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Some Renaissance Versions of the Pythagorean Tetrad1

Published online by Cambridge University Press:  02 January 2019

S. K. Heninger Jr.
S. K. Heninger Jr.*
Affiliation:
Duke University
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Extract

In 1538 when Sir Thomas Elyot printed his Dictionary, he included the following entry for Pythagoras: ‘An excellente Phylosopher, whose Phylosophye was in mystycalle sentences, and alsoo in the Scyence of noumbers.’ The ‘mystycalle sentences’ were the Carolina aurea and Symbola, collections of spurious precepts with hidden meanings which had received extensive explication; and ‘the Scyence of noumbers’ recalled Pythagoras’ fundamental postulate that all things have innate numerical relationships. Elyot's entry indicates concisely what facets of the Pythagorean doctrine appealed to the Renaissance and how Pythagoras could appear as the fountainhead of both mysticism and physical science. Reuchlin cited Pythagoras as source of the mystical wisdom contained in De arte cabalistica, while Copernicus in De revolutionibus orbium coelestium claimed support from the ancient Pythagoreans for his belief that the earth moved.

Type
Research Article
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Studies in the Renaissance , Volume 8 , 1961 , pp. 7 - 35
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Copyright © Renaissance Society of America 1961

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Footnotes

1

Read at the Southeastern Renaissance Conference at the University of North Carolina 26 April 1958.

References

2 (Haguenau, 1517), epistle dedicatory to Pope Leo x.

3 (Nuremberg, 1543), prefatory letter to Pope Paul III. For Copernicus’ debt to Pythagoreanism, see Burtt, E. A., The Metaphysical Foundations of Modem Physical Science (London, 1927), pp. 40–44 Google Scholar; and Armitage, Angus, Copernicus (London, 1938), pp. 20–25 Google Scholar.

4 See the author's preface to Dialogo … sopra i due massimi sistemi del mondo (Florence, 1632). In January 1611 Tommaso Campanella wrote an enthusiastic letter to Galileo extolling the Sidereus nuncius: ‘Tu, vir clarissime, non modo restituis nobis gloriam pythagoreorum a grascis subdolis subreptam, eorum dogmata resuscitando, sed totius mundi gloriam tuo splendore exstinguis’ (Campanella, Lettere, ed. Vincenzo Spampanato, Bari, 1927, p. 165). See also Campanella, The Defense of Galileo, tr. Grant McColley (Northampton, Mass., 1937), p. 11: ‘Galileo's theory of the motion of the earth, of a central Sun, and of the systems of stars with waters and earthly elements is indeed an ancient conception. It comes from the mouth of Moses himself, and from Pythagoras.’ Cf. pp. 11-12, 72-73. Galileo, however, explicitly rejected the number symbolism of the Pythagoreans.

5 (London, 1653), fol. BI: ‘What is Plato but Moses Atticus? And for Pythagoras it is a thing incredible that he and his followers should make such a deal of doe with the mystery of Numbers, had he not been favoured with a sight of Moses his Creation of the world in six days, and had the Philosophick Cabbala thereof [not been] communicated to him, which mainly consists in Numbers.’

6 The True Intellectual System of the Universe (London, 1678), p. 370.

7 Note at the end of this article the editiones principes of the major Pythagorean publications between 1474 and 1695. This rather lengthy list by no means exhausts Pythagorean literature in this period. For a critical survey of all Pythagorean writings in the classical period, see Zeller, Eduard, A History of Greek Philosophy, tr. Alleyne, S. F. (London, 1881), 1, 306–323 Google Scholar.

8 Nicomachus’ Arithmetical libri duo, translated by both Apuleius (no longer extant) and Boethius, was the most influential arithmetical text in the middle ages. The editio princeps of the Greek text was printed in Paris, 1538. Boethius’ version first appeared in Opera (Venice, 1491-1492). There is a modern translation into English with invaluable notes by Martin Luther D'Ooge (Ann Arbor, Mich., 1938).

9 Nicomachus’ Manuale harmonicum was first printed in Aristoxenus, Nicomachus, Alypius, auctores musices antiquissimi, ed. Jan van Meurs (Leyden, 1616).

10 Boethius* De musica libri quinque, a redaction of Nicomachus’ musical work, was first printed in Opera (Venice, 1491-1492).

11 The De anima mundi et natura libellus of Timaeus Locrus was first printed with Nicephorus Blemmidas, Logica et al. (Venice, 1498). Although modern scholars know this work to be a spurious paraphrase of Plato's Timaeus, the Renaissance did not doubt its authenticity.

