Archytas of Tarentum was a central figure in fourth-century Greek life and thought and the last great philosopher in the early Pythagorean tradition. He solved a famous mathematical puzzle, saved Plato from the tyrant of Syracuse, led a powerful Greek city state, and was the subject of three books by Aristotle. This first extensive study of Archytas' work in any language presents a radically new interpretation of his significance for fourth-century Greek thought and his relationship to Plato, as well as a full commentary on all the fragments and testimonia.
Author(s): Carl Huffman
Publisher: Cambridge University Press
Year: 2005
Language: English
Pages: 682
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Figures......Page 11
Preface......Page 13
part one Introductory essays......Page 19
sources......Page 21
chronology......Page 23
family, teachers and pupils......Page 24
archytas and tarentum......Page 26
archytas’ private life and character......Page 36
the death of archytas and horace’s “archytas ode”......Page 37
reception......Page 39
other men named archytas......Page 43
writings......Page 48
archytas and plato......Page 50
appendix to chapter 1 : the authenticity of the seventh letter......Page 60
chapter ii The philosophy of Archytas......Page 62
archytas as a mathematician......Page 64
archytas and his predecessors......Page 69
archytas on the value of the sciences......Page 75
logistic as the fundamental science......Page 86
optics and mechanics......Page 94
conclusion: archytas, plato and aristotle......Page 101
appendix to chapter ii: archytas and the platonic method of division......Page 107
chapter iii The authenticity question......Page 109
part two Genuine fragments......Page 119
A. Porphyry, On Ptolemy’s Harmonics 1. 3 (Düring 55.27–58.4)......Page 121
B. Porphyry, On Ptolemy’s Harmonics (Düring 80.28–81.16; for the apparatus and the text of the quotation from Archytas see…......Page 125
C. Nicomachus, Introduction to Arithmetic 1. 3.3 (p. 6.8–7.6 Hoche; for the apparatus see Text A above)......Page 126
E. Plato, Republic 530d......Page 127
G. Joannes Philoponus, On Nicomachus’ Introduction to Arithmetic (p. 7 Hoche)......Page 128
H. Asclepius of Tralles, On Nicomachus’ Introduction to Arithmetic (p. 28 Tarán)......Page 129
Authenticity......Page 130
Context......Page 132
Archytas and the sciences: Fragment 1, lines 1–7......Page 144
The acoustic theory of Archytas: Fragment 1, lines 7–43......Page 147
Porphyry, On Ptolemy’s Harmonics 1. 5 (Düring 92.9–94.28)......Page 180
Text B. Iamblichus, On Nicomachus’ Introduction to Arithmetic 113.12–113.21 (Pistelli)......Page 182
Text D. Iamblichus, On Nicomachus’ Introduction to Arithmetic 118.19–119.3 (Pistelli)......Page 183
The context in Porphyry (see also Düring [1934] 177–78)......Page 184
From what work of Archytas does Fragment 2 come?......Page 185
Archytas’ account of the three means (see also D’ Ooge et al. 1926: 21–22 and Barker 1989: 42–43)......Page 186
Archytas and the history of means (see also Heath 1921: 84–86; Thomas 1939: i. 110 ff.; Burkert 1972a: 440 ff.; Mueller 1997…......Page 188
Detailed commentary......Page 195
Iamblichus, On General Mathematical Science 11 (44.10–17 Festa)......Page 200
Authenticity......Page 201
Context......Page 202
Is Fragment 3 one fragment or two?......Page 204
From what book does Fragment 3 come?......Page 205
Importance of the fragment......Page 206
Detailed commentary......Page 211
Authenticity......Page 243
Context......Page 245
Title of the work from which Fragment 4 comes......Page 246
Importance of the fragment......Page 250
Detailed commentary......Page 258
part three Genuine testimonia......Page 271
A1 Diogenes Laertius, Lives of the Philosophers VIII. 79–83......Page 273
A1a Athenaeus Mechanicus, On War Machines 5.1 (Schneider 1912: 10)......Page 274
A1b Vitruvius, On Architecture I. 1.17......Page 275
A1e Themistius, Orations 17 (215c5 Hardouin; 308: 14–16 Schenkl–Downey)......Page 276
A2 Suda 4121......Page 277
A3 Horace, Odes I. 28......Page 278
A3b Scholia to Horace (Porphyrio, Holder 1894)......Page 280
