8 ff.), 596;(382.7), Mathematics Useful for Reading Plato (p. 1.15), 596 472;(2.3–15) = (A15, Text A), 367, 371, in Ph. = CAG ix–x (161.14–15), 115;(247.33), 372, 375, 377, 378, 391, 398;(20.19–20) = 511;(429.8–430.34), 510;(431.4–431.16) = (A20), 31, 67, 99, 483, 486–87;(21.19–21), (A23), 31, 68, 85, 86, 88, 92, 99, 508, 510–12, 486;(22.5–10) = (A21), 31, 67, 99, 485; 522, 537;(432.20), 511, 512;(433.13), 512; (47.7–8), 472;(47.18–72.20), 472;(49.6), (465.23–468.18), 541;(466.8), 542; 472;(50.4), 147;(56.9–61.18), 472;(56.9), (467.26–468.3) = (A24), 23, 31, 56, 68, 85, 474;(56.10–59.3), 472, 473;(58.14–15), 474; 92, 99, 295, 540, 562;(468.5), 542; (59.4 ff.), 138, 142;(59.4–60.11), 472–73; (732.26–733.1), 527;(732.31–2), 138–58 (59.9), 473;(60.13), 147;(60.16 ff.), 473; Sophocles (60.16–61.23) = (A19a), 62, 100, 139, 451, Antigone (192), 154 470;(61.19), 472;(64.1), 472;(66.22), 142; Fr. (843), 193, 195 (76.21), 426, 458;(80.15), 439;(82.6), 180; OC (254–55), 567 (106. 7–11) = (B5), 32, 280;(106.15), 180 Speusippus Theophrastus (Fr. 28,Taran),´ 439, 487, 536 Char. (21.9), 301 Stobaeus CP (v. 1.3), 525 i (Pr. 4) = (Fr. 4), 30, 51, 65, 68–72, 83, 93, HP (i. 1.9), 523, 525;(i. 1.12), 523;(i. 12), 525; 97, 98–99, 129, 189, 190, 204–05, 218, 225, (iv. 2.5), 157;(iv. 8.3.7), 525;(iv. 8.5.6), 525 332;(7.10), 607;(41.2), 597;(369.9–11), Metaph. (6a) = (A13, Text H), 7, 45, 48, 607 51–52, 55, 67, 438, 582, 585, 593 ii (7.20.93), 219;(23.4), 212;(122.11), 599; Sens. (51), 251;(53), 476;(59), 134 (125.2), 599;(128.23), 605 Theophylact iii (1.172), 215 Epistulae (127.48–51) = (A1g), 259 iv (1), 184;(1.132), 599;(1.133), 607;(1.139) = Theopompus (Fr. 3), 30, 55–56, 66, 72–74, 75, 89, 96, FGrH (259), 230 98–99, 182, 232, 332, 503, 515, 600, 605; Thesleff, Pythagorean Texts of the Hellenistic (1.142), 185;(1.144), 185;(32.1.15), 26 Period Stoicorum Veterum Fragmenta (SVF –H.von (3.9–8.19), 596;(3.19), 60;(6.14), 227;(7.10), Arnim, ed.) 607;(8.26–15.2), 599;(8.32–3), 599;(11.8–9), ii (206), 451;(227.25), 203;(230), 451;(863–4), 599;(11.9–10), 599;(14.1 ff.), 203;(14.15), 561;(868), 561 60;(15.3–19.2), 596;(15.15–20), 596;(17.9), iii (95.3), 203 60;(19.3–20.17), 597;(19.10), 60;

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650 Index locorum

Thesleff (cont.) vi (8.2), 13;(38.5), 212;(39), 217;(44), 9; (19.14 ff.), 483;(19.19–20), 93, 597; (72.5), 14;(104), 9 (21.6–32.23), 595;(22.12), 60;(22.14), 595; vii (11), 222;(33), 9, 291;(67), 193 (31.33), 219;(33.1–35.30), 184;(33.1–36.11), 599; viii (75.2), 200;(86.5.1), 220;(91), 9;(93.3), (33.8–9), 604;(33.14–15), 605;(33.15–17), 605; 200 (33.18), 602;(34.3–10), 599;(34.4–34.10), 170; Tzetzes (34.10–11), 601;(34.25), 602;(34.30–31), 604; Epistulae (75) = (A5b12), 33, 273 (35.24–25), 606;(36.4), 605;(36.12–39.25), Historiae (x. 988–92) = (A5b13), 33, 274 597;(37.18), 219;(38.14–15), 93, 601;(38.14 ff.), 251;(38.24–39.25), 597;(39.4–25), 92, 598; Valerius Maximus (40.1–16), 598;(40.17–43.23), 606;(40.22), iv (1. ext. 1) = (A7, Text F), 286, 289 606;(43 ff.), 226;(43.8–18), 606;(43.24–45.4), viii (7. ext. 3) = (A5b6), 33, 271;(12. ext. 1), 598;(44.26), 598;(44.27–28), 598;(44.35), 599; 369 (45.20–30), 608;(46.1–7), 255, 607;(46.8–15), Varro 608;(46.20–47.6), 609;(47.8–13), 607; Res Rusticae (i. 1.8) = (B8), 27, 31, 281 (47.14–17), 607;(47.18–22), 606;(47.19–22), Vergil 341;(47.23), 184;(47.23–26), 599; Aen. v (489), 577; vii (810), 577 (47.27–48.2), 597;(47.29–48.1), 483;(48.3–6), Ecl. (viii. 75), 280 597;(48.22), 219;(50.11–12), 201;(59), 228; Vitruvius (68.26), 605;(68.29), 201;(71.21–22), 604; i (1.17) = (A1b), 29, 78, 257 (73.10), 207;(76.2–3), 604;(77.1–9), 607; vii (Pr. 14) = (B7), 28, 31, 78, 281, 303 (81.22), 201;(103.5), 93;(108.12), 207; ix (Pr. 13–14) = (A15c), 24, 28, 366, 384;(8.1), (118.1–4), 93;(118.23), 207;(119.25), 219; 29;(8. 2–3), 574 (119.28–120.2), 605;(124.11–138.22), 608; (146.1–22), 598;(146.7), 227;(146.14), 598; Xenocrates (146.15), 598;(146.16), 227;(146.21), 599; Fr. (15), 484, 487 (164.30), 219;(190.1), 605;(190.8), 203;(192.22 Xenophanes (DK) ff.), 203 (Fr. 18), 195 Thucydides Xenophon i (24), 216;(70), 249;(76), 315;(80), 159; Aeges. (x .2), 219 (87.2.2), 150;(97.2.7), 248 An. (v. 4.28), 157 ii (13), 11;(13.95), 249;(40), 203;(95), Cyr. (i. 6.4), 291;(vii. 1.22), 604;(vii. 5.86), 215 338;(viii. 7.3), 222 iii (45.4), HG (ii. 1.10), 26;(ii. 3.10), 26;(v. 2.5), 561 207;(62.3–4), 212;(82.8), 207 iv (40.2.6), 150;(65), 567;(122), 202 Zeno of Elea (DK) v (105), 315 (A29), 136

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General index

Reference should also be made to the Index Locorum for the names of ancient authors. General references to an author’s works are given at the end of the listing for each author. Specific references are found in the Index Locorum.

Aalders, G. J. D., 600, 601–05 anecdotes, 18–19, 100, 287, 338–41, 542, 593; and abacus table, 610 Archytas’ theory of definition, 504 Academy, xi, 42, 95, 319–20, 377, 501, 589–90, anger, 19, 73, 288–90, 339–40 592; on the one, 484 angle of incidence, 555 Ackrill, J. L., 61, 335 animals, 594; parts of, 517–20, 525–28 acoustics, 30, 99, 113–14, 129–48; Archytas’ Annas, J., 487, 606 theory in A19a, 473–75 Anonymus Iamblichi, 208 Adam, J., 210, 385, 386, 390, 439, 442 Antiochus of Ascalon, 93, 599 adminiculum, 297, 561, 568 Antiphanes, 535, 536 Adrastus, commentator on the Timaeus, 180, antiphonoi, 445 472 Antisthenes, 230 Aelian, as source for A8, 298–99 apatheia, 602–03, 605 aether, 526, 591, 594 Aphrodite, 160 Agesilaus, 34 apotom¯e, 455 agriculture, 27–28, 31 appearance vs. reality, 152 air, compressed, 573–79; as the medium of Apuleius, 25, 86, 99; Archimedes as a source for sound, 131, 133–34, 140–41, 562; and the Archytas’ optics, use of, 554–55; as a source visual ray, 569 for A25, 553–54, 560; Apology, 553 pseudo-Albertus Magnus, The Marvels of the arbitrator, Archytas’ definition of, 497–99, 500, World, 25, 610–11 507 Alcibiades, 34 Archedemus, 8, 37–38 Alcmaeon, 527, 557 Archelaus, 54; on sound, 134 Alcman, 27 Archestratus of Gela, 318 Alexander of Aphrodisias, Archytas’ argument Archimedes, 14, 23, 78, 384, 577; Catoptrics, 553, for an unlimited universe, response to, 544, 554–55; On the Sphere and Cylinder, 345; 548–49; Plato’s theory of motion, criticism Sand Reckoner, 22, 374 of, 510–11 Archippus, 6 Alexander the Molossian, 10 Archita Tharentinus, On Events in Nature, Alexander Polyhistor, 94; Pythagorean Memoirs, 611–14 556 Architas (later spelling of Archytas), 25, altar, Archytas’ definition of, 497–99, 500, 507 610–14 amminiculum, see adminiculum Archytas (This is a selective listing. Please also Ammonius son of Hermeias, 125 consult the table of contents and other subject analogy, 341 headings), acoustic theory, 129–48, 473–75, Anaxagoras, 34, 134, 547 562; and aether, 591–93; on agriculture, Anaximander, 547 27–28, 31; anger of, 288–90; on arithmetic, Andronicus of Rhodes, 93, 596 31, 32, 48; and artillery, 14, 17, 82;

