Some Renaissance Versions of the Pythagorean Tetrad

1540. HENINGER S.K. Jr., Some Renaissance versions of the | Pythagorean tetrad: StudRen 8 1961 7-33. | + È 1 RENIN GERS K. | décrit, images à l’appui, la fortune que connaît en particulier la tétrade The First Italianate Englishmen i MIER È, 197 | tab \ Pares Apres un résumé des principales théories de Pythagore, Heninger : dans la physique, la théologie, la médecine, la météorologie, l’alchimie | ‚ etla poésie de la Renaissance. . eZ Some Renaissance Versions Rowland Whyte, Elizabethan Letter-Writer 217 of the Pythagorean Tetrad' LISLE C. JOHN Music and The Mad Lover 236 | JOHN P. CUTTS | ) Sacred ‘Parody’ of Love Poetry, and Herbert N 1538 when Sir Thomas Elyot printed his Dictionary, az he included the following entry for Pythagoras: “An 249 28 y excellente Phylosopher, whose Phylosophye was in ROSEMOND TUVE y= | SIA ‘I was but an inverted tree’: j Notes toward the History of an Idea A. B. ILLUSTRATIONS page 12 trae Of quaunes AU ESS mina aurea and Symbola, collections of spurious precepts with hidden meanings which had received extensive explication; and ‘the Scyence of noumbers’ recalled Pythagoras’ fundamental postu- | late that all things have innate numerical relationships. Elyot's entry indicates concisely what facets of the Pythagorean doctrine appealed to Ä of.both mysticism and physical science. Reuchlin cited Pythagoras as | The semen se rela solids (Kepler, Harmonice mundi, 1619) È | | CHAMBERS È | 291 mystycalle sentences, and alsoo in the Scyence of )}} noumbers.’ The “mystycalle sentences’ were the Carthe Renaissance and how Pythagoras could appear as the fountainhead | source of the mystical wisdom contained in De arte cabalistica,? while 13 Copernicus in De revolutionibus orbium coelestium claimed support from Tetrad of elements and qualities 15 | the ancient Pythagoreans for his belief that the earth moved. In the È Tetrad (Peyligk, Philosophiae naturalis compendium) The number four as a solid 16 17 | next century Galileo expounded a Pythagorean cosmology refined by Copernicus, while Henry More used Pythagoras to devise the Conjec- È Theological tetrad I ; Christ and the four elements (Bartholomaeus Anglicus i De proprietatibus rerum, 1482) 20 lin or n°the Southeastern Renaissance Conference at the University of North Caro- "I} The four elements (Isidore of Seville, De natura rerum, 1472) The natural sciences (Isidore of Seville, De natura rerum, 1472) 5 21 22 | i hermaphrodite : (Thurneysser, Quinta x essentia, s 1 $74) The alchemical 23 È Wind-rose (Apianus, Cosmographicus liber, 1524) 24 à Wind-rose (Aristotle, Meteorologica, 1519) > ‘ The© signs si of f thethe zodiac zodia (Kalendar of Shepherds, 1503) 25 26 Philosophers’ stone (Ashmole, Theatrum chemicum Britannicum, 1652) 27 Celtis, Quatuor libri | Tie i Lady Philosophy in tetrads (Celtis, Quatuor libri amorum, 1502) i SEe of = a. , or libri amorum (1502) '| 30 31 1958. | 4 See the author's preface to Dialogo . . . sopra i due massimi sistemi del mondo (Florence, i 1632). In January 1611 Tommaso Campanella wrote an enthusiastic letter to Galileo ex- | tolling the Sidereus nuncius: ‘Tu, vir clarissime, non modo restituis nobis gloriam pythagoreorum a græcis subdolis subreptam,eorum dogmata resuscitando, sed totius mundi gloriam tuo splendore eee 1927, p. 165). See Campanella, Ur red = = A efense 0 ileo, tr. Grant ese”, ey (No: ampton, Mass., 1937), p. 11: ‘Galileo’s theory of the motion ofthe earth, ofa central Sun, | | | 1” 22 thagoreanism, A, Burtt, The Metaphysical o lern1938), Physicalpp. 20-25. Science (London, 1927),seepp.E.40-44; and Angus Armitage, Foundations Copernicus (London, 29 Moguncia Metropolis (Celtis, Quatuor libri amorum, 1 502) 23 (Haguenau, 1517), epistle dedicatory to Pope Leo x. (Nuremberg, 1543), prefatory letter to Pope Paul=e Forjhe os debt to Pyand 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.