12 The text attributed to Ocellus Lucanus is probably not authentic but was accepted in the Renaissance. It was first printed as De universi natura brevis et absoluta qualitatum elementarium enarratio (Paris, 1539).

13 The editio princeps was an Aldine publication (Venice, 1501).

14 The most notable passages in which Aristotle discusses Pythagorean doctrine are De coelo 290 b 12-291 a 28, 293 a 15-293 b 21, and Metaphysica 985 b 23-990 a 32, 1080 a 37-1080 b 21, 1083 b 8-1085 a 2, 1090 a 16-1090 a 35, 1091 a 13-1091 b 15. See also De anima 404 a 16-404 a 20, 407 b 20-407 b 23.

15 Especially the spurious De placitis philosophorum.

16 The first half of Book xv is devoted to a favorable exposition of Pythagoreanism.

17 Pythagoras figures most prominently in (a dialogue in which one speaker is a cock, the present incarnation of Pythagoras), in (a satire in which several philosophies of life are offered for sale), and in (an answer to the protest over in which the ancient philosophers return to avenge the calumny).

18 For sources relating to these legendary travels, see Enfield, William, The History of Philosophy (London, 1837), PP. 212–214 Google Scholar, and Zeller, , History of Greek Philosophy, 1, 327–335 Google Scholar. Although Enfield and Zeller rightly submit these authorities to question, the Renaissance did not. See, for example, Alexandro, Alexander ab, Genialium dierum libri sex (Paris, 1570), fol. 49v-50Google Scholar.

19 Full accounts of this ‘school’ are in Diogenes Laertius and Iamblichus; see also Aulus Gellius, Noetes Atticts, I.ix. 1-12, and Burley, Walter, Liber de vita et moribus philosophorum, ed. Knust, Hermann (Tubingen, 1886), pp. 70–72 Google Scholar. Burley's imitation of Diogenes Laertius was first printed at Cologne in 1467, and was exceedingly popular in the late fifteenth century (at least twenty incunables). For a modern reconstruction of the beliefs promulgated in Pythagoras’ school, see Enfield, History of Philosophy, pp. 217-230, and Cornford, F. M., ‘Mysticism and Science in the Pythagorean Tradition’, Classical Quarterly XVI (1922), 139 Google Scholar ff.

20 ‘Isidorus vero .III. ethimologiarum dicit: Numeri disciplinam apud grecos primum Pythagoram nuncupant perscripsisse’ (Burley, De vita, p. 68). The reference to Isidore is Etymologic, III.ii.I. Cf. Diogenes Laertius, Vita;, VIII, 11-12, and Batman uppon Bartholome, His Book De Proprietatibus Rerum (London, 1582), fol. 5. For modern opinions, see Zeller, , Greek Philosophy, I, 347 Google Scholar; Nicomachus, Arithmetic, ed. D'Ooge, pp. 18-19; and Sarton, George, A History of Science: Ancient Science through the Golden Age of Greece (Harvard Univ. Press, 1952), pp. 203 Google Scholar ff.

21 See Iamblichus, Vita, chap. 19. See also Zeller, Greek Philosophy, 1, 419-425; Burnet, John, Early Greek Philosophy (4th ed., London, 1945), pp. 107–108 Google Scholar; and Dantzig, Tobias, Number: the Language of Science (N. Y., 1930), pp. 40–45 Google Scholar.

22 Pythagoras’ claim to medical knowledge rests mainly upon his disciples, Alcmaeon and Empedocles: see Enfield, History of Philosophy, pp. 232-233; Burnet, John, Greek Philosophy: Parti, Thales to Plato (London, 1928), pp. 41, 49–51 Google Scholar; and Sarton, History of Science, pp. 214-215. Hartmann Schedel, after lauding Pythagoras’ pioneering in cosmology, music, and mathematics, added: ‘et medicinam non neglexit’ (Liber chronicarum, Nuremberg, 1493, fol. 61v).

23 Pythagoras discovered the numerical ratios which determine the concordant intervals of the musical scale; ergo, ‘Hie Pytagoras, ut ait Boecius in primo musice, artis musice inventor fuisse apud grecos dicitur’ (Burley, De vita, p. 68). The reference to Boethius is De musica, 1, x. André Dacier gives an open-minded review of scholarship on Pythagoras’ invention of ‘harmonical Measures’ (The Life of Pythagoras, etc., tr. Nicholas Rowe, London, 1707, pp. 82-83). See also Burnet, Thales to Plato, pp. 45-49.