651

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652 General index

Archytas (cont.) Archytas, author of On Agriculture, 27–28 astronomer, 22–24, 29, 53, 65, 85, 293, Archytas, author of Art of Cookery, 26 295–96; author of Euclid, Elements VIII?, Archytas, ephor at Sparta, 26 469–70; author of On Mechanism?, 28–30, Archytas Maximus, The Circular Theory of the 82; author of Sectio Canonis?, 468–69;on Things in the Heaven, 614 calculation, 218; cenotaph of, 21; and Archytas of Amphissa, 26 children, 18, 300, 302–07; chronology of his Archytas of Mytilene, 24, 26–27 life, 5–6; concordance, 445–50; cosmology, Archytas, the architect, author of On 85–86; criticism of, 24; death of, 19–21; Mechanism, 28–30, 82, 303, 571 definitions, 66–67, 490–503; as democrat, Archytas the builder, 29, 302–03 190; Doric dialect, xiii, 31, 92;dove,571–79; Archytas the elder, 25–26 early sources for, 3–4, 91; elements of pseudo-Archytas geometry, 350–51; epistemology, 55–56, Concerning the Whole System of Categories, 92, 65–66, 127, 149–52; on equality, 214–15; 95, 595–96 experiments, 141–42; family, 6; father, 6;on Letter to Dionysius II, 608 friendship, 294–96; as a general, 3, 11–14, Letter to Plato, 608 20, 38; general autokrator¯ , 13–14; geometer, On Being, 598 21, 65, 83, 85; harmonics, 24, 41, 46–47, On Intelligence and Perception, 92, 597–98 48–49, 51, 54, 60–64, 65, 87, 410–28;as On Law and Justice, 97, 166, 170, 178, 183, 184, Italian philosopher, 95; kinship of sciences 599–606 in, 64; leader of Italian league, 10; limiters On Moral Education, 93, 606–07 and unlimiteds, 66–67, 84, 485, 495–99, On Opposites, 92, 595, 596 502; logistic, 68–76, 240; mathematician, On Principles, 93, 597 41, 44, 45–46, 46–51, 71, 465, 466–70; On the Good and Happy Man, 93, mathematics, abstract nature of (see also 599 Eratosthenes), 29, 45–46; mechanics, 14, On Wisdom, 227, 598–99 28–29, 30, 31, 76–83, 531, 571–79;on Ten Universal Assertions, 595, 596–97 motion, 505, 509–15, 518–22; and the Arion (Pythagorean), 33 multitude, 12, 18; and mystical side of Aristaeus of Croton, 176 Pythagoreanism, 23, 24–25; name, 619–20; Aristarchus of Samos, 558 on numbers as causes, 488–89; obscurity of Aristides Quintilianus, 138 his musical theory, 24; on the one, 483–85, Aristippus, 229, 230–31 486–87; optics, 76–77, 88, 553–69; physical aristocracy, and the harmonic mean, 603–04 elements, lack of discussion of, 67–68, 562; Ariston, 229, 230 theory of pitch, 140, 141–48; on plants, Aristophanes, 113 27–28; on pleasure, 19, 294–96, 300, Aristophilides, 9 331–37; on predecessors, 51, 139, 169, Aristotle, 150; acoustics, 113–14, 131, 141, 143; and 430–31, 438; private life, 18–19; collected aether, 591–93; on agriculture, 27–28;on books of Pythagoras, 617; as a Pythagorean, analogia, 179–80; and Archytas, 42, 84–86, 8, 45, 127–28, 172, 586; prominent in the 88–89; books on Archytas, 4, 8, 45, 451, 512, pseudo-Pythagorean tradition, 91, 92; 583–94; testimonia about Archytas, 92, 99; pupils of, 7–8; reception, 21–25;inRepublic on circular motion, 527; on the clapper of vii, 41, 385–92; on the sciences, 57–68, 76, Archytas, 302–04; on concord, 201–02;on 83–85, 126–29, 232–40; and the Sectio the writers on concords, 447–50;on Canonis, 130;intheSeventh Letter, 34; and definition, 490–503; on history of slaves, 18; style, 147–48, 353; and swearing, definition, 491–94; on the democratic 338–40; teachers of, 6–7; and Tarentum, revolution in Tarentum, 17–18, 184;on 8–18; teaching method, 319–20; speaker of dynamics, 89, 537; on equality, 213–14;on Plato’s Timaeus?, 46, 586; weaknesses of friendship, 295; on guest-friends, 37;on character, 19, 288–90, 292; writings, 30–32, harmony of the spheres, 137–38; on justice, 167–68, 187–88; Discourses (Diatribes), 30, 46–47, 191–93, 223; does not use logistic, 98, 240, 349; Harmonics, 30–31, 51, 66, 98, 226, 243; on mechanics, 81–82, 393;on 115, 126, 148–49, 167–68, 187–88, 349, 474; motion, 509–15, 520–22, 526; on optics, On Mathematics, 126, 167–68; On Music, 563; on parts of animals and plants, 522–23; 167–68; On Sciences, 30, 98, 185, 187–88, 349 on pitch, 140; on place, 549; on pleasure,

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General index 653

334, 335–37; point, definition of, 501;on astronomy, 22–24, 29, 53, 57–58, 60, 64, 65, 76, proportion, 529; criticism of 85, 128–29, 243, 295–96; in Plato, 395;in Pythagoreans for not using physical Nicomachus, 116 principles, 68, 521, 562, 593; on early Athena, 493 Pythagoreans, 489, 519, 534, 583–94; Athenaeus, Aristoxenus’ Life of Archytas, distinction between Pythagoreans and use of, 4; as source for A8, 298–99;asa Plato, 484; Pythagoreans glorified at the source for A9, 311–12 expense of, 95–96, 99–100; on Pythagorean Athenaeus Mechanicus, 29, 78 optics, 557, 558, 568; on the sciences, 76–77, Athenodorus of Tarsus, 298–300 227, 232; as a source for A22, 490–503;on Athens, 12, 13; and Tarentum, 9, 11 swearing, 338–39; on the Tarentine atomism, 132–33, 546 constitution, 217; Timaeus, summary of, Atticus, 330 585, 587–88; as author of the treatise by aulos, 142, 145, 146–47, 161, 475, 476–77 Timaeus Locrus, 587; on universal and authenticity (see the relevant sections of the particular and Archytas Fr. 1, 59–60;onthe commentaries on fragments and testimonia), unlimited, 541–43, 545–46, 548; parallels to xi; scholarly consensus about the fragments vocabulary in Fr. 1, 113; on wisdom, 227, of Archytas, 97–98; technical mathematics 235, 245; Categories, 92, 93, 595–97; On as a criterion for, 97–99, 406 Generation and Corruption, 92, 95; Autolycus of Pitane, 120 Mechanical Problems, 76, 77, 78, 81–82, 393, automata, 78, 82–83, 137, 571; history of, 574–77 519, 520, 527–28, 531–33; Metaphysics, 598–99; Meteorology, 615; Nicomachean Babylonians, 176 Ethics, 93; Politics, 600; Posterior Analytics, Bailey, C., 132 76–77, 85, 536; Problems, 113, 516–18, Ban¯uM¯us¯a, 346–48, 575 612 Barbera, A., 454, 464; on date and authorship of Aristoxenus, 26, 37, 95, 220, 228, 250, 292, 455, the Sectio Canonis, 466 479; as an Aristotelian, 321; on the attack Barker, A., xi, 49, 87, 112, 118, 127, 131, 305, 412, on Pythagoreans, 6; harmonics as presented 432, 437, 446, 448, 482;onFr.1, 126, in Ptolemy, 407–09; influence of the 129–30, 135, 137, 138, 139–40, 143, 145, 146, biography of Archytas on the later 148, 159–60;onFr.2, 168, 181;onA19, 464; tradition, 4, 24; on the last Pythagoreans, 6, on Archytas’ harmonics, 410, 415, 416, 417, 8; provides evidence for the foundation of 418–20, 421, 422–23, 426;onthe Archytas’ divisions of the tetrachord in Aristotelian Problems, 517; on concordance, musical practice, 412–13; relationship to 446–47; on Nicomachus’ theory of Archytas, 4; reliability of as a source for concordance, 449; on Plato’s criticism of Archytas, 4–5, 19, 289–90, 310–12, 320, 332, Pythagorean harmonics, 414, 423–24;on 333–34; as a source for Cicero, 293–94, Ptolemy’s Harmonics, 407, 425; Ptolemy’s 324–28; as a Tarentine, 321; Life of Archytas, Harmonics, parts based on Archytas, 426; 3, 4, 6, 7, 12, 13, 18–19, 30, 31, 92, 100, 184, on punctuation of A17, 437;on 211, 216, 232, 287–88, 298, 299–300, 338, Pythagorean harmonics, 428;on 340–41, 451, 480, 542, 571; Life of Socrates, Pythagorean method for determining 288, 290; On the Pythagorean Life, 287–88, relative concordance, 434–35;ontheSectio 296; Pythagorean Precepts, 184 Canonis, 454, 457, 466, 468; on the syrinx, arithmetic (see also logistic), 53–54, 76, 567; 476–77; on Theon, 472–73; on the two Archytas on, 31, 32, 48; in Nicomachus, 116; primary forms of being, 121, 155 in the proem to Stobaeus, 228; relation to Barnes, J., 44, 55, 85, 136, 232, 535, 541, 545, 547, logistic, 68–69 548, 549 arithmology, 48 Barton, T., 606 Arius Didymus, 93, 599, 605 Beare, J. I., 133, 555, 557 Arnobius, as source for A21a, 488–89 beauty, definition of, 503 Artemon, 15, 82 Becker, O., 53 artillery, 77; supposedly designed by Archytas, beginning, of Archytas’ Harmonics, 60–64, 115 14–17, 82; torsion, 16 being, two primary forms of, 121, 122, 124–25, 155 Asclepius of Tralles, 122 belly-bow (gastraphet¯es), 15–16 astrology, 22 Best and Brightman, 610–11