tura cabbalistica, a mystico-moral interpretation of Genesis. Pythagoras was easily adapted to any one’s philosophy, especially at a time when mysticism and science had not become dissociated. The harmonious world-view of Pythagoras was hugely satisfying, and the precise body of belicfs attributed to him was highly mcaningful in the Renaissance even if not today. For that reason Ralph Cudworth pronounccd categorically: ‘Pythagoras was the most eminent of all the ancient Philosophers,6 In the annals of philosophy, Pythagoras himself is an exceedingly tenuous figure. Neither he nor his immediate disciples left any writings because the master insisted upon oral transmission of his teachings and swore the initiated few to the utmost secrecy. Plato, obsessed as he was with Pythagorean doctrine, recorded no direct information about the founder of the school; and Aristotle, though he examined Pythagorean tenets in considerable detail, never spoke about Pythagoras, but always in a general way about the Pythagoreans. By late classical times, however, the fame of this enigmatic figure demanded scholarly investigation, and a sizable corpus of neo-Pythagorean literature developed. Most of this the Renaissance inherited and avidly enhanced.’ There were two biographies of Pythagoras in the spirit of hagiography: a largely legendary Vita by Porphyry in the third century and a much better known account by Iamblichus, a student of Porphyry. There were the Carmina aurea and the Symbola, two lists of aphorisms purportedly prescribed by Pythagoras for his disciples, and a copious commentary on the Carmina aurea by Hierocles in the fifth century. There were several apocryphal letters. Pythagorean arithmetic had been set forth by Nicomachus of Gerasa,* Pythagorean musicology had been elaborated by Nicomachus? and Boethius,!° Pythagorean cosmology had been delineated by Timaeus Locrus!! and Ocellus Lucanus,!? while Pythagorean ethics had been poignantly illustrated by Philostratus' 8 Vita Apollonii Tyanei.!* In addition to these neo-Pythagorean writings and in addition to Plato's Timaens and Aristotle’s De calo and Metaphysica," there was full coverage of Pythagoras in Diogenes Laertius’ Vita (vur. 1-50), and there were frequent references to Pythagoreanism in several standard classical texts: Plutarch’s Opuscula moralia,® Ovid's Metamorphoses,! and Lucian’s Dialogues." This large and varied body of literature was completely assimilated into the mainstream of Renaissance thought. Interest in Pythagoras was first ancillary to the rise of Neoplatonism in the Florentine Academy, and a brief consideration of his tradition shows why. In the sixth century 8.c., after reaching manhood in his native Samos, Pythagoras undertook a quest for knowledge, which, according to ancient sources, gave him firsthand experience among the Phoenicians, the Chaldeans, the Persian magi, the Hindus, the Arabians, the Jews, the Thracians, the Druids of Gaul, and especially the Egyp- (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 Timacus 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. 5 (London, 1653), fol. Bi: “What is Plato but Moses Atticus? And for Pythagoras it is a AJPT 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 elething 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, sce Eduard Zeller, A History of Greek Philosophy, tr. S. F. Alleyne (London, 1881), mentarium enarratio (Paris, 1539). 1, 306-323. which one speaker is a cock, the present incarnation of Pythagoras), in BIQN TIPAZIZ (a satire in which several philosophics of life are offered for sale), and in ANABIOTN TEZ 8 Nicomachus’ Arithmeticæ libri duo, translated by both Apuleius (no longer extant) and Bocthius, was the most influential arithmetical text in the middle ages. The editio princeps of the Greek text was printed in Paris, 1538. Bocthius’ version first appeared in Opera 13 The editio princeps was an Aldine publication (Venice, 1501). 14 The most notable passages in which Aristotle discusses Pythagorean doctrine are De celo 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. 16 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 ONEIPOZ H AAEKTPTON (a dialogue in H AAIETZ (an answer to the protest over BINN HPAZIZ in which the ancient philosophers return to avenge the calumny).

tians.!8 Rather late in life, after syncretizing the wisdom of all these disparate cultures, Pythagoras settled at Crotona in Magna Grecia, where he founded a secret brotherhood which held out to its members the He posited a spherical earth in a circular orbit,? an infinite universe, ? a deistic monotheism,”’ and an immortal soul subjected to reward and punishment.”* For such a man, a golden thigh was a minor accomplishhope of divine perfection.!* Each brother was dedicated to the release of his soul from its encumbering body, a purification to be effected through contemplation of the universal order revealed in nature. To achieve this ment. 10 oRrOeaNd purpose, Pythagoras offered instruction which began with mathematics, then progressed to a study of nature and an investigation of primary TOCRATEI principles, and finally promised knowledge of God. Despite the concomitant mysticism, the master and his immediate followers made exen traordinary scientific discoveries. Pythagoras was the acknowledged father of pure arithmetic and geometry,” of numerology,”! of internal medicine,?? of acoustics and musicology,”* and of literary emblems.?* DSai=tAnri?àmLetaAMlstnrekmea 18 For sources relating to these legendary travels, see William Enfield, The History of L+e eun Aa Philosophy (London, 1837), pp. 212-214, and Zeller, History of Greek Philosophy, 1, 327- 335. Although Enfield and Zeller rightly submit these authorities to question, the Renaissance did not. See, for example, Alexander ab Alexandro, Genialium dierum libri sex (Paris, 1570), fol. 49-50. 19 Full accounts of this ‘school’ are in Diogenes Laertius and Iamblichus; sec also Aulus Gellius, Noctes Attice, 1.ix.1-12, and Walter Burley, Liber de vita et moribus philosophorum, ed. Hermann Knust (Tübingen, 1886), pp. 70-72. 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 belicfs promulgated in Pythagoras’ school, see Enfield, History of Philosophy, pp. 217-230, and F. M. Cornford, ‘Mysticism and Science in the Pythagorean Tradition’, Classical Quarterly xvi (1922), 139 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 Etymologia, m.ii.1. Cf. Diogenes Laertius, Vite, vm, 11-12, and Batman uppon Bartholome, His Book De Proprietatibus Rerum (London, 1582), fol. 95. For modern opinions, see Zeller, Greek Philosophy, 1, 347; Nicomachus, Arithmetic, ed. D'Ooge, pp. 18-19; and George Sarton, A History of Science: Ancient Science through the Golden Age of Grecce (Harvard Univ. Press, 1952), pp. 203 ff. 2! See lamblichus, Vita, chap. 19. See also Zeller, Greek Philosophy, 1, 419-425; John Burnet, Early Greek Philosophy (4th ed., London, 1945), pp. 107-108; and Tobias Dantzig, Number: the Language of Science (N. Y., 1930), pp. 40-45. 22 Pythagoras’ claim to medical knowledge rests mainly upon his disciples, Alcmaeon and Empedocles: see Enfield, History ofPhilosophy, pp. 232-233; John Burnet, Greek Philosophy: Part I, Thales to Plato (London, 1928), pp. 41, 49-51; 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 chronicarım, Nuremberg, 1493, fol. 61"). 23 Pythagoras discovered the numerical ratios which determine the concordant intervals of the musical scale; ergo, ‘Hic 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 11 Pythagoras’ invention of ‘harmonical Measures’ (The Life ofPythagoras, 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 Hieroglyphica of Horapollo and the mystic symbols of the Kabalists, were assimilated by Neoplatonists of the Florentine Academy and eventually gave risc to the prolific emblem literature of the sixteenth century. See Plutarch, Of Isis and Osiris in Moralia, tr. Philemon Holland (2d ed., London, 1657), p. 1051; Vincenzo Cartari, Les Images des dieux des anciens, tr. Antoine du Verdier (Lyons, 1581), p. 4; Lilio Gregorio Giraldi, Libelli duo . . . in altero Pythagoræ symbola . . . sunt explicata (Basle, 1551), pp. 71-85 (prefatory letter to Pico della Mirandola); G. P. Valeriano, Hieroglyphica (Basle, 1556), title page; and Pierre Bayle, Dictionaire historique et critique (Rotterdam, 1697), ‘Pythagoras’, foomote 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 Sce Diogenes Laertius, Vite, vt, 48. ‘It is well known that the Pythagoreans held the Motion of the Earth about the Sun’ (Henry More, Conjectura cabbalistica, 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 J. L. E. Dreyer, A History of Astronomyfrom Thales to Kepler (2d ed., N. Y., 1953), pp. 37-38. For modern evaluation of Pythagoras’ contributions to astronomy, see Burnet, Early Greek Philosophy, pp. 110-111; Theodor Gomperz, Greek Thinkers, tr. Laurie Magnus (N. Y., 1908), 1, 110 ff.; Sarton, History of Science, pp. 212-213. Pierre Duhem began his monumental Le Systéme 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; and Plutarch, Opinions of Philosophers in Moralia, pp. 671, 672 [n, 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 ofthe Cælestiall Orbes, London, 1576, reprinted in Alexandre Koyré, From the Closed World to the Infinite Universe, Baltimore, 1957, p. 37). See also Zeller, History of Greek Philosophy, 1, 466-468; and Burnet, Early Greek Philosophy, p. 108. 37 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; lamblichus, Vita, chap. 30; Bayle, Dictionaire, ‘Pythagoras’, footnote N; and Enfield, History of Philosophy, pp. 227-228. 38 *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 [rv, vii]; Natalis Comes, Mythologie (Padua, 1616), pp. 147 [u1, xx], 537-538 [x ‘De Lethe fluvio’]; and Zeller, Greek Philosophy, 1, 481-487.

