1 Part of the research for this paper was carried out with the aid of a grant from the American Council of Learned Societies, to which body I extend my thanks. I take this opportunity to thank also Columbia University for generously allowing me the use of their library facilities. To Professor Paul Oskar Kristeller I am indebted for a number of helpful comments and criticisms. Thanks to the generosity of the Folger Shakespeare Library, I was able to see many rare items in Washington, D.C.

2 For medieval natural philosophy as the origin of Galilean science see Pierre Duhem, Etudes sur Léonard de Vinci, série m, ‘Les Précurseurs Parisiens de Galileo’, Paris, 1913, pp. v-vi, for example. Duhem's views have been substantially modified and extended by A. Maier (Die Vorldufer Galileis im l4.Jahrhundert [Rome, 1949]) and by Clagett, Marshall (Science of Mechanics in the Middle Ages [Madison, Wise, 1959])Google Scholar, among others. Cf. Crombie, A. C., Augustine to Galileo, 2d ed., corr. ed. (London, 1964)Google Scholar.

For the view that renaissance humanists obstructed the evolution of science see Duhem, Etudes, in, 123-124,180-181; Dana B. Durand, ‘Tradition and Innovation in Fifteenth- Century Italy: II Primato dell'Italia in the Field of Science’, in Journal of the History of Ideas, IV (1943), 1-20; Thorndike, Lynn, ‘Renaissance or Prenaissance?’, in Journal of the History of Ideas, IV (1943), 65–74 Google Scholar; Harcourt Brown, ‘The Renaissance and Historians of Science’, in Studies in the Renaissance, vn (1960), 27-42; Klein, Robert, ‘Les Humanistes et la Science’, in Bibliothèque d'Humanisme et Renaissance, XXII (1961), 7–16 Google Scholar.

3 For a thorough critique of the Duhem thesis see Edward Rosen, ‘Renaissance Science as seen by Burckhardt and his Successors’, in Helton, Tinsley, ed., The Renaissance: A Reconsideration of the Theories and Interpretations of the Age (Madison, Wise., 1961), pp. 77– 103 Google Scholar. See also Alexandre Koyré, Etudes Galiléennes (reprinted Paris, 1966), especially at p. 16; idem, ‘Les Origines de la Science moderne: Une Interpretation nouvelle’, in his Etudes d'Hisioire de la Pensée Scientifique (Paris, 1966), pp. 48-72. However, Koyré, ‘L'Apport scientifique de la Renaissance’, in his Etudes d'Hisioire, pp. 38-47, states (pp. 38, 41) that the humanists (érudits) had little interest in mathematics and that their contribution to science was perhaps involuntary. See also Stillman Drake, Galileo Studies. Personality, Tradition and Revolution (Ann Arbor, Mich., 1970). Cf. the incisive review article by Schmitt, Charles B., ‘A Fresh Look at Sixteenth-Century Mechanics’, in Studies in History and Philosophy of Science, 1 (1970), 161–175 Google Scholar. For favorable estimates of the influence of humanism on renaissance science see Paul Oskar Kristeller, ‘The Place of Classical Humanism in Renaissance Thought’, in his Studies in Renaissance Thought and Letters (Rome, 1956), pp. 11-15, emphasizing the need for further research; Eugenio Garin, Scienza e Vita Civile net Rinascimento Italiano (Bari, 1965); idem, ‘Gli Umanisti e la Scienza’, in Rivista di Filosofia, ui (1961), 259-278; Carlo Maccagni, ed., Atti del Prima Convegno Internazionale di Ricognizione delle Fonti per la Storia della Scienza Italiana: I Secoli XIV-XVI. Pisa, Domus Galilacana, 14-16 Settembre 11)66 (Florence, 1967), particularly the essays therein by Vasoli, Arrighi, Maccagni, and Garin. Cf. Rose, Paul Lawrence and Drake, Stillman, ‘The Pseudo-Aristotelian Questions of Mechanics in Renaissance Culture’, in Studies in the Renaissance, XVIII (1971), 65–104 CrossRefGoogle Scholar.

4 In a paper read to the Columbia University Renaissance Seminar in March 1971 I tried to define the mathematical renaissance in terms of publishing and editorial programmes. I am presently, preparing a new edition of Baldi's Vite de’ Matematici

5 Koyré, Etudes d'Histoire, p. 41, instances Kepler's use of the Conica of Apollonius (virtually unknown in the Middle Ages) in framing his planetary laws. In his later writings, Duhem tried to incorporate the Archimedean renaissance into his thesis by claiming that the sixteenth-century revival signified merely the grafting of Greek mathematics onto the body of scholastic natural philosophy. Sec P. Duhem, he Système du Monde (Paris, 1913-1960), x, 45.

6 To illustrate the mathematical interests of humanists I shall be citing some medieval, as well as classical, mathematical manuscripts which were to be found in humanist libraries.

7 Vespasiano da Bisticci, Vite di Domini Illustri del Secolo XV, ed. Paolo d'Ancona and Erhard Aeschlimann (Milan, 1951), describes many Quattrocento collections. For modern notes on these libraries see Sabbadini, Remigio, he Scoperte dei Codici hatini e Greci ne Sccoli XIVe XV (reprint, ed. E. Garin, Florence, 1967), 1,183–207 Google Scholar; Kibre, Pearl, ‘The Intellectual Interests reflected in Libraries of the Fourteenth and Fifteenth Centuries’, Journal of the History of Ideas, VII (1946), 257–297 CrossRefGoogle Scholar; Bolgar, R. R., The Classical Heritage and its Beneficiaries from the Carolingian Age to the End of the Renaissance (New York, 1964), pp. 455 Google Scholar ff.; Dorothy M. Robathan, ‘Libraries of the Italian Renaissance’, in James Westfall Thompson, ed., The Medieval hibrary (New York, 1957), pp. 509-588; Eugenio Garin, ha Cultura del Rinascimento. Prqfilo Storico (Bari, 1967), pp. 60-70. A useful bibliographical guide is Giannetto Avanzi, hibri, hibrerie, Biblioteche neli'Umanesimo e nella Rinascenza, 2d ed., 3 dispense (Rome, 1954-1956). Several medieval catalogues are printed in Gustavus Becker, Catalogi Bibliothecarum antiqui (Bonn, 1885). Theodor Gottlieb, Über mittelalterliche Bibliotheken (Leipzig, 1890). For contemporary notes on renaissance libraries see Angelo Rocca, Bibliotheca Apostolica Vaticana (Rome, 1591), pp. 383— 403.

8 Schum, W., Beschreibendes Verzeichnis der Amplonianischen Handschriften-Sammlung zu Erfurt (Berlin, 1887), pp. 798–808 Google Scholar, prints the titles of mathematical manuscripts in the 1412 list.

9 Kristeller, Paul Oskar, ‘Studies in Renaissance Humanism during the Last Twenty Years’, Studies in the Renaissance, IX (1962), 7–30 CrossRefGoogle Scholar, at p. 22.

10 A forthcoming article of mine deals with the place of mathematics in humanist education.

11 See Woodward, William Harrison, Vittorino da Feltre and other Humanist Educators: Essays and Versions (Cambridge, 1897), p. 237 Google Scholar.

12 Petrarch, Opera Quae Extant Omnia (Basle, 1581), pp. 747-749. ‘Quid torquetur astrologus! Quid insudat curiositas vana Matheseos?’ (p. 747). Cf. the letter to Boccaccio, ‘De Astrologorum Nugis’, pp