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654 General index

biology, 59; Archytas on, 31 on authenticity of, 226, 233–34, 250;ona Bion of Borysthenes, 24, 228, 229, 230, 619 fragment of Aristotle in Iamblichus, birds, use of in automata, 575 563–67; on geometric equality, 209;onthe Biton, 78 harmonic mean, 174; on history of means, Blass, F., xiii, 117–18, 119–20, 149, 152–54, 159, 170; on the monad and the one, 484–85;on 188, 193, 194, 219, 251; on the unity of Fr. 3, proportion of equality, 529; on Pythagoras 186–87 as inventor of the word philosophy, 311;on blending, of sounds, see mingling Pythagorean Memoirs, 557; on Pythagorean Bluck, R. S., 82, 360 optics, 558; on pseudo-Pythagorean Boethius, 30, 142, 610; Archytas’ proof in A19, writings, 93–95, 98, 595, 598, 599, 600, 602, criticism of, 461–63, 466; on degrees of 606–07 concordance, 433; on harmony of the Burnet, J., 335 spheres, 138; his mathematical works, Burnyeat, M., 77, 233, 234, 499; on Archytas’ nature of, 453–54; on Nicomachus’ theory emphasis on proof, 564; Archytas the first of concordance, 448–49; as a source for to develop the science of optics, 563;on A19, 455–56, 457, 460; as a translator of Archimedes’ Catoptrics, 555;onthe Ptolemy’s Harmonics, 409, 433, 455; De fragment of Aristotle in Iamblichus’ De Institutione Arithmetica, 454–55; De Comm., 565–68; Plato distinguishes form Institutione Musica, 455 and matter, 491; on Plato’s comments on pseudo-Boethius, 610 the language of geometry, 396; on Platonic Bolus of Mendes, 611 harmonics, 398–99 Bonitz, H., 450 Butheros, 228 Bostock, D., 492, 497, 504 Butler, H. E., 481 Bowen, A. C., xi, 112, 127, 130;onFr.1, 126, 127, Butler and Owen, 568–69 129, 137, 138, 141, 142, 147–48, 153, 155, 158, 160; on differences between the Sectio Caeneus, 519, 534–36 Canonis and Archytas, 469 calculation, 72–75, 84, 187, 188–92, 199–200, Bower, C. M., 409, 448–49, 454–55 201–02, 202–06, 211, 235–38, 332–33, 605; Brandwood, L., 43 persuasive power of, 218, 221, 222; prevents Brauer, G. C., 9, 10, 82 injustice, 220–23 Briggs, W. W., 381 Callicles, 97, 207–11, 311, 314–17 Brisson, L., 42–43, 608–09, 620 Cambiano, G., xi, 15, 16, 59, 69, 72, 79, 82, 370, Brontinus, 597 380, 518, 533, 538 Brown, M. S., 360, 394 Cameron, A., xv Brumbaugh, R. S., 304 Canachus, 576–77 Brunt, P. A., 43 canonists, 167 Bryson, 230 Carneades, 93, 606 Buck, C. D., 123–24, 149, 153–54, 156, 158, 160, Carra de Vaux, B., 575 178, 181 Carteron, H., 537 bull-roarers, 25, 141–42, 145, 147, 159–60, 161, Carthage, 28 303, 306–07 Casaubon, I., 300 Bulmer-Thomas, I., 345, 357, 359 Caskey, E. G., 43 Burkert, W., 16, 26, 42, 44, 93, 134, 138, 147, 241, Cassio, A. C., xiv, 122, 149, 153 318, 325, 327, 390, 472, 500, 509, 526;on catalogue of Pythagoreans (in Iamblichus), 26 A12, 506;A16, on authenticity of, 406;on categories, see under Aristotle and A17, 438;onA19, 455, 459–67, 486;onA23, pseudo-Archytas 511–12; Archytas, on authenticity of the Cato the elder, 326, 328–29, 331, 337 fragments, 97; on Archytas’ harmonics, Caulonia, 9 410, 413, 415–17, 422, 427; on Archytas as a Caven, B., 10 mathematician, 47–49, 71; Aristotle’s works Centrone, B., 94, 595, 599, 601, 604, 606–07 on the Pythagoreans, 584–85, 588–90, 591; Chamaeleon, 27 on Aristoxenus as a source for Cherniss, H., 42, 136, 396, 447, 500, 502, 543, Pythagoreanism, 334; on the definition of a 545–46, 589 point, 501; on derivation sequences, 485, children, 18, 74, 299, 300, 301, 302–07; protected 502;Fr.1, on authenticity of, 112, 114;Fr.4, from swearing, 338–39

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General index 655

Chilon, 215 Damippos, 605 chromatic tetrachord, 62–64, 411; Archytas’ Daunians, 9 description of, 420–23; lowest interval of, Davies, M., 381 409 Deane, P., 43 Chrysippus, theory of vision, 569 decad, treatise on by Archytas?, 32 Ciaceri, E., 14, 18, 20 definitions, Archytas’ work on, 31, 51, 66–67, Cicero, Archytas, reports about, 4, 21, 24, 33, 34, 74–76, 84–85, 99, 189, 485, 487, 490–503, 293–96, 297; Archytas’ speech on pleasure, 603; in Aristotle, 490–503; history of, dating of, 330; Archytas’ speech on pleasure, 491–94; Pythagorean, 491–94; use of as a source for, 328–31; use of Aristoxenus, analogy (similarity) in, 341, 494, 496–99, 324–28; on the harmony of the spheres, 500, 506–07; use of number in, 492–94, 137–38; on Plato’s travels to Italy, 330 495; use of proportion in, 494, 496–99, 501, circle, as the best plane figure, 526; and soul in 503 pseudo-Archytas, 607 Delatte, A., 97, 600, 602 Clagett, M., 346–47 Delian problem (see also duplication of the clapper (invention of Archytas), 19, 29, 30, 82, cube), 370–72, 375, 376–78, 385–92, 397 302–07 Delphi, 9 Clark, G., 291 Demetrius of Magnesia, 28 Clavaud, R., 33–34 democracy, 9, 17–18, 73, 89, 190, 206, 207; and Cleanthes, 229, 230 equality, 211–13, 214–15; and the geometric Cleinias, 284, 288, 292, 296, 609 mean, 603; at Sparta, 602 Cleotas, 576–77 Democritus, 27, 28–30, 53–54, 96, 132–33, 134, Cobet, C. G., 291, 322 150, 152, 184, 476, 546, 571; definitions of, coinage of Italian league, 10 491; epistemology, 219–20; potential is collection and division, 61, 89–90 actual for eternal things, 543; unlimited Colson, F. H., 480 universe, 547; on vision, 557 Columella, 21, 27–28 demonstrations, 71, 72, 237–38, 248–49 comets, 557, 559 Demosthenes, 33–34 comma, 455–56 Denniston, J. D., 245, 247 concord (political), 166–67, 190–93, 200–02, derivation sequence, 485, 487, 489, 501, 502–03 206, 214–15, 235, 515, 605 Despotopoulos, C., 204 concordance, 62, 166, 445; Archytas’ theory of, diagrams, 566 445–50; degrees of, 51, 54, 62, 443; dialectic, 42, 57, 96 discovery of ratios governing concords, diatonic tetrachord, 62–64, 411, 412; 472–73; method of, 49, 87, 418–20, 421–22, Pythagorean diatonic, 417 423, 424; and ratios of numbers, 474, 477 diatribe, 228–32 Conon of Samos, 23 Dicaearchus, 6, 327 constitution, mixed at Sparta, 602 Dicks, D. R., 53 Cooper, G. L., 450 Didymus, 450; divisions of the tetrachord, 416; Cornford, F. M., 180, 513, 561 as a Pythagorean, 428; as a source for A17, cosmology, 85–86, 481–82, 546–48, 559 437–38; as a source for Ptolemy, 425, 431–32 cosmos, 543 Diels, H., 14, 15, 16, 82, 157, 194, 244, 248, 251, counterweights, 573–79 292, 542, 608 Coxon, A. H., 542 Diels–Kranz (DK), 291, 336, 542, 600;onA9a, Critias, 34 325;A10a, text of, 578; omit A11a, 340;on Croton, 6, 7, 9–11 A12, 506;A17, punctuation of, 437;A23, Ctesibius, 574–77 extent of, 511;onA23a, 516; on Archytas, cube, 175 xii–xiii, 4, 91, 97–98, 112, 167, 172, 181;on Cumae, 15, 16 pseudo-Boethius, 610; dialect of Archytas, Cuomo, S., 77, 393–94 practice regarding, xiii–xiv, 149;Fr.1, text curves, 518, 524 of, 152–54;Fr.3, authenticity of, 183, 187; cylinder, see semicylinder Fr. 3, text of, 194, 199, 220;Fr.3, unity of, 186–87;Fr.4, authenticity of, 226 Damascius, as a source for Aristotle’s books on Dies, A., 335 Archytas, 588–91 difference, and motion, 509–14