13 ously discussed even so late as Johann Kepler, from whose Harmonice mundi figure 1 is taken.?! Because of this cosmological geometry, Pythagoras was acknowledged as the first philosopher.? In fact, he invented the name ‘philosopher’ to replace the presumptuous gogés or sapiens.?? More important, Pythagoras was credited with originating the term ‘cosmos’. And as might be expected, this cosmos is represented in a geometrical design, a tetrad (fig. 2). Arranged in a square were the four basic qualities, the contraries opposite one another: hot opposite cold, and dry opposite moist. The four elements, partaking of these four HOT MOIST In the Renaissance, Pythagoras was perhaps best known for his theory about the transmigration of souls—the “Pythagorean metempsychosis’ that Faustus, according to Marlowe, so pitifully envied at the end of his hedonistic career. But much more fundamental to the Renaissance world-view was the discovery attributed to Pythagoras of the mathematical relationships in musical harmony and the application of these harmonic ratios to the physical universe. In Plutarch’s words, as translated by Philemon Holland, Pythagoras ‘held that the principle of all things were Numbers, and their symmetries, that is to say the proportions that they have in their correspondency one unto another . . . are tearmed by him Gcomcetricall’.2” For the Pythagorcans, God was the arch-geometer,*° and He had fashioned each of the four elements so that its inherent shape was one of the four regular solids: fire was a pyramid, earth a cube, air an octahedron, and water an icosahedron. God had used the dodecahedron, the fifth regular solid, as a model for the universe in its entirety. This lore had been accepted by Plato in the Timaeus (5sD-56c), and the geometrical designation of the elements was seri22 Opin. ofPhil., p. 660 [1, iii]. Cf. Aristotle, Metaphysica 985 b 23-986 a 21. % See Plutarch, The Symposiaques in Moralia, pp. 628-630 [vın, 2]. DRY COLD 2. Tetrad of qualities 31 (Linz, 1619); figure 1 is inserted after fol. *4. On the elemental solids, see Plutarch, Opin. of Phil., p. 671 (a, vi], and Platonique Questions in Moralia, p. 836 [no. 4]; Peter Crinitus, De honesta disciplina (Basle, 1532), p. 206 [xm, x]; Dacier, Life ofPythagoras, pp. 72-73; Zeller, History of Greek Philosophy, 1, 436-438; and Eva Sachs, Diefünfplatonischen Körper (Berlin, 1917). 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 copés. 3 This is probably the most widespread story about Pythagoras. The locus classicus is Cicero, Disputationes Tusculane, v, 3-4. Cf. Iamblichus, Vita, chap. 12; Isidore, Etymologie, vm.vi.2; and Hermannus Torrentinus, Dictionarium poeticum (Paris, 1550), ‘Pythagoras’. % See Diogenes Laertius, Vite, vm, 48; Plutarch, Opin. ofPhil., p. 670 [n, i]; Photius, Myriobiblon (Geneva, 1611), col. 1318; and Thomas Stanley, The History of Philosophy (London, 1656), p. 14.