24 Pythagoras delivered his moral teachings in the form of dicta with recondite meanings, hence the Symbola. This practice derived from his extended visit among the priests of Egypt. These Symbola, reinforced with literary esoterica such as the Hieroglyphka of Horapollo and the mystic symbols of the Kabalists, were assimilated by Neoplatonists of the Florentine Academy and eventually gave rise to the prolific emblem literature of the sixteenth century. See Plutarch, , Of his and Osiris in Moralia, tr. Holland, Philemon (2d ed., London, 1657), P. 1051 Google Scholar; Cartari, Vincenzo, Les Images des dieux des anciens, tr. Verdier, Antoine du (Lyons, 1581), p. 4 Google Scholar; Giraldi, Lilio Gregorio, Libelli duo … in altero Pythagorœ symbola … sunt explicata (Basle, 1551), pp. 71–85 Google Scholar (prefatory letter to Pico della Mirandola); Valeriano, G. P., Hieroglyphka (Basle, 1556)Google Scholar, title page; and Bayle, Pierre, Dktionaire historique et critique (Rotterdam, 1697)Google Scholar, ‘Pythagoras’, footnote H. Claude Mignault (better known as Minos) wrote a ‘Syntagma de symbolis’ which after 1573 became a frequent addition to Alciati's Emblemata. The ‘Syntagma’ offered a history of symbols from their invention through the Chaldeans, Egyptians, and Hebrews, to Pythagoras and beyond. This is the best summary of Pythagoras’ contribution to the emblem tradition.

25 See Diogenes Laertius, Vitœ, VIII, 48. ‘It is well known that the Pythagoreans held the Motion of the Earth about the Sun’ (Henry More, Conjectura cabbalistka, p. 154). Although this interpretation of Pythagorean cosmology is not strictly true, Copernicus and others attributed a heliocentric universe to Pythagoras. For other discoveries made by Pythagoras in astronomy, see Dreyer, J. L. E., A History of Astronomy from Thales to Kepler (2d ed., N. Y., 1953), pp. 37–38 Google Scholar. For modern evaluation of Pydiagoras’ contributions to astronomy, see Burnet, Early Greek Philosophy, pp. 110-111; Gomperz, Theodor, Creek Thinkers, tr. Magnus, Laurie (N. Y., 1908), I, 110 Google Scholar ff.; Sarton, History of Science, pp. 212-213. Pierre Duhem began his monumental Le Systeme du monde with ‘L'Astronomie pythagoricienne’ (Paris, 1913).

26 See Aristotle, Physica 202 b 36-203 a 16, 204 a 8-204 a 34, 213 b 22-213 b 27 a nd Plutarch, Opinions of Philosophers in Moralia, pp. 671, 672 [II, ix, xiii]. Thomas Digges’ famous diagram of an infinite heliocentric universe is drawn ‘according to the most auncient doctrine of the Pythagoreans’ (in A Perfit Description of the Calestiall Orbes, London, 1576, reprinted in Koyre, Alexandre, From the Closed World to the Infinite Universe, Baltimore, 1957, p. 37 Google Scholar). See also Zeller, , History of Creek Philosophy, 1, 466–468 Google Scholar; and Burnet, , Early Greek Philosophy, p. 108 Google Scholar.

27 Cudworth quoted St. Cyril: ‘Pythagoras held there was One God of the whole Universe, the Principle and Cause of all things, the Illuminator, Animator and Quickener of the Whole, and Original of Motion; from whom all things were derived, and brought out of Nonentity into Being’ (Intellectual System, p. 377). The reference to St. Cyril is Contra Julianum (Leipzig, 1696), p. 30 [Liber 1]. See also Cicero, De natura deorum, 1, xi; Iamblichus, Vita, chap. 30; Bayle, Dktionaire, ‘Pythagoras’, footnote N; and Enfield, History of Philosophy, pp. 227-228.

28 ‘Pytagoras primus apud grecos invenit immortales esse animas, sed erravit ponendo eas de corpore ad corpora transire’ (Burley, De vita, p. 78). Cf. Plutarch, Opin. of Phil., p. 683 [IV, vii]; Comes, Natalis, Mythologies (Padua, 1616), pp. 147 Google Scholar [III, XX], 537-538 [x ‘De Lethe fluvio’]; and Zeller, Greek Philosophy, 1, 481-487.