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656 General index

Dijksterhuis, E. J., 554 elements, of arithmetic, 50, 467–68;of Dillon, J., 93, 484, 553, 597 geometry, 50–51, 350–51, 357–60, 399–400; Dillon and Hershbell, 250, 287, 288, 291, 296 of music, 148; physical, 67–68 Diogenes Laertius, 30; on Archytas as the Elter, A., 615 founder of mechanics, 79–80, 81, 82–83; Empedocles, 26, 290, 520; definitions, 491;on Archytas, life of, 4, 6; Archytas, on other sound, 134; sphere, 547; supposed pupil of men named, 26–29; on Aristotle’s writings Archytas, 7, 26; on vision, 557 on Archytas, 583–84; on Bion, 24;on ends, 606 Plato’s travels, 33; title Diatribai in, enharmonic tetrachord, 62–64, 411 229–31 Epaminondas, 34 Diogenes of Apollonia, 134 ephors, 18 Dion, 32, 34, 40, 94 Ephorus, 39 Dionysius the musician, 445 Epictetus, 228, 230 Dionysius I of Syracuse, 9–10, 15, 35, 40; sale of Epicureans, 85, 203; argument for an unlimited Plato, 33 universe, 546; theory of vision, 555 Dionysius II of Syracuse, 10, 11, 32, 34–36, 41, Epicurus, 132–33, 219 311, 317, 587, 608, 609 epimoric ratio, see superparticular ratio Dionysus, 306–07 epistemology, 185–86, 219–20; in Archytas, Diotogenes, 604, 607 55–56, 58, 65–66, 74–76, 127, 137, 188–90; Dirlmeier, F., 336 in Aristotle’s account of the Pythagoreans, discord, 200–02, 207, 215, 217 564; vocabulary of, 149–52, 153 discovery, 55–56, 74–76, 185–86, 188–90, 193, equality, 73, 184, 190–93, 211–15; geometric, 191, 195, 196, 202 208–10; and motion, 515; proportionate, dissimilars, see similars 503; two kinds, 213–14 distinctions, value of in the sciences, 58–60, Eratosthenes, 14, 29, 79, 619; Archytas’ solution 89–90 to the duplication, complaints about, 348, divided line, 92 356, 375–76, 379, 394, 397; Delian problem, division, see collection account of, 370–92; divisions of the Dodds, E. R., 208, 240 tetrachord, 416 ; duplication of the cube, Dodwell, C. R., 613 345, 354; letter to Ptolemy Euergetes, dogs, 301 372–76; and means, 171; as a Pythagorean D’Ooge, M. L., 123, 167, 168, 439, 454 harmonic theorist, 428; Platonicus, 370–85 Doric dialect, xiii–xiv, 31, 92, 95, 96, 122, 123–24, Erotic Oration, 5, 33–34 125, 149, 152, 153–54, 155–56, 158–59, 178, ethics, Archytas on, 31, 73–74, 84 179, 244, 251, 290 Eubulides, 433 dove, wooden (invention of Archytas), 30, Euclid, and the Delian problem, 372; Catoptrics, 82–83, 571–79 554–55; Elements, 209, 350–51, 357–60; Drachmann, A. G., 576 (i–iv), 50;(vi), 50;(vii), 467, 470;(viii), duplication of the cube (see also Delian 47, 469–70;(xi), 50; Optics, 76, 560, 563; problem), 7, 14, 16, 22, 29, 31, 41, 46, Phaenomena, 120; Sectio Canonis, 47, 48, 48, 49, 50, 74, 78, 79–81, 83, 98, 100, 130, 167, 399, 408, 415, 454, 457–58, 345–401, 502; connection to doubling the 464–66, 468; (composed by Archytas?), square, 360–61; “Plato’s solution,” 347–48, 468–69; (date and authorship of), 466, 380–81, 383, 401; reduction of the problem 470 to finding two mean proportionals, Euctemon, 53 292 Eudemus, 50–51, 98; Archytas, references to, 4, During,¨ I., xiii, 154, 155, 156, 157–59, 166, 179, 46, 86, 92, 99, 509, 585; Archytas’ life, 181, 413, 437, 583–85 evidence for the chronology of, 5;onthe dyad, 93, 509 duplication of the cube, 344, 348–49; used dynamics, 537 by Eutocius, 346; on Hippocrates of Chios, 357–59; on the history of means, 170, 176; Echecrates, 33, 609 on the Platonic and Pythagorean account Edelstein, L., 39, 43 of motion, 511–15; as a source for A24, education, 189–90 541–44; style of, 348–49; Physics, 542, Einarson and DeLacy, 482 590 Elea, 9 Eudorus, 93, 596, 597

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General index 657

Eudoxus, xii, 5, 65, 79, 390; acoustic theory, 473, 232–40, 243; in Nicomachus, 116; and 477–78; Archytas, pupil of, 6, 7, 477–78; optics, 559, 563; in Plato, 209–10; relation and the Delian problem, 371–72; to logistic, 68, 69–72, 232–40, 249–50 duplication of the cube, 345, 375–76, 383, Gerard of Cremona, 346 385, 391; on means, 171–72; on pleasure, 316; Giani, S., 606–07 theory of proportion, 7; use of zodiac, 606 Gigante, M., 14 Eunapius, 25 Gil, M., 615 Eurytus, 7, 25, 26, 33, 45, 48, 51–52, 91, 593–94; gods, 25, 202 relation to Archytas, 7, 55, 67, 69, 438 Goldstein and Bowen, 65 Eusebius, 25 Gomme, A. W., 11 Eutocius, as a source for Archytas’ duplication of Gosling and Taylor, 314, 316, 335 the cube, 344–49 Gottschalk, H. B., 226, 230, 595 even, see number Gow, A. S. F., 160 evenness, and motion, 515 grammar, subordinate to music, 479–80 Evenus of Paros, 479 great and the small, 511, 513 excess, term in music theory, 166–67, 170 Gregorius Aneponymus, 597 experiments, 129, 141–42; acoustical, 134–35 Gregory of Corinth, 31 Griffith, G. T., 11 Fantham, E., 330 Gruppe, O. F., xi, 97, 600, 601 Farinator, M., 611 Gudeman, A., 330 Favorinus, 82; as a source for A10a, 571–72, 573, guest-friendship, 35–37, 42 579 Gulick, C. B., 301, 321 Festa, N., 194 Gulley, N., 43 fever, 611 Guthrie, W. K. C., xi, 6, 43, 44, 45, 212, 245, 250, Finley, M. I., 42–43 502, 527, 591 fire, 519, 534 fish, 341 Hahm, D. E., 569 Flashar, H., 517, 527, 529, 538, 539 Hankinson, R. J., 89, 537 flutes, 27, 31 Harder, R., 94, 608 Folkerts, M., 610 harmonics (see also acoustics, Archytas, and form and matter, 84–85, 490–91, 494–96, 497, music), 57–58, 64, 76, 87, 89, 126, 128–29, 515, 521, 522, 588–91, 594, 597 188; and optics, 566–67, 568;overviewof Forms, see Plato Greek harmonic theory, 410–11; in Plato, Fornara, C. W., 12, 13, 14 395, 398–99 Forster, E. S., 301, 517, 524, 529, 538, 539 harmony, in the pseudo-Pythagorean texts, 96 fourth, see tetrachord Hartenstein, G., 601 Fowler, D. H., 241, 387 Harvey, F. D., 205, 213–14, 220 Frank, E., xi, 45, 130, 133, 141, 304, 422, 516–22, Harward, J., 620 529, 563, 591, 593 Heath, T. L., 46, 53, 120, 241, 380, 460, 465, 541, Fraser, P. M., 372, 373 554;onanalogia, 529; on definitions of the Fraser and Matthews, 593 point, 501–02; duplication of the cube, 349, Freeman, K., 156, 196, 349 360, 517; on history of means, 170, 180;on friendship, 19, 74, 294–96, 568; and equality, 212 Pythagorean calculus, 440;on Frischer, B., 20, 21, 22 superparticular ratios, 458–59 Fritz, K. von, 43, 52–53, 153, 292, 600 heaven, 545; fixed, 542, 550 Furley, D. J., 132–33, 543, 545, 546, 547, 548 hedonism (see also pleasure), 7, 36 hedonistic calculus, 332 gal¯en¯e, 75 Heiberg, J. L., 81, 248, 389 Gallop, D., 334, 524 Heinimann, F., 315 gastraphet¯es (see belly-bow) Hense, O., 185, 194, 299, 598 Gauthier and Jolif, 335 Heraclea (colony of Tarentum), 10–11, 18 Gellius, Aulus, 82; on Plato’s travels, 330;asa Heracles, 305 source for A10a, 571–72, 573–74, 578, 579 Heraclides of Pontus, 310; On Pleasure, genus and species, 61 316 geometry, 72, 76, 79, 80, 83, 98, 99, 226, 564, Heraclitus, 56, 150, 488 567; Archytas on, 31, 65, 85, 128–29, Herman, G., 36, 37