qualities, then also formed a tetrad (fig. 3). Using the terminology of 15 N Empedocles, a follower of Pythagoras, we can see that Hate operating between the opposites would produce an outward thrust tending to disrupt the cosmos. But Love between the elements that share a common quality—for instance, air and fire share the quality ‘hot’ —would form a tension around the circumference of the circle. As Pierre de la Primaudaye explained in his Third Volume of the French Academie: AIR The elements are agreeable one to another, with their coupled qualities. ... So that the fower elements are (as if each one of them had two hands, by which they held one another) as in a round daunce:** or else, as if they were conjoined and linked togither, as with chains and buckles.#6 FIRE MOIST The system is stable because it is harmonious, because it incorporates extremes. In this configuration, there is a perfect balance of tensions, a reconciliation of opposites, an orderly arrangement of a unified whole. In the words of Nicomachus: WATER Harmony always arises from opposites; for harmony is the unification of the diverse and the reconciliation of the contrary-minded,5” NS UE” According to Hierocles, as translated by John Hall, this was Pythagoras’ greatest achievement: ‘the knowledge of the Creative Tetrad'. EARTH 3. Tetrad of elements and qualities After delineating this mechanism for cosmos, Pythagoras applied the 35 This was the notion of the cosmic dance; cf. Guillaume Saluste du Bartas, Devine Weekes and Workes, tr. Joshua Sylvester (3d ed., London, 1611), p. 33: 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, pattern to the various categories of existence: Indeed the Tetrad cements al things that have any existence together, as the Elements, Numbers, Seasons of the year, and periods of Age. Neither are we to doubt that these flow not from the Tetrad as the root and spring: for the Tetrad, as we said before, is in Merrily sporting on a Holy-day, the Creatour and cause of all things, the Intellectuall God, the Sonne of the Celestial And lusty dancing of a lively Round, About the May-pole, by the Bag-pipes sound; and Sensible God.5? Hold hand in hand, so that the first is fast (By means of those between) unto the last. % Tr, R. Dolman (London, 1601), p. 179. Macrobius had described the mechanism ot the tetrad in complete detail in his Commentary on the Dream of Scipio, tr. William H. o Stahl (N. Y., 1952), p. 105 (1.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, vu.vii.25.7-9) 37 Arithmetic, tr. D'Ooge, p. 260. 38 Hierocles upon the Golden Verses of Pythagoras (London, 1657), p. 127. Le Pythagoras was the first man in western culture to propose a persistent pattern that prevails throughout each level of creation—which is, of course, the ideological basis for the entire microcosm-macrocosm analogy. This integrated system provided a basis for scientific hypothesis and for optimistic philosophical speculation. As Dacier said: “He first call'd the Universe xécyov, Mundum, to mark the Beauty, the Order and the Regularity that reign thro’ all its Parts.’ It was recognized that xbouos means ‘embellishment’ as well as ‘order’. 89 Ibid., p. 126. Life ofPythagoras, p. 74.

"Pzima combinario valis ter, the south wind. The third combination, between moist and cold, produces water, phlegm, winter, old age, and Favonius, the west wind. The fourth combination, between cold and dry, produces earth, black bile, autumn, decrepitude, and Boreas, the north wind. The fifth combination, however, between dry and moist, is impossibilis, as is also the sixth combination between hot and cold. % Subfolan? e ELA 3= 3 AT E Sanguis E Zidoleéris aTtAlb>iEeg S sii Ziqua DW) È $ odg, - È Zerra Aisdancolia E di à wr 3 Flegma Hfiibitas, Dians, Fanoop Frigibitaf 7 17 o DN $. The number four as a solid The fundamental importance of the number four was verified to the Pythagoreans by other impressive evidence. The name of God in all languages is composed of four letters: e.g., Zeus, Jove, and Jehovah.* Geometrically speaking, the number four provides the first solid body (fig. 5): 1 makes only a point, 2 makes only a straight line, 3 makes only a plane surface, but 4 makes a solid with volume, * and therefore is the proper number to represent the extended universe. What clinched the essentiality of four, however, was its relationship to the perfect number, ten; 14+-243-4+4=10, and consequently four contains within itself the potentiality of perfection.** The idea of cosmos, then, was a central thesis of Pythagoreanism, and Zeraa combinario yalis 4. Tetrad (Peyligk, Philosophiae naturalis compendium) 42 This was a major point of contact between Pythagoras and the Jews: Pythagoras’ rerpaxrbs (see note 44) was equated with the Hebrew tetragrammaton. “Therfore did the de, vPAWeT1I6R1dn Figure 4 is a Renaissance version of figure 3 taken from Johann Peyligk, Philosophiæ naturalis compendium, printed in 1499 (sig. 111).4 At the corners are the four basic qualities. On the periphery of the tetrad the possible combinations of these qualities are indicated, while diagonally across the tetrad the impossibility of combinations is noted. The first combination, between hot and dry, produces fire, choler, summer, youth, and Subsolanus, the east wind. The second combination, between hot and moist, produces air, blood, spring, adolescence, and Aus- Pythagorians sweare by this number, as by some holy thing, making (as may be easily conjectured) allusion to that great fower-lettcred name of the Hebrues’ (La Primaudaye, French Academie, p. 178). See also Bayle, Dictionaire, ‘Pythagoras’, footnote u; and Dacier, Life of Pythagoras, pp. 32, 316. 43 Hierocles, Upon the Golden Verses, tr. Hall, p, 126 [conun, on Il. 47-48]. La Pri» maudaye 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, (Venice, 1540), fol. 3"; and Oronce Find, De mundi sphæra (Paris, 1542), reprinted in 434-436. 44 This relationship between 4 and 10 was expressed in a sacred symbol . called the rerpaxrés. For an explanation of why 10 represents perfection, a see Nicomachus, Arithmetic, tr. D’Ooge, p. 219, n. 1. See also La Primauu. daye, French Academie, p. 178; Zeller, 1, 427-428; and Cornford, ‘Mystiè à à © cism and Science’, Classical Quarterly xv (1923), 1 ff. For a critique of these various arguments for the special significance of four, see Cudworth, Intellectual Edna Kenton, The Book of Earths (N. Y., 1928), p. 170. System, p. 376. 41 Cf. the diagrams in Agostino Nifo, In libris Aristotelis meteorologicis commentaria