29 Opin. of Phil., p. 660 [I, iii]. Cf. Aristotle, Metaphysial 985 b 23-986 a 21.

30 See Plutarch, The Sytnposiaques in Moralia, pp. 628-630 [VIII, 2].

31 (Linz, 1619); figure I is inserted after fol. *4. On the elemental solids, see Plutarch, Opin. of Phil., p. 671 [II, vi], and Platonique Questions in Moralia, p. 836 [no. 4]; Crinitus, Peter, De honesta disciplina (Basle, 1532), p. 206 Google Scholar [XIII, X]; Dacier, Life of Pythagoras, pp. 72-73; Zeller, , History of Greek Philosophy, 1, 436–438 Google Scholar; and Sachs, Eva, Die fünf platonischen Körper (Berlin, 1917)Google Scholar. The symbolism of the dodecahedron has been recently employed by Salvador Dali in his ‘Sacrament of the Last Supper’ (National Gallery of Art, Washington, D. C).

32 Thales was probably a generation older than Pythagoras, but he inaugurated no continuing tradition. The seven wise men of Greece, of course, also antedated Pythagoras; but he superseded them by choosing the appellation ‘philosopher’ in place of .

33 This is probably the most widespread story about Pythagoras. The locus classicus is Cicero, Disputationes Tusculanœ, v, 3-4. Cf. Iamblichus, Vita, chap. 12; Isidore, Etymologic, VIII.vi.2; and Torrentinus, Hermannus, Dictionarium poeticum (Paris, 1550)Google Scholar, ‘Pythagoras’.

34 See Diogenes Laertius, Vita;, VIII, 48; Plutarch, Opin. of Phil., p. 670 [II, i]; Photius, , Myriobiblon (Geneva, 1611)Google Scholar, col. 1318; and Stanley, Thomas, The History of Philosophy (London, 1656), p. 14 Google Scholar.

35 This was the notion of the cosmic dance; cf. du Bartas, Guillaume Saluste, Define Weekes and Workes, tr. Sylvester, Joshua (3d ed., London, 1611), p. 33 Google Scholar:

Water, as arm'd with moisture and with cold,

The cold-dry Earth with her one hand doth hold;

With th'other th'Aire: The Aire, as moist and warm,

Holds Fire with one; Water with th'other arm:

As Country Maydens, in the Month of May,

Merrily sporting on a Holy-day,

And lusty dancing of a lively Round,

About the May-pole, by the Bag-pipes sound;

Hold hand in hand, so that the first is fast

(By means of those between) unto the last.

36 Tr. R. Dolman (London, 1601), p. 179. Macrobius had described the mechanism of the tetrad in complete detail in his Commentary on the Dream of Scipio, tr. William H. Stahl (N. Y., 1952), p. 105 [i.vi.25-28]. Cf. Giovanni Battista della Porta, Natural Magick [1658], ed. Derek J. Price (N. Y., 1957), p. 5. Edmund Spenser described the elemental cosmos with surprising succinctness:

… Water fights

With Fire, and Aire with Earth approaching neere:

Yet all are in one body, and as one appeare.

(Faerie Queene, vn.vii.25.7-9)

37 Arithmetic, tr. D'Ooge, p. 260.

38 Hierocles upon the Golden Verses of Pythagoras (London, 1657), p. 127.

39 Ibid., p. 126.

40 Life of Pythagoras, p. 74.

41 Cf. the diagrams in Nifo, Agostino, In libris Aristotelis meteorologicis commentaria (Venice, 1540), fol. 3V Google Scholar; and FinéS, Oronce, De mundi sphcera (Paris, 1542)Google Scholar, reprinted in Edna Kenton, The Book of Earths (N. Y., 1928), p. 170.

42 This was a major point of contact between Pythagoras and the Jews: Pythagoras’ 5e-graphic mime-subtype="gif" xlink:href="S0081865800002445_inline6"/> (see note 44) was equated with the Hebrew tetragrammaton. ‘Therfore did the Pythagorians sweare by this number, as by some holy thing, making (as may be easily conjectured) allusion to that great fower-lettered name of the Hebrues’ (La Primaudaye, French Academie, p. 178). See also Bayle, Dictionaire, ‘Pythagoras’, footnote H; and Dacier, Life of Pythagoras, pp. 32, 316.

43 Hierocles, Upon the Golden Verses, tr. Hall, p. 126 [comm. on 11. 47-48]. La Primaudaye turned even this notion into a tetrad: ‘All quantitie is divided into fower, to wit, into a point, into a length, bredth, and depth’ (French Academie, p. 177). See also Aristotle, De anima 404 b 18-404 b 24; Henry More, Conjectura cabbalistica, p. 152; and Zeller, 1, 434-436.