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658 General index

Hermodorus, 32, 33, 35, 39, 511 Pythagoreans, catalog of, 95; On the Heron of Alexandria, 77, 78, 575–77 Pythagorean Life, xii, 26, 189 Hestiaeus (father of Archytas), 6 Iapygians, 9, 17 Hesychius of Miletus, on Aristotle’s writings on Ibn Ab¯iUs.aybi a,ëSources of Information on the Archytas, 583–84 Classes of Physicians, 616 Hett, W. S., 524, 529, 532, 538, 539;onthe Idomeneus of Lampsacus, 535 proportion of equality, 536 impact, 60–62, 130, 132–33 Hicks, R. D., 450, 619 includo, 578 Hignett, C., 12, 14 incommensurability, 52, 71, 226, 233–34 Hill, D., 574–75 indefinite, and motion, 510–12, 521 Hipparchus, the astronomer, 558 indifferents, 606 hippargetai, at Sparta, 602 inequality, and motion, 509–14, 518–19, 521 Hippasus, 20, 52–53, 54, 91, 138–39; acoustical infinite universe, see unlimited universe experiments, 135, 473; degrees of initiations, 306–07 concordance, 433; on means, 174 injustice, 220–23, 288–90 Hippocrates of Chios, 7, 50–51, 52–53, 57; inquiry, 185–86, 187, 188–90, 195, 196 Archytas, relation to, 345; and elements, intelligible, see sensible 357–59, 400, 564–65; optics, 77, 557–59; interval, 166–67, 169–70 quadrature of lunes, 358–59; reduction of ipse dixit, 189–90 the problem of the duplication of the cube Irwin, T., 42, 153, 191, 203, 209, 335, to finding two mean proportionals, 350, 603 360, 370, 374, 382, 386, 387 Isocrates, 34, 150, 229; on equality, 213; on secret Hippocrates of Cos, 89–90 Pythagorean doctrines, 535–36 Hippocratics, 58, 89–90, 113; diagignÛskein in, Italian league, 9–11, 13 150–52; On Regimen, 57 Italian philosophy, 95 Hippolytus, references to pseudo-Archytan works, 596 Jablonski, W., 556 Hipponium, 9 Jacoby, F., 535 Hoche, R., 149 Jaeger, W., 592 Hoffmann, P., 596 al-Jazar¯i, 575 homonoia, see concord Jerome, 32 Horace, Archytas Ode, 19–20, 21, 22, 23, Joachim, H. H., 335 24 Jocasta, 212 Hornblower, S., 11 Jocelyn, H. D., 228–32 Hort, A., 523 Joly, R., 89 Huffman, C. A., xiii, 6, 7, 16, 32, 33, 39, 44, 53, Jones, W. H. S., 319 54, 58, 67, 72, 89, 137, 152, 154, 174, 175, Juba II of Lybia, 94 204, 210, 220, 222, 228, 238, 250, 317, 332, justice, 89, 190–93, 216, 218, 223, 235–39, 288–90, 415, 485, 495, 543, 547, 557, 565, 568, 591;on 314, 315; cosmic, 212; definition of, 492–93, authenticity of Fr. 1, 112, 121 503; and equality, 213 H. unayn ibn Ish. ¯aq, Maxims of the Philosophers, 615 Kahn, C., 6, 42, 84 Hussey, E., 81, 537 Kallikratidas, 93 hypat¯e, 24 kanon¯ , in Ptolemy’s Harmonics, 407–08; used by Pythagoras, 472–73 Iamblichus, xii; accepts Archytas’ works on Keuls, E., 305–06 categories as genuine, 95, 596; use of Keyser, P., 23, 42 Aristoxenus as a source, 287–88, 292;Fr.1, Kindstrand, J. F., 24, 619 quotation of, 125;Fr.3, as source for, king, as animate law, 604 185–87, 197;Fr.3, text of, 194–95;onthe Kingsley, P., 14, 15–16, 25 history of means, 170–77; Nicomachus’ Kirk, Raven, and Schofield, 44 Introduction to Arithmetic, commentary on, Klein, J., 69, 241, 243 124–25; and optics, 565; preserves a Knorr, W. R., 47, 77, 233;onA19, 247;on fragment of Aristotle in De Comm., 563–67; Archimedes’ Catoptrics, 554–55;onthe on Pythagorean friendship, 296; duplication of the cube, 346, 347, 348, 349,

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General index 659

380, 381; on Eratosthenes’ account of the logistic, 46, 65, 68–76, 84, 98, 99, 128–29, 210, Delian problem, 370, 374, 382; 226–27, 232–40, 249–50, 515 Eratosthenes’ letter to Ptolemy, on the Long, A. A., 557 authenticity of, 373–74, 376; internal vs. Long, H. S., 619 external stimuli to mathematical Long and Sedley, 219, 246, 450, 603 development, 378; mechanical lot, 213 interpretation of Archytas’ solution, 397; Lucanians, 9–10 on Plato’s objection to Archytas’ solution, Lucretius, 132–33, 546 394; Theodorus as Plato’s teacher in Lumen animae, 25, 611–14 mathematics, 470; follows van der Waerden luxury, 298–99, 300, 311 in assigning Euclid viii and the Sectio to Lyceum, 319–20, 327 Archytas, 468, 470 Lynch, J. P., 190, 319–20 knowledge, 188–90, 193–94, 196 Lysippus, 577 Kopff, E. C., 194, 381 Lysis, 6, 26, 34, 94 koroi, at Sparta, 602 Krafft, F., 78, 517, 527, 531 MacDowell, D. M., 338 Kraut, R., 42, 339, 548 machines, 28–30, 31, 78, 528 Krischer, T., 81–82 MacKay, L. A., 20 krotala, 306 magnitude, 116 Kucharski, P., 89 Mansfeld, J., 89 Kuhner,¨ R., 450 manuscripts, of fragments and testimonia of Archytas, xiii; of Porphyry’s commentary Lactantius, 288–89 on Ptolemy’s Harmonics, xiii, xiv Lamb, W. R. M., 240 Marcovich, M., 535, 619 Lapiths, 534–36 Marg, W., 587 Lasserre, F., 127, 130, 175 marriage, definition of, 493 Lasus of Hermione, 54, 137, 138–39, 473 Marrou, H. I., 480 law, 604 Marsden, E. W., 15–17, 576 Le Blond, J. M., 492, 496 Massinissa, 298 learning, 55–56, 185–86, 188–90, 193, 196 mathematicians, meaning of the term in the Ledger, G. R., 43 doxography, 557–58 leimma, 416, 417, 418, 422 mathematics (see also number, sciences and Lemos, N., 340 specific sciences), and artillery, 16; technical Leodamas, 5, 46 nature of, xii, 585; and wisdom, 598–99 Leon of Phlius, 310 Mathiesen, T. J., xiii, 159, 304–06 Leon, the mathematician, 5, 359 Mathieu, B., 32 Leonidas of Tarentum, 305–06 matter, see form Lesher, J. H., 245 McKirahan, R., 232 leveling, as a policy of lawgivers, 314, 317, 321–22 means (see also proportion), Archytas’ account Levison, Morton and Winspear, 43 of, 168–70; arithmetic, 179, 213, 223, Lewis, B., 615 418–19, 421, 423, 603; change of name from Lewis, V. B., 42 subcontrary to harmonic, 170–75; divide libramentum, 577–78 the octave, 62; geometric, 208–10, 213, 223, lichanos, 411, 412, 417, 421–22 419, 603; history of, xii, 170–77, 178; and Lieberg, G., 336 logistic, 69; subcontrary (harmonic), 166, limiters and unlimiteds, 66–67, 69–71, 84, 170–75, 176–77, 178, 418–19, 421, 423, 435–36, 485; in definitions, 495–99, 502 603–04; three types, 30–40, 51, 98, 99, Lindberg, D. C., 555, 560 179–81, 604 line, 499–03; created by motion of a point, measurement, 63, 145 502–03 mechanical devices (see automata and artillery) Lintott, I., 217 mechanical instruments, 379–81 Lloyd, G. E. R., xi, 32, 34–35, 42–43, 50, 57, 89, mechanics, 28–30, 76–83, 379, 384, 531, 571–79; 141, 158, 232, 248, 507; on the development meaning of the term in antiquity, of elements in geometry, 357–59, 400 393–94 Loewenthal, A., 615 medicine, 57, 58, 89–90