the tetrad—sometimes called the “quaternion’—was the symbol which expressed this all-inclusive principle. The tetrad was the basic pattern which subsists throughout the universe. In consequence, there are not only four elements, but also four humors, four seasons, four ages of man, four corners of the world, four cardinal winds, four mental faculties, four rivers of Paradise and four of Hell, four archangels, four evangelists, four cardinal virtues, and so on literally ad infinitum. La Primaudaye quoted Hierocles on this point: Hierocles the interpreter of Pythagoras, doth so extoll this number of fower, that he affirmeth it to be the cause of all things, and that nothing can be said or done, which proceedeth not from it, as from the roote and foundation of all nature (p. 178). Lists of evident tetrads must have becn an integral part of the Pythagorean doctrine from its inception. In extant writings, however—and we must remember that the Pythagoreans were sworn to secrecy and oral communication—explicit delineation of specific tetrads begins in the second century B.c. with the Expositio rerum mathematicarum ad legendum Platonem utilium by Theon of Smyrna, who explicated eleven tetrads.* But from then on, the tetrad enjoyed a continuous and prolific tradition,“ culminating for the Renaissance in the elaborately diagrammed ‘Scale of the Number Four’ in Henry Cornelius Agrippa’s De occulta philosophia which includes no less than thirty-one tetrads.* Since the tetrad pattern is omnipresent, it was used in the Renaissance to depict the first principle in many different fields of knowledge: “All the foundation of every deepe studie and invention, must be settled upon the number of fower, bicause it is the roote and beginning of all 45 Ed. Eduard Hiller (Teubner ed., Leipzig, 1878), pp. 93-106. The editio princeps, Greek text with Latin translation, appeared in Paris, 1644. 4 For cxamples well-known in the Renaissance, see Philo Judacus, De plantatione Noë, 120 ff., and De opificio mundi, 48 ff.; Plutarch, Opin. ofPhil., p. 661 [1, iii]; Hierocles, Upon the Golden Verses, p. 126; Isidore, De natura rerum, vii, 4, xi, 1-3; Martianus Capella, De nuptiis philologiæ et Mercurii, u, 106 ff., vu, 734; Carolus Bovillus, Liber de sapiente (1509), in Individuum und Kosmos in der Philosophie der Renaissance, ed. Ernst Cassirer (Leipzig, 1927), pp. 311-312; Du Bartas, Devine Weekes, pp. 40, 361; La Primaudaye, French Academie, 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 William Lilly, Christian Astrology (London, 1647), p. 183. For modern studies of the origin of the tetrad traditionin literature, see Armand Delatte, Etudes sur la littérature pythagoricienne (Paris, 1915), p. 255, and Paul Kucharski, Etude sur la doctrine pythagoricienne de la tétrade (Paris, 1952), pp. 18-26. 47 Tr. J[ohn] F[reake?] (London, 1651), pp. 186-187.

numbers.” In natural philosophy, as already noted, the tetrad explained the arrangement of the four elements; in theology, it represented the relationship between Christ and the evangelists; in medicine, it balanced the four humors and differentiated the four ages of man; in meteorology, it provided a wind-rose; in astrology, it organized the twelve signs of the zodiac into four seasons; and in alchemy, it showed how the philosophers’ stone was the perfect center of the universe. My purpose now is to consider representative examples of these Renaissance tetrads. Figure 6% is an illumination from a twelfth-century breviary. This theological tetrad shows the Lamb of God in the center, the four evan- EL % justice, temperance, and fortitude). Such a tetrad is more typical of the middle ages than of the Renaissance, although Henry More provided a belated gloss for it: “There was a very pleasant River that water’d this Garden [of Eden], distinguishable into four streams, which are the four Cardinal Virtues, which are in several degrees in the Soul.’ Now moving into the era of the printed book, we see in figure 75! an illustration from a French version of Bartholomaeus Anglicus’ De proprietatibus rerum, printed in 1482. Christ stands in the midst of the four clements and represents the ideal synthesis of these mundane materials. The elements are not arranged in a true tetrad pattern—that is, gelists with their symbols in the squares surrounding Him (Matthew, John, Luke, Mark), the four rivers of Paradise (the Phison, the Tigris, the Euphrates, and the Geon), and the four cardinal virtues (prudence, SESSO) ee ] ee N a’ 7. Christ and the four elements (Bartholomaeus Anglicus, De proprietatibus rerum, 1482) 48 La Primaudaye, French Academie, p. 177. 4% Reproduced in C. G. Jung, Psychology and Alchemy (N. Y., 1953, Bollingen Series XX), p. 125. © Conjectura cabbalistica, p. 38. See also La Primaudaye, French Academie, p. 179. 51 Reproduced in Jung, Psychology and Alchemy, p. 127.