A3d Diogenes Laertius, Lives of the Philosophers IV. 52 (= Bion Fr. 227, Lloyd-Jones and Parsons 1983: 86; Kindstrand Fr. 7)......Page 281
A3f John the Geometer......Page 282
A4a L. Annaeus Florus, Epitome of Roman History I. 13.2–3......Page 283
A5 Plato, Letter VII......Page 284
A5a1 Plutarch, Dion......Page 286
A5a2 Aelius Aristides, To Plato: In Defense of the Four (section 232 Jebb, 377 Lenz and Behr 1978. Cf. the scholia ad loc., Dindorf III. 677)......Page 287
A5b3 Cicero, Tusculan Disputations V. 23.64......Page 288
A5b7 Apuleius, On Plato I.3......Page 289
A5b9 Olympiodorus, Commentary on the First Alcibiades of Plato 2. 86–93......Page 290
A5b12 Tzetzes, Letters 75 (Leone 1972: 110. 22)......Page 291
A5c1 [Demosthenes] LXI, Erotic Oration 44......Page 292
A5c3 Philodemus, History of Philosophers: Index of Members of the Academy PHerc. 1021, V. 32–VI. 12, Dorandi 1991: 134–35......Page 293
A6 Proclus, Commentary on Book One of Euclid’s Elements Prologue 11. 66.4–18 (Friedlein)......Page 294
A6b Iamblichus, On the Pythagorean Life (Deubner 1937)......Page 295
A6e Eusebius, Against Hierocles XI (Kayser 1870: 380.5 ff.)......Page 296
A6g Gregory of Corinth, On Dialects, preface (pp. 1–7 Schaefer 1811)......Page 297
B5a Jerome, Letter XLIX (XLVIII) 19. 4–5 (Hilberg 1910: 384.10 ff.)......Page 298
B8a Columella, On Agriculture I. 1. 7......Page 299
B8b Pliny, Natural History I.8c; I.14c; I.15c; I.17.c; I.18.c......Page 300
A7 Iamblichus, On the Pythagorean Life 197–98 = Aristoxenus Fr. 30 (=49) Wehrli......Page 301
Text B. Plutarch, On the Education of Children 14. 10d (ca. AD 50–ca. AD 120)......Page 302
Text E. Cicero, On the Republic I. 38.59 (1st century BC)......Page 303
Text G. Lactantius, On the Anger of God 18.4 (ca. AD 240–ca. AD 320)......Page 304
Context in Iamblichus and Iamblichus’ use of Aristoxenus as a source......Page 305
Importance of the testimonium......Page 306
Detailed commentary......Page 308
Authenticity......Page 311
Context......Page 312
Importance of the testimonium......Page 313
Detailed commentary......Page 314
A8 Athenaeus, Sophists at Dinner XII, 519b......Page 315
Context......Page 316
Detailed commentary......Page 318
Authenticity......Page 320
Context......Page 321
Importance of the testimonium......Page 322
A9 Athenaeus, Sophists at Dinner XII. 545a (Aristoxenus Fr. 50, Wehrli)......Page 325
Authenticity......Page 328
Context in Athenaeus......Page 329
The argument of Polyarchus......Page 330
Detailed commentary......Page 335
A9a Cicero, Cato the Elder on Old Age (12. 39–41)......Page 341
Authenticity and Cicero’s source......Page 342
The structure and content of Archytas’ speech on pleasure......Page 349
The originality of Archytas’ argument and its relation to Plato and Aristotle......Page 351
A11 Aelian, Historical Miscellany XIV. 19......Page 355
Importance of the testimonium......Page 356
A11a Aelian, Historical Miscellany X. 12......Page 358
Detailed commentary......Page 359
A14 Eutocius, Commentary on Archimedes’ On the Sphere and Cylinder II (III. 84.12–88.2 Heiberg/Stamatis)......Page 360
Authenticity......Page 362
Context......Page 363
Analysis of Archytas’ solution......Page 367
Plato’s Meno and Archytas’ solution to the duplication of the cube......Page 378
A15 Eutocius, Commentary on Archimedes’ On the Sphere and Cylinder II (III. 88.3–96.27 Heiberg/Stamatis)......Page 379
A15a Plutarch, Table Talk VIII. 2.1, 718e (Hubert 1971: 261.27–262.13)......Page 382
A15b Plutarch, Marcellus XIV. 5–6 (Ziegler 1994: 123. 6–22)......Page 383
A15c Vitruvius, On Architecure IX. Prologue 13–14 (Krohn 1912: 199. 13–27)......Page 384
Text B. Plutarch, The E at Delphi 6, 386d–f (Patton 1929: VI. 5–18)......Page 385
Text C. Plutarch, On the Sign of Socrates 7, 579b–d (Patton 1929: III. 469–70)......Page 386
Summary of other texts......Page 387
Contents and contexts......Page 388
Eratosthenes’ account of the Delian problem and Republic vii......Page 403
Plato’s criticism of Archytas’ proof......Page 410
A16 Ptolemy, Harmonics I. 13–14 (Düring 1930: 30–32; cf. II. 14, Düring 1930: 70–73)......Page 420
Authenticity......Page 424