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660 General index

medieval period, reception of Archytas, 25 Mustilli, D., 82 Meineke, A., 248, 251 mysteries, 159 Mejer, J., 28 Melissus, 545 nature, and convention, 207, 313–15 Menaechmus, 345, 358, 375–76, 380, 383, 385 Nauck, A., 291, 296 Menelaus of Alexandria, 346–47 Nearchus, 326, 328–29 Mercken, H. P. F., 530 necessity, 87–88 Merlan, P., 196, 484 n¯enemia, 75 mesolab, 79, 372 Neoclides, 5 Messapii, 9, 14, 291 Nepos, on Plato in Syracuse, 39, 40 metaphor, and definition, 506–07 Netz, R., 352, 381, 566 Meton, 53 Neuenschwander, E., 348 Metopos, 93, 605 Neugebauer, O., 120 Michael of Ephesus, 530 Nicias, 12 Miletus, 15, 16 Nicomachus, 93, 148; Archytas, text of, 149, millet seed, 54 153–55; Archytas’ book, on the title of, 126, Minar, E. L., 18, 600 167; on concordance, 448–50; degrees of mind, definition of, 493 concordance, 433; on harmony of the mingling, of sounds, 435, 443 spheres, 138; on the history of means, 150; Minos, 374–75 metaphysics of, 116, 122, 124–25, 155; mirrors, 553–54, 555–56, 557 method of quoting texts, 114–25; use of missile analogy, in acoustics, 143 paraphrasing, 116–17;onpythmenes, 439; Moles, J. L., 228 Introduction to Arithmetic, 115, 241, 454, 501; Momigliano, A., 5, 317, 327 Introduction to Music, 433, 448, 450, 455 monad, 93, 483–85, 486–87 Niessen, F., xv, 615 monochord, 219 Nisbet and Hubbard, 20, 21, 22 Moraux, P., 94, 95, 96, 583–86, 595, 600 non-being, and motion, 509–13 Morrison, J. S., 23, 600 nothing, 549 Morrow, G., 42–43, 94, 609 number (see also arithmetic and logistic.), 65–66, motion, 74, 85–86, 87–88, 99, 505, 509–15, 137; in Archytas and Philolaus, 424–25, 518–22; in acoustics, 130, 474, 478; 483–85, 534, 594; as cause of things, 488–89, circular/curved, 517, 518, 520–21, 524, 521; in definitions, 492–94, 495; in Eurytus 526–29, 532–33, 538–39, 591–93, 594;of and Philolaus, 55, 67, 593–94;evenand geometrical figures, 394–96; instrumental, odd, 122, 234, 240, 486–87, 493; even-odd, 528–29; as matter, 522, 591; natural, 518, 486–87;five,493; four, 493; nuptial, 89, 520–21, 524, 526–29, 538, 539;in 236, 430, 436–37, 439, 442; prime, 122, 461, proportion, 537–38; in a straight line, 464–65, 468, 493; in ratios of concords, 532–33 474, 477; science of, 240; seven, 493; Mourelatos, A. P. D., 57, 153, 395 square, 492; and the state, 72–73; two, 493; Mueller, I., 46, 49, 53, 57, 240, 391;onA17, 438; unit as starting point of, 499–503 on authenticity of Fr. 4, 226;onFr.4, 233; on history of means, 170; on Plato’s O’Brien, D., 133 solution to the duplication of the cube, Ocellus, 92, 93, 94, 95, 591–92, 607 380; on Platonic harmonics, 399;on octave, added to another concord, 445; cannot Platonic number theory, 242 be divided in half, 62; structure of, 62 Mullach, F. A., 246 odd, see number Muller,¨ A., 616 Oenopides, 53 multiple ratios, 414, 444, 461–62 oligarchy, 207, 212; and the arithmetic mean, multitude, 116; the, 12, 18 603; and equality, 212, 214; at Tarentum, Munzer,¨ F., 330 17–18 music (see also harmonics and acoustics), 188, Olympiodorus, 94 243, 244; meaning of the term in O’Meara, D., 44 Quintilian, 479–80; in Nicomachus, 116; one, the, 67, 234, 435, 483–85, 486–87;as superior to grammar, 479–80 even-odd, 486–87; not a number, 460 Musonius Rufus, 228, 230 opinion, definition of, 493

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General index 661

opportunity, definition of, 493 pseudo-Philolaus, on the division of the tone, opposites, table of, 510–12, 521, 590–91, 594, 599 456 optics, 31, 76–77, 85–86, 88, 528, 553–69; and Philoponus, 31, 534, 591; commentary on harmonics, 566–67, 568 Nicomachus, 125 orgasm, argument from, 336 philosopher king, 44, 89, 190, 236 Orphism, 306–07 Photius, 25, 227 orrery, 23 physics, 586, 594 Ostwald, M., 211–12, 336 pitch, 61, 62, 113–14, 117, 129; Archytas’ theory of, 140, 141–48, 468, 474–75, 478; theory of Pape and Benseler, 593, 619 Lasus and Hippasus?, 473; in the Sectio Pappus, 77–78, 81, 373, 382; definition of Canonis, 130 mechanics, 393–94 planets, 65 paraphrasing, in Nicomachus, 116–17;in plants, 594; parts of, 517–20, 525–28 Porphyry, 118 Plato, 78, 91, 129, 150, 229; acoustics, 113–14, parhypat¯e, 411, 413 130–31, 135, 141, 143;onanalogia, 179–80; Parmenides, 547–48 anecdotes about his anger, 287, 288–90; particular, see universal and parts and wholes. Archytas, attack on for using instruments parts, instrumental and non-instrumental, 518, in mathematics, 14, 30, 79, 356, 378–84; 522–24; uniform and non-uniform, 522–23 Archytas, chronology relative to, 6; parts and wholes, 58, 59–61, 65, 89–90, 125, 128, Archytas, influence of on Plato, xi, 7, 32–33, 137, 151 469; Archytas, letters to, 94; Archytas, Pausanias, usage of the word temenos, 318–19 quotes from, 92, 114; Archytas, references Peck, A. L., 522 to, 8; Archytas, relationship to, xii, 3, Penner, T., 42 25–26, 32–42, 83–89, 97, 296, 328–30, 360; perception, in harmonic theory, 407, 423 and Archytas’ speech on pleasure, 328–30; Pericles, 12, 13, 15, 34, 82 on Archytas’ stereometry, 359, 392–401;on Periktione, 598 arithmetic and logistic, 68–69, 240–44;on Peripatos, 585–86 astronomy, 395; on circular motion, 527;on Persaeus, 229, 230 concord, 200, 201–02; on concordance, Persians, and the pursuit of pleasure, 313–14; and 446–50; cosmos has a limit, 548; and the swearing, 338 Delian problem, 370–72; on democracy, Peucetii, 9 213; diatonic scale in the Timaeus, 412, 418; phenomenal world, see sensible and intelligible. duplication of the cube, supposed solution philanthropos¯ , 605 to, 347–48, 380–81, 383, 401; on equality, Philo of Alexandria, 93, 94 213; failure to mention optics and Philo of Byzantium, 78, 575–77 mechanics, 76; Forms, 152, 226, 567, 600, Philolaus, xi, 6, 7, 8, 26, 33, 44, 45, 47, 97, 134, 601; on geometry, 209–10; geometry, 228; and aether, 591–92; relation of his absurd language of, 395–96; ideal numbers, philosophy to that of Archytas, 65–67, 234; and language of Fr. 3, 184; on learning, 424–25, 481, 486, 489, 521–22; as teacher of 193; letter to Dion, 94; on logistic, 226; Archytas, 7, 34, 46; astronomy, 53; mathematics and morality, 191; on means, cosmology, 85, 547; definitions, 495;as 171; on motion, 133, 505, 510–15, 521, 537; teacher of Democritus, 133; diatonic scale numbers, generation of, 487; number, on of, 63–64, 412, 415, 416, 417–19, 421, 422, the value of, 239; on the one and dyad, 484, 426; harmonics, 54; on the harmonic mean, 486–87, 509; on optics (vision), 86, 88, 173–75; knowledge and number, 65–66, 555–57, 559–63; on pitch, 140; on pleasure 69–71, 424–25, 489, 534, 564–65; limiters in comparison to Archytas, 334–35; points a and unlimiteds, 66–67, 69–71, 435–36, 495; geometrical fiction, 502; physical world, on means, 176; inventor of mechanical disdain for, 83, 237; Pythagoras, ninth in devices, 29; medicine, 58, 152; method of succession from, 33; on Pythagorean archai, 67, 89–90; on the one, 483–85; harmonics, 49, 63–64, 84, 392, 398–99, 414, optics, 77, 557–59, 567–68; on the priority 423–25, 485; Pythagorean mathematical of geometry, 69–71, 72, 236–37; on similars terminology, use of, 430, 436–37, 439, 442; and dissimilars, 435–36; and the Pythagoreans glorified at the expense of, “subcontrary,” 176–77; on void, 543, 547 95–96, 99–100, 311; and the Pythagoreans