23 The little world of man traditionally integrated the four humors, as in figure 10,5 where the alchemical hermaphrodite is surrounded by the signs of the zodiac. But man was also the embodiment of other tetrads. The four ages of man corresponded to the four seasons, as Peter Crinitus noted: % Has autem ætates idem Pythagoras quatuor anni temporibus condigna similitudine comparabat: videlicet verno tempori pueros, æstati adolescentes, autumno iuvenes, hyemi senes.54 FLEGMAT SANGVIN 9. The natural sciences (Isidore of Seville, De natura rerum, 1472) fire and water, though opposites, are juxtaposed; but this oversight can be explained, I believe, by the probability that this illustration derived from another drawing, a woodcut in the first edition of Isidore of Seville's De natura rerum, printed in 1472 (fig. 8). Here we have the four elements similarly arranged, to illustrate the Pythagorean tenet printed around the rim: Creatura solidata est secundum geometricam rationem. This first edition of Isidore provides another woodcut (fig. 9), illustrative of the natural sciences, which shows how the tetrad pattern subsists in the related cosmoi of mundus, annus, and homo. For mundus, there are the four elements; for annus, there are the four seasons which corre spond to the four elements; and for homo, there are the four corresponding humors. All is interrelated, unified, harmonious; and the medieval flavor of Isidore is nicely retained in the delicate interlacings. In his Devine Weekes and Workes, du Bartas likewise expounded ‘a fourefolde Consort in the humors, seasons, and elements’ (pp. 377-378). 52 These correspondences between the elements, the seasons, and the humors were commonplace in classical, medieval, and Renaissance thought; see Rosemond Tuve, Seasons and Months (Paris, 1933), pp. 54, 68, 98. The tradition derived from Hippocratic and Galenic medicine, but no doubt originated in theories enunciated by Alcmacon, 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 10. The alchemical hermaphrodite (Thurneysser, Quinta essentia, 1574) harmonious mixture of the qualities’ (Kathleen Freeman, Ancilla to the Pre-Socratic Philosophers, Cambridge, Mass., 1948, pp. 40-41). . $3 From Leonhard Thurneysser, Quinta essentia (Leipzig, 1574), reproduced in Paracelsus, Selected Writings, ed. Jolande Jacobi (New York, 1951, Bollingen Series Xxvm), i ti De honesta disciplina, p. 88 [v, ix]. Crinitus was quoting Diogenes Laertius, Vite, vin, 10. Cf. Ovid, Metamorphoses, xv, 199-213.

S. K. HENINGER, JR. 25 nt fr duro er ABC cc yo - Auer mous Syoroiy . Luro DIES zéoneme Suord San ds Ado Cerne Va Aa e dt %% de en à SI ons 2 old ¿237 El EC ge 2% baa È = a Da. Te a TATE = sti en is Ys 211 Mu, moby Grptenriouerits parties ce Dal Bomrtw Seprntrio xv / Hl à MER Mquélo Borcas TRE 3818 © Le: A | con ¡PA / 014838 x &Be Rottredt of mono utp msi où nn 5133 og = 3 ab «per ei “go i Scptentrio 12. Wind-rose (Aristotle, Meteorologica, 1519) °* 11. Wind-rose (Apianus, Cosmographicus liber, 1524) Paracelsus formed a tetrad from the four basic tastes: The body has four kinds of taste—the sour, the sweet, the bitter, and the salty... . Everything bitter is hot and dry, that is to say, choleric; everything sour is cold and dry, that is to say, melancholic [etc.].55 Alexander ab Alexandro applied the tetrad to man’s soul: Pythagorei per quaternionem: siquidem hunc numerum ad anime integritatem spectare dicunt: in his fuere mens, scientia, opinio, & sensus.®° 55 Paracelsus, Writings, p. 93. 5 Genialium dierum libri sex, fol. 266". Alexander is quoting Plutarch, Opin. of Phil., The tetrad therefore presented a psychological as well as physiological integration of the human microcosm. Meteorologists used a tetrad to set forth the winds, such as the representative wind-rose in Apianus Cosmographicus liber of 1524 (fig. 11). The twelve winds are named in various languages, and each cardinal wind is also identified with its appropriate element: the south wind with air, the west wind with water, the north wind with earth, and the east wind with fire. A more complex, though less decorative, wind-rose appeared in Johann Eck’s edition of Aristotle’s Meteorologica prepared for the University of Ingolstadt in 1519 (fig. 12). Here are not only the p. 661 [1, 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.

27 Here followeth the Figure conteynang all the fecrets of the Treaufe both great & {mall points of the compass and the twelve winds (given in four groups of three), but also the twelve signs of the zodiac (given in four groups of three), the four basic qualities, the four humors, the four ages of man, the four seasons, and the four elements. The tetrad arrangement of the twelve signs of the zodiac was, of course, an astrological commonplace. It was also a commonplace, inherited from the middle ages, to associate a human occupation with each of the twelve months.’ The resultant arrangement, such as figure 13 from the Kalendar of Shepherds (1503), epitomized the good life, a perfect integration of all human experience. In the center medallion the lady with her flowers beneath a green tree and the gentleman beside his 57 This tradition is brilliantly documented by Miss Tuve, Seasons and Months, pp. 122170. fire beneath a bare tree suggest the reconciliation of opposites, of summer and winter, of female and male—in fact, as in figure 10, they represent an hermaphrodite, the obvious symbol of completeness used by the alchemists. From astrology to alchemy was a short hop, and without surprise we