Context in Ptolemy......Page 425
Porphyry’s commentary on Ptolemy......Page 427
Archytas’ division of the tetrachord in the three genera......Page 428
Detailed commentary......Page 443
A17 Porphyry, On Ptolemy’s Harmonics I. 6 (Düring 1932: 107.15–108.21)......Page 446
Authenticity......Page 448
Context in Porphyry......Page 449
The ranking of concords: an overview of Testimonium A17......Page 450
Detailed commentary......Page 455
A18 Porphyry, On Ptolemy’s Harmonics I. 6 (Düring 1932: 104. 4–16)......Page 461
Context in Porphyry......Page 462
The theory of concordance in A18......Page 463
Detailed commentary......Page 468
A19 Boethius, De Institutione Musica III. 11 (Friedlein 1867: 285.7–286.19)......Page 469
Authenticity......Page 471
Boethius’ source......Page 472
Context in Boethius/Nicomachus......Page 473
Context in Archytas......Page 474
Archytas A19......Page 475
Final assessment of the argument......Page 484
A19a Theon of Smyrna, Mathematics Useful for Reading Plato (Hiller 1878: 60.16–61.23)......Page 488
Context......Page 490
Archytas’ acoustic theory in Testimonium A19a......Page 491
Detailed commentary......Page 493
Authenticity......Page 496
Detailed commentary......Page 497
Authenticity......Page 499
Importance of the testimonium......Page 500
Context......Page 501
Content of the testimonium......Page 502
A21 Theon of Smyrna, Mathematics Useful for Reading Plato (Hiller 1878: 22.5–10)......Page 503
Content......Page 504
Authenticity and significance......Page 506
A22 Aristotle, Metaphysics VIII. 2 (1043a14–26)......Page 507
Context and extent of the testimonium......Page 508
Archytas’ theory of definition......Page 509
Is there further testimony about Archytas’ definitions in Aristotle?......Page 517
Detailed commentary......Page 521
A12 Aristotle, Rhetoric III. 11 (1412a9–17)......Page 523
Content of the testimonium......Page 524
A23 Eudemus, Physics Fr. 60 Wehrli = Simplicius, In Aristotelis Phys. III. 2 (CAG IX. 431.4–431.16)......Page 526
Context and extent of the testimonium......Page 527
What does A23 tell us about Archytas’ theory of motion?......Page 530
Context......Page 534
Extent of the testimonium......Page 535
Significance of the testimonium......Page 536
Detailed commentary......Page 540
A24 Eudemus, Physics Fr. 65 Wehrli = Simplicius, In Aristotelis Phys. III. 4 (CAG IX. 467.26–468.3......Page 558
Context......Page 559
Nature and extent of the testimonium......Page 560
Archytas’ argument......Page 562
A25 Apuleius, Apology 15–16 (see Butler and Owen 1914 and Helm 1912)......Page 568
Text A. Aëtius IV. 14.3 (Diels, Dox. 405. 15–22......Page 569
Text C. Iamblichus, On General Mathematical Science XXV (Festa 1891: 78.8–18)......Page 570
Context and source......Page 571
Archytas’ theory of vision in Apuleius......Page 573
The position of Archytas in the history of optics......Page 574
Aristotle’s evidence for early Pythagorean work on optics......Page 581
Detailed commentary......Page 586
A10a Aulus Gellius, Attic Nights X. 12.8–10 (Marshall 1968)......Page 588
Context......Page 589
The nature of Archytas’ dove......Page 590
Archytas’ dove in the context of the history of ancient automata......Page 592
Detailed commentary......Page 595
A13 Text A. Diogenes Laertius, Lives of the Philosophers V. 25 (Life of Aristotle)......Page 597
Text B. Hesychius, Life of Aristotle (Aristotelis . . . Fragmenta, Rose 1886: 14)......Page 598
Text F. Damascius, Commentary on the Parmenides (= De Principiis II. 172.16–22 Ruelle [Westerink and Combès 1986: LVI–LVII and CLI] = Rose 1886: 164–65)......Page 599
Text H. Theophrastus, Metaphysics 6a15–27 (Ross-Fobes 1929: 12)......Page 600
Aristotle’s treatises on Archytas and the Pythagoreans......Page 601
Authenticity of Aristotle’s works on Archytas and the Pythagoreans......Page 602
Aristotle’s two treatises on Archytas......Page 604
Conclusion......Page 612
Appendix 1 Spurious writings and testimonia......Page 613
Appendix 2 Archytas’ name......Page 637
Bibliography......Page 639
Select index of Greek words and phrases discussed in the text......Page 656
Index locorum......Page 659
General index......Page 669