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662 General index

Plato (cont.) Ptolemy, commentary on, 117–20, 409–10, of the table of opposites, 590–91;onthe 431–32, 437, 444–45;onpythmenes, 438–39, sciences, 57–58, 84, 232, 559–60;on 441; as source for A18, 450, 451; as source similarity and dissimilarity in the Timaeus, for fragments of Archytas, xiii, 99; as source 436; on stereometry, 377, 385–92;on for the text of Archytas, 149, 153–55;onthe swearing, 338–39; theory of recollection, titles of Archytas’ books, 126, 167–68, 187; 185–86, 189, 197–98; travels to Italy, 330; History of Philosophy, 616; Isagoge, 597 tripartite soul, 92, 207, 607; on wisdom, 71, Powell, J. G. F., 295, 323, 325–30, 334, 336, 337 235, 245; Epinomis, 122–23, 592; Gorgias, 97; Praechter, K., 606 Meno, 360–61, 372; Ninth Letter, 36, 609; Praxiphanes, 229 Phaedo, 8, 613; Phaedrus, 23, 89–90, 613; Pritchett, W. K., 14 Philebus, 89–90, 191; Republic, 214; Republic Proclus, 22, 470; Commentary on Book 1 of vi, 92; Republic vii, 41, 57–58, 59, 63–64, Euclid, 5; on the duplication of the cube, 64, 76, 84, 97, 210, 377, 385–92; Republic x, 345–46 23; Seventh Letter, 3, 8, 32, 34, 608, Procopius, 113 620; authorship of, 38–39, 40, 42–43; proof, 72, 237–38; Archytas’ use of, 48, Sophist, 598; Thirteenth Letter, 609, 620; 49–1, 56, 232, 248–49, 466–70, 564–65; and Timaeus, 4, 31, 63–64, 85–88, 92, 93, 98, diagrams, 566; no mean proportional 114, 176, 399, 418, 424, 448, 513–15, 561, between numbers in superparticular ratio, 584, 585, 586–88, 613; Twelfth Letter, 46, 62–64, 74, 233, 415–16, 419, 455–70; 608 admired by Pythagoreans, 564; reductio, 56, play, 299 460, 462, 463–65, 467, 546 pleasure (see also hedonism), 19, 56, 73–74, 191, Propertius, presentation of Archytas, 21–24 211, 236, 294–96, 298–99, 300, 313–16, 320, proportion (analogia; see also means), 179–81;in 326, 328; Archytas’ speech on, 331–37; Archytas’ philosophy, 66, 72–73, 74–76, Platonic account of in the Phaedo, 329 84, 89, 189, 190, 192, 205–06, 494, 529–39; pleonexia, 99, 174, 191, 206–11, 216–18, arithmetic, 206, 520–21, 529–34, 601;in 314–17 definition, 494, 496–99, 501, 503;“of Pliny the elder, 21, 27–28, 571 equality,” 518, 520–21, 529–33, 536, 538–39; Plutarch, glorifies Plato at the expense of the geometric, 205–06, 214, 519, 529–34, 601; Pythagoreans, 329–30; on harmony of the studied by geometry, 210; harmonic, spheres, 138; on Plato in Syracuse, 36, 39, 529–34, 601; and motion, 519–22, 537–38; 40; quarrel between Plato and Archytas, 14, multiple, 519, 534 30, 79–80, 378–84; on the speech on Protagoras, 136, 439, 598 pleasure in Tarentum, 329–30; De Musica, Psellus, 25 482 pseudo-Pythagorean texts, 127, 595–609; central pneumatics, 575–76 characteristics of, 92–93; clever forger in, point, 67; defined as “unit having position,” 501; 93–96, 99; letters in, 94; motivations for, definition of, 499–503 94–96; style of, 96; time and place of polar error, 194, 381 origin, 93–94 Polyarchus, 4, 36, 73, 97, 184, 211, 310–18, 320, psithyra¯, 306 321–22, 332–33 Ptolemy, 30, 46–47, 48, 99, 117, 118, 146, 148, Polybius, 602 166; Archytas, sources for his report on, Polyclitus, 72, 220, 238 425; Archytas’ harmonics, criticisms of, 413, polymathia, 55–56 414–17, 427–28; Archytas’ scalar divisions, Pontius, C., 329, 330 statement of the principle governing, poor, see rich 426–27; concords, ranking of, 432; Porphyry, 30, 145–46; aether, ascribed to harmonics, theory of in Book i, 407–09;on Aristotle and Archytas, 591–92; Archytas’ the octave, 446, 450; Pythagorean and book, did not have, 438; on Archytas’ Aristoxenian harmonics, dichotomy theory of concordance, 446; Didymus’ between, 423; Pythagorean harmonics, book, uses, 437;Fr.2, context for, 166–67, critique of, 407–08, 427, 431–32, 444; 169, 181; method of quoting texts, 114–25; Pythagorean ranking of concords, critique paraphrasing in, 118;on of, 433–34; on reason and perception as the pseudo-Pythagorean texts, 112, 617–18; criteria, 407, 423, 426

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General index 663

Ptolemy (Neoplatonist), on the writings of Reid, J. S., 296 Aristotle on Archytas, 583–84 religion, 25 pulley, 82, 573–74, 577 Rhegium, 9 punishment, 191, 222, 288–90 Rhodes, P. J., 12 Purcell, N., 9–11, 19 Ribezzo, F., 291 Pythagoras, xi, 6, 25, 26, 33, 44–45, 47, 52, rich and poor, 73, 184, 190, 192, 205, 214, 216–18, 127–28, 482, 607; acoustical research, 223, 237–38, 317 134–35, 142, 472–73, 474; and aether, Riginos, A. S., 33, 40, 100, 210, 287, 289, 370, 591–92; on anger, 288; books of, 617; and 384, 385 friendship, 212; matter, supposed views on, Ritter, C., 43 588–91; on means, 170, 173, 176; motion, Roman reception of Archytas, 21–24 supposed definition of, 514; and Numa, 327; de Romilly, J., 200 numbers, as the cause, 488–89; philosophy, Rose, V., 584 inventor of the word, 310–11; polymathia Ross, W. D., 487, 502, 504, 534–35, 542, 588 of, 55–56; in the pseudo-Pythagorean Rouse, M. A. and R. H., 611–14 tradition, 91, 94; teaching in sanctuaries, Ryle, G., 93, 587–88 319; vision, supposed theory of, 556, 558 Sachs, E., 376, 381–82, 385–90, 592 Pythagorean arithmetic, 53–54 Salmon, E. T., 328 Pythagorean calculus, 440 Santirocco, M., 20 Pythagorean geometry, 52 Sayre, K., 42 Pythagorean harmonics, 54, 430–31; in Ptolemy, Schmidt, W., 572–74, 578 407–09, 427 Schofield, M., 42–43, 201 Pythagoreanism, as a closed shop, 127–28; and Schurmann,¨ A., 78, 572 cosmic justice, 212; education in, 189–90; sciences, 51, 57–85;inFr.1, 126–29, 148; friendship in, 296; as an Italian philosophy, hierarchy of, 232–40; kinship of, 64, 327, 329; as a monolithic system, 44; 121–22, 124–25; names of, 128–29;in prevalence of spurious texts in, 91; secret Nicomachus, 116; order of, 128–29; “those doctrines, 535–36; teaching method, 319–20 concerned with the sciences,” 51–52, 54, 57, Pythagoreans, acoustical research, 134–35; and 58, 61, 126–29, 129, 132 applied mathematics, 16; Aristotle’s books screw, 82 on, 584–85; definitions, 491–94; definition Sedley, D., 203, 547 of a point, 501; derivation sequence of, 502; seeking, see inquiry on justice, 223; on motion, 510–12;on self-control, 19, 235, 287, 290, 314, 322, 332–33, optics, 557–59; Plato’s attack on in Republic 338–40 vii, 84; predecessors of Archytas, 51–57, semicylinder, 354 127–28, 131, 172; on soul, 504 Seneca, On Tranquility of Mind, 299 pythmenes, 431, 438–41 Senn, G., 141 sensible vs. intelligible, 57–58, 59, 63, 71, 84, 86, quadrature of lunes, 358–59 237, 244, 378, 380, 394, 397, 424–25, quadrivium, 388–89, 559 483–85, 521 Quintilian, 21; as a source for A19b, 479–81 separation, 496, see also sensible vs. intelligible Seyffert and Muller,¨ 297 Raeder, H., 43 shapes, 72, 238 Rashed, M., xv, 616 Shorey, P., 42, 246, 388, 395, 396, 437, 504 ratio, 166–67, 567; multiple, 122 similars and dissimilars, in Pythagorean rattle, see clapper harmonics, 431, 433–36, 441–43 reason, 73–74, 87–88, 332–33; in harmonic Simplicius, 95, 115; on Alexander’s argument theory, 407, 423, 426 against infinite space, 549; on Aristotle’s receptacle, 513–15, 519, 521, 590 discussion of motion, 510–14; on Aristotle’s reciprocity, 492–93 summary of the Timaeus, 587–88; use of recollection, theory of, 185–86, 189, 197–98 Eudemus, 346; accepts pseudo-Archytan reconciliation, 215–16 works as genuine, 596; as a source for A24, reductio, see proof 541–42, 544 reed (kalamos), 142, 146–47, 160, 475, 476–77 Sinclair, R. K., 12