find the alchemists relying upon the tetrad to explain the mystery of the philosophers’ stone. Elias Ashmole in his Theatrum chemicum Britannicum (1652) reproduced an intricate diagram (fig. 14) showing, amongst a myriad of other things, the four elements with the stone placed idealistically at their conjunction. Where air, water, earth, and fire come together in perfect balance, there is the centrum lapidis. The Renaissance can boast at least one major creative work based on the tetrad: the long Latin poem of Conrad Celtis, Quatuor libri amorum (Nuremberg, 1502). The title page (fig. 15) reveals an elegant tetrad CONIRA DICELTIS PROTVCH 28 PRIMIINTERGERMANOSIM? Jee ZEN PLKATORUSSMANIBVS POEE È "Md TELAVREATIQYAT VW ON ORLIBRIAMORVM LA: Ph SECVNDVMQA A 3 ts dy which includes the four cities at the geographical extremes of Germany, the four bodies of water which mark its boundaries, the four parts of the day, and the four ages of man. In the center is Bohemia and the Elbe. The work is organized according to this plan.5® After the prefatory matter, but preceding the text of the poem itself, there is a woodcut by Albrecht Diirer (fig. 16) depicting Lady Philosophy enthroned amidst a tetrad of the wisest men from the most renowned civilizations: Ptolemy, representing the priests of Egypt and Chaldea; Plato, representing the philosophers of Greece; Cicero and Vergil, representing the orators and poets of Rome; and Albertus Magnus, representing the scholars of Germany. From the corners blow the four cardinal winds: Eurus, associated with fire and choler; Zephyrus, associated with air and blood; Auster, associated with water and phlegm; and Boreas, associated with earth and black bile. And the whole is entwined with garlands appropriate to the seasons to form a pseudo-cosmos. Immediately preceding each of the four books of this poem is an appropriate woodcut setting forth a prospect of the city to which the book is dedicated, including the river that flows by it; and at the top is indicated the corresponding season, age of man, part of the day, wind, humor, zodiacal sign, quality, element, and color. For example, figure 17, which introduces book 11, shows Mainz on the Rhine; and in the boxes at the top we have, in correspondence, autumn, youth, sunset, Zephyrus, phlegm, Libra, heat, water, and red. Our observation that these correspondences do not jibe with those established by the tetrad on the title page bespeaks our interest in fact rather than in poetry. The tetrad also appears prominently in the writings of Thomas Browne, thatinquiring medicus religiosus. He confided: ‘I have often admired the mysticall way of Pythagoras, and the secret Magicke of num58 See Lewis W. Spitz, Conrad Celtis (Cambridge, Mass., 1957), pp. 86-87. nepores Ai) TVORLATE GILG) GERMANIE FELICI REY Ra TERINEPLL fee A VINTA AG ) À N sere n vehes Terp.wonstes Germania ad QUiTUOR fareng rudinis ur ciusdem cante pre ni a E ur h 4 m. RATISPONA pores" KLafudins . N A MOGVNGÉ À MP. RHEN\ S O 7 a he BP vez vin deal Cass W | SENEC TVs E e ; 5 (ef Auetea INN NON JT MURS Ey erFF 1; OT TT IAE LITALoTe. LOMO um Ain oneeuune bi: 4g ts Cunoy¿1 gm Pd UN QUI lette in si Notti tust ms THOS Erich PIN Où be Im 15. Title page of Celtis, Quatuor libri amorum (1502)

Jophısmme Creci vocanrL ari Sapteactars . Eurus zephir» Egipc . wCnatders memuenene GRIS CRI] vere an, é Den „> _ Lmn rmunı here German: ampliguer e n AA my A ee: x ata, | S, K. HENINGER, JR. Sanguine EC AS \RSVLA GALLA PR a DMAusisdedieatum te * E Ry Af x | ’ ÈL t «È ss + = 03 e ad a h Airuno tuuenr? Occas? Zephia Fragma ‘ A u) u. Lar? Gex aride "| e \ À = u y Ls Al - 2 à \ . y | . > om. | | 4 — Fran lps iD [4 a TEA an 3 Quicquit hab quid Terra quid Aca & atquoro _Quicquidintumanisaebusdresse pores 1-- Erdéusinra 9quicquid facitigneus orbe Phlosopmamc> pectonecuncra geno — 2 aes È 3 5 er; 16. Lady Philosophy in tetrads (Celtis, Quatuor libri amorum, 1502) = T:At4 ry YENES ; 7 ne ANoguncia AA cTRopol oP ts i io ] = a Di Ege: i te amaries Rhenoin Gallia vsgyadnova Mera & Taeuerim >>. 17. Moguncia Metropolis (Celtis, Quatuor libri amorum, 1502)

Then cold and hot and moist and dry In order to their Stations leap, And musıck’s pow’r obey. From Harmony, from heavenly Harmony This universal Frame began: bers.'** By his usual method of conglomerating authorities, Browne educed the fact that when Cyrus planted his gardens he ordered the trees in rows which formed a ‘Quincuncial Lozenge’—in fact, a continuous tetrad. Browne observed that tetrads are an omnipresent pattern in both art and nature, and he exhorted his fellow scientists to continue the search for them: A large field is yet left unto sharper discerners to enlarge upon this order, to search out the quaternio’s and figured draughts of this nature, and moderating the study of names, and meer nomenclature of plants, to erect generalities, disclose unobserved propricties, not only in the vegetable shop, but the whole volume of nature. Yet Browne was not willing to subscribe to unbridled numerology: To enlarge this contemplation unto all the mysteries and secrets, accommodable unto this number, were inexcusable Pythagorisme,5! This denunciation of esoteric Pythagorism was no doubt for the benefit of the Cambridge Platonists. In baroque form the tetrad appears on the title page of Sandys’ translation of Ovid's Metamorphoses (1632).%? The splendid engraving presents Jove as fire, Juno as air, Neptune as water, and Ceres as earth, with the pointed inscription: Ex his oriuntur cuncta. An accompanying poem which gives ‘the minde of the frontispeece’ begins: From Harmony to Harmony Through all the Compass of the Notes it ran, The Diapason closing full in Man. This poem reflects the inevitable culmination of Renaissance humanism. The chief product of creation is man, in whom is heard the diapason of nature, the perfect harmony of God’s great variety. The philosophers’ next task, clearly, was to analyze the make-up of this abstract harmony; the time was ripe for psychology, for Descartes, Locke, Berkeley, and Hume. The proper study of mankind became not God, not the heavens, not the universe, but man. Nonetheless, the tetrad persisted. And today, in the terminology of Jung, modern man must still integrate his personality according to the archetypal pattern of the mandala, which in actuality is a tetrad. Duke University Fire, Aire, Earth, Water, all the Opposites That strove in Chaos, powrefull Love unites; And from their Discord drew this Harmonie, Which smiles in Nature. In this same vein, Dryden opened his well-known ‘Song for St. Cecilia’s Day’: From Harmony, from heav'nly Harmony This universal Frame began; When Nature underneath a heap Ofjarring Atomes lay, And cou’d not heave her Head, The tuneful Voice was heard from high, Arise, ye more than dead. 59 Religio Medici, ed. Jean-Jacques Denonain (Cambridge, 1953), p. 19 (1, xii]. e The Garden of Cyrus printed with Pseudodoxia Epidemica (4th ed,, London, 1658), PP. 72-73. 61 Ibid., p. 69. $3 Cf. the title page of G. B. della Porta's Natural Magick (1658). 63 Jung, Psychology and Alchemy, pp. 91 ff.