44 This relationship between 4 and 10 was expressed in a sacred symbol called the . For an explanation of why 10 represents perfection, see Nicomachus, Arithmetic, tr. D'Ooge, p. 219, n. 1. See also La Primaudaye, French Academie, p. 178; Zeller, 1, 427-428; and Cornford, ‘Mysticism and Science’, Classical Quarterly XVII (1923), 1 ff. For a critique of these various arguments for the special significance of four, see Cudworth, Intellectual System, p. 376.

45 Ed. Eduard Hiller (Teubner ed., Leipzig, 1878), pp. 93-106. The editio princeps, Greek text with Latin translation, appeared in Paris, 1644.

46 For examples well-known in the Renaissance, see Philo Judaeus, De plantatione Noë, 120 ff., and De opificio mundi, 48 ff.; Plutarch, Opin. of Phil., p. 661 [1, iii]; Hierocles, Upon the Golden Verses, p. 126; Isidore, De natura rerum, vii, 4, xi, 1-3; Martianus Capella, De nuptiisphilologies et Mercurii, II, 106 ff., VII, 734; Bovillus, Carolus, Liber de sapiente (1509), in Individuum und Kosmos in der Philosophic der Renaissance, ed. Cassirer, Ernst (Leipzig, 1927), pp. 311–312 Google Scholar; Du Bartas, Devine Weekes, pp. 40, 361; La Primaudaye, French Academic, pp. 177, 179 [a redaction of Hierocles]; John Davies of Hereford, Microcosmos (1603), ed. A. B. Grosart (London, 1877-1878, Chertsey Worthies’ Library), pp. 30-32; and Lilly, William, Christian Astrology (London, 1647), p. 183 Google Scholar. For modern studies of the origin of the tetrad tradition in literature, see Delatte, Armand, Études sur la littérature pythagoricienne (Paris, 1915), p. 255 Google Scholar, and Kucharski, Paul, Étude sur la doctrine pythagoricienne de la tétrade (Paris, 1952), pp. 18–26 Google Scholar.

47 Tr. J[ohn] Ffreake?] (London, 1651), pp. 186-187.

48 La Primaudaye, French Academie, p. 177.

49 Reproduced in Jung, C. G., Psychology and Alchemy (N. Y., 1953, Bollingen Series XX), p. 125 Google Scholar.

50 Conjectura cabbalistka, p. 38. See also La Primaudaye, French Academic, p. 179.

51 Reproduced in Jung, Psychology and Alchemy, p. 127.

52 These correspondences between the elements, the seasons, and the humors were commonplace in classical, medieval, and Renaissance thought; see Tuve, Rosemond, Seasons and Months (Paris, 1933), pp. 54 Google Scholar, 68, 98. The tradition derived from Hippocratic and Galenic medicine, but no doubt originated in theories enunciated by Alcmaeon, most prominent of the Pythagorean physicians, who had postulated: ‘Health is the equality of rights of the functions, wet-dry, cold-hot, bitter-sweet and the rest…. health is the harmonious mixture of the qualities’ ( Freeman, Kathleen, Ancilla to the Pre-Socratic Philosophers, Cambridge, Mass., 1948, pp. 40–41 Google Scholar).

53 From Thurneysser, Leonhard, Quinta essentia (Leipzig, 1574)Google Scholar, reproduced in Paracelsus, , Selected Writings, ed. Jacobi, Jolande (New York, 1951, Bollingen Series XXVIII), P.93 Google Scholar.

54 De honesta disciplina, p. 88 [v, ix]. Crinitus was quoting Diogenes Laertius, Vitœ, VIII, 10. Cf. Ovid, Metamorphoses, xv, 199-213.

55 Paracelsus, Writings, p. 93.

56 Genialium dierum libri sex, fol. 266v. Alexander is quoting Plutarch, Opin. of Phil., p. 661 [i, iii], or Hierocles, Upon the Golden Verses, p. 126. Cf. Aristotle, De anima 404 b 25-404 b 27; see Kucharski, Étude sur la tétrade, pp. 11 ff.

57 This tradition is brilliantly documented by Miss Tuve, Seasons and Months, pp. 122-170.

58 See Spitz, Lewis W., Conrad Celtis (Cambridge, Mass., 1957), pp. 86–87 CrossRefGoogle Scholar.

59 Religio Medici, ed. Jean-Jacques Denonain (Cambridge, 1953), p. 19 [1, xii].

60 The Garden of Cyrus printed with Pseudodoxia Epidemica (4th ed., London, 1658), PP-72-73-

61 Ibid., p. 69.

62 Cf. the title page of G. B. della Porta's Natural Magick (1658).

63 Jung, Psychology and Alchemy, pp. 91