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664 General index

Sinclair, T. A., 600, 605 Stratton, G. M., 557 Singer, C., 82 strife, see discord skill (techn¯e), 527–28 strings, used in acoustical experiments, 142 slaves, 18, 288–90, 300, 301 Sturm, A., 345, 370, 376, 377–78, 380, 383 Smith, A., 616 substance, 597 Smith, H. W. R., 160, 305–06 substrate, 597 Smith, R., 249 Suda, 6 Smyth, H. W., 292, 619 sun, 493 Socrates, 34, 230, 290, 491 superparticular ratios, 49, 74, 412, 415–16, Solmsen, F., 43, 88, 382, 526, 527, 545, 592 422–23, 427, 455–70; definitions of, 458–59; Solon, 34 supposedly required in Pythagorean sophists, 479 harmonics, 414–17, 422–23, 426–27, 444 Sophonias, 597 suspendo, 577–78 Sophron, 480–81 swearing, 19, 338–40 Sorabji, R., 527, 530, 546, 548–49, 596 Sybaris, 9 soul, definition of, 493; Pythagorean view of, Sybarites, 300, 301, 338 504; in pseudo-Archytas, 607; tripartite, see Sykutris, J., 609 Plato Syracuse, 10, 14, 15 sound, Archytas’ account of, 60–62, 129–38, 161; Syrianus, 95 definition of, 140–41; medium of (see also syrinx, 145, 147, 160, 476–77 air), 140–41; as a missile of air, 140, 143; Szlezak, T. A., 78, 81, 595–97 Presocratic accounts of, 133–35; quantitative nature, 148; vocal, 142–43, 144–45, 146–47 Tannery, P., 81, 82, 172, 346, 347, 359, 610;on space, 547, 549 A19, 454, 460, 464; on text of A19, 462;on Sparta, 9, 18, 601–02 Archytas’ dove, 571; on Archytas’ Spence, I. G., 11 harmonics, 410, 418–19 Speusippus, 439, 586, 603; derivation sequence, Taran,´ L., 125, 439, 484, 487, 500, 502 502; on the one, 484, 487; on the point and Tarentum, 3, 5, 21; cavalry, 11; demise of, 19;asa the unit, 500; reveals forbidden things, democracy, 9, 17–18, 184, 206, 217; history 535–36 of, 9–11; and Italian league, 9–11; military sphaeric, 116, 120–21 forces, 11; Plato’s dealings with, 35–41; Sphaerus, 229, 231 power of, 11; supports Peloponnesians vs. sphere, as the best shape, 526;in Athens, 9; Pythagorean community at, pseudo-Archytan texts, 615 6–7; and Sparta, 601; and Syracuse, 36, 601 spheres, music of, 61, 131, 135, 137–38, 150, 481–82 Taylor, A. E., 387 Spintharus, 4, 287, 288, 290, 292 temperance, see self-control Sporus, 347 tetrachord, Archytas’ description of, 30, 48–49, square, doubling, 360–61; and soul, 607 62–64, 98, 409, 410–28; genera of, 408–09 starting points (see also elements), 358–59 Teucer of Carthage, 28 state, the, 16, 84, 89, 188, 190–93, 204, 205–06, Thales, 488 211, 235–39; threatened by the pursuit of Theaetetus, 5–6, 46, 386, 387, 389, 391; and pleasure, 333 Euclid vii, 468; use of means, 176 Stenzel, J., 500 Theano, 287 stereometry (solid geometry; See also geometry), Theiler, W., 600, 603, 604–05 80, 84, 377, 385–92 Theodorus of Cyrene, 52, 205, 210 Stewart, J. A., 335 Theodosius of Bithynia, 120 sticks, used in experiments, 141–42, 142, 144, 147, Theon, 32, 138–39, 554; Delian problem, account 545, 562 of, 371, 384; on Eratosthenes’ Platonicus, Stobaeus, xiii; proem, 227–28; as source for Fr. 3, 382; on means, 180;onpythmenes, 439; 184–85, 186–87 ratios which govern the musical concords, Stoics, 203, 603; theory of vision, 555–56, 561, 569 on discovery of, 472–73; as a source for Strabo, on the history of Tarentum, 5, 11 A19a, 474–75; as a source for A20, 483–85; Strange, S., 87 as a source for A21, 486; Mathematics Useful strat¯egos, 11–14, 18, 38 for Reading Plato, 470 strat¯egos autokrator¯ , 13–14 Theophilus, De Diversis Artibus, 613–14

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General index 665

Theophrastus, 27–28, 55, 67, 585; on Eurytus, Vitruvius, 21; references to Archytas, 28–29 593; parallels to vocabulary in Fr. 1, 113;on Vlastos, G., xi, 42, 208, 360; on equality, 212 parts of animals and plants, 523; on pitch, Vogel, C. J. De, 289, 292, 294, 330, 589 140; on Presocratic accounts of sound, 134; Vogel, M., 417, 419 On Music, 118; On Pleasure, 316; De Sensu, voice, see sound 133 void, 543 Theopompus, 230 volume (loudness), 113–14, 143–45, 148 Thesleff, H., 31, 91–92, 94, 98, 100, 440, 595–609, 617–18 Wachsmuth, C., 227, 248 Thibodeau, P., 554 Wackernagel, J., 149 third, minor, 413–14, 420 Waerden, B. L. van der, 130, 147, 233, 349, 381, Thomas, I., 112, 380; duplication of the cube, 387, 419, 460, 618; on Archytas’ 349; on history of means, 170 mathematics, 47, 352, 353, 464, 468–70; Thorndike, L., 612–13 Euclid vii existed before Archytas, 467; thought experiment, 23, 56, 336, 337, assigns Euclid viii to Archytas, 469–70; 545–46 assigns the Sectio Canonis to Archytas, Thrasymachus, 207–11, 314–17 468–69 Thucydides, 150, 214 Wallach, B. P., 228 Thurii, 9, 10 Watson, J. S., 481 Timaeus (historian), 39 Wehrli, F., 288, 290, 311, 314, 325, 326, 334–35, Timaeus of Locri, 33, 176, 584; speaker in 479 Plato’s Timaeus, 86; author of Wellmann, M., 610–11 pseudo-Pythagorean treatise, 92, 93, 98, West, D., 20 406, 587–88 West, M. L., 159, 305–06 time, 596 Westerink, L. G., 345, 588 Timotheus, 5, 33–34 Westlake, H. D., 43 Timpanaro Cardini, M., xi, 97, 193, 196, 199, White, N., 42 292, 572, 573, 579, 610 wholes, see parts tone, can’t be divided in equal parts, 455–56 Wilamowitz-Moellendorf, U. von, 43, 370, 377, toys, 302–07 388, 619; on the authenticity of Tredennick, H., 504, 535 Eratosthenes’ letter to Ptolemy, 373–74 Trendall and Cambitoglou, 304 Wilkinson, L. P., 20 Tryphon, 31 Williams, G., 20 Tzetzes, 33 Wilson, N. G., 299 Winnington-Ingram, R. P., 48, 406, 410, 412–14, unevenness, and motion, 511–15, 518–19 427 unit, 67, 460, 487; definition of, 499–503; wisdom, 71, 232, 234–39, 598–99 in pseudo-Archytas, 607 Wolfer, E. P., 370, 374–75, 378, 381–82 universal and particular, 59–60, 125, 128, 237 world soul, 87 universe, definition of, 543 Wright, M. R., 557 unlimited (see limiters and unlimiteds), Aristotle Wuilleumier, P., 10, 11, 12, 14, 20, 38 on, 541–43 unlimited universe, 31, 85–86, 496; Archytas’ Xenocrates, 484, 487, 502, 586 argument for, 22, 23, 31, 85–86, 87, 99, 295, Xenophon, 34, 113 336, 542–50, 562 Urmson, J. O., 541 Zeller, E., 45, 93, 94, 97, 167, 187, 589, 600, 606, Usener, H., 228 608 Zeno of Citium, 229, 230 Valerius Maximus, 21 Zeno of Elea, 54, 135; paradox of the millet seed, Varro, 21, 27–28, 93 136 virtue, definition of, 605 Zeyl, D. J., 240, 561 virtues, 312–14 Zhmud, L., 127, 134, 138, 141, 170, 346, 349, 373, vision, see optics 377, 384 visual ray, 555–62, 565, 569, 612; compared to a zodiac, 606 hand, 558, 561–62 Zopyrus, 15–17

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