APPENDIX Dardi Bembo, tr., Commento di Ieroclefilosofo sopra i versi di Pitagora, detti d’oro (Venice, FIRST EDITIONS OF MAJOR PYTHAGOREAN PUBLICATIONS TO 1700 Giovanni Aurispa, tr., Hieroclis .. . in aureos versus Pythagoræ opusculum præstantissimum et religioni christianæ consentaneum (Padua, 1474). Pythagoras, Carmina aurea, in Constantinus Lascaris, Erotemata ... (Venice, 1494). Marsilio Ficino, tr., Pythagoræ philosophi aurea verba. Symbola Pithagoræ philosophi, in Iamblichus de mysteriis Ægyptiorum, Chaldæorum, Assyriorum et al. (Venice, 1497). Philippo Beroaldo, tr. and comm., Pythagoræ symbola moraliter explicata (Bologna, 1500). Stefano Negri, Commentarioli in aurea carmina Pythagoræ, in Elegantissime e greco authorum subditorum translationes (Milan, 1521). Johannes Alexander Brassicanus, tr. and comm., Proverbiorum symmicta. Quibus adjecta sunt Pythagoræ symbola XVIII (Vienna, 1529). Veit Amerbach, tr. and comm., Poemata Pythagoræ et Phocylidis (Strasbourg, 1539). Lilio Gregorio Giraldi, Libelli duo, in quorum altero enigmata pleraque antiquorum, in altero Pythagoræ symbola . . . sunt explicata (Basle, 1551). Joachim Camerarius, ed., Pythagore versus aurei in Libellus scolasticus utilis (Basle, 1551). Nicold Scutellio, tr., Pythagore vita ex Iamblicho collecta (Rome, 1556). Michael Neander, tr. and comm., Pythagoræ carmina aurea in Opus aureum et scholasticum (Basle, 1559). Jean de Strazecle, tr. and comm., Aureorum Pythagore carminum, quibus ratio vite bene ac sapienter instituende continetur, brevis explanatio (Paris, 1562). Claude Mignault, ‘Syntagma de symbolis, stemmatum et schematum ratione, que insignia seu arma gentilitia vulgo nominantur: deque emblematis’, appended to Andrea Alciati, Emblemata (Antwerp, 1573). Jean Antoine Baif, tr., Les vers dorés de Pitagoras in Etrénes de poézie fransoeze (Paris, 1574). Jean de Sponde, ed. and tr., Pythagoreorum veterum fragmenta politica in Aristotelis politicorum libri octo (Basle, 1582). Willem Canter, ed. and tr., Pythagoreorum veterumfragmenta ethica in Aristotelis ethicorum Nicomachiorum libri decem (Basle, 1582). Joannes Curterius, ed. and tr., Hieroclis philosophi commentarius in aurea Pythagoreorum carmina (Paris, 1583). Théodore Marcile, tr. and comm., Aurea Pythagoreorum carmina (Paris, 1585). Joannes Arcerius Theodoretus, ed. and tr., Iamblichi . . . De vita Pythagore . . . Addite sunt in fine Theanus, Myiæ, Melissa & Pythagoræ aliquot epistolia (Heidelberg, 1598). Didier Hérauld, Adversariorum libri duo. Quibus adjunctus est animadversionum eiusdem in librum Jamblichi de vita Pythagora (Paris, 1599). Joachim Zchner, ed. and tr., Pythagoræfragmenta (Leipzig, 1603). 35 1604). Conrad Rittershus, ed., Malchus [i.e., Porphyry] de vita Pythagore (Altdorf, 1610). Giovanni Donati Ferrario, tr., [Porphyrii] Pythagora vita (Milan, 1629). Lucas Holstein, ed. and tr., Porphyrii liber de vita Pythagore. . . . Dissertationem de vita et scriptis Porphyrii et ad vitam Pythagora observationes adjecit . .. (Rome, 1630). Johann Elichmann, tr., Aurea carmina Pythagore in Simplicii commentarius in enchiridion Epicteti . . . (Leyden, 1640). Thomas Stanley, tr. and comm., Carmina aurea in Poems (London, 1651). Meric Casaubon, Note ad commentarium Hieroclis in aurea carmina in Hieroclis de providentia etfato . . . (London, 1655). John Hall, tr., Hierocles upon the Golden Verses ofPythagoras (London, 1657). [Count] Francesco Berni, Arcana moralia ex Pythagoræ symbolis collecta (Ferrara, 1669). John Norris, tr., Hierocles upon the Golden Verses of the Pythagoreans (London, 1682). Edmund Arwaker, Thoughts Well Employ'd; or, the Duty of Self-Observation. To which are Added Pythagoras's Golden Verses Made Christian (London, 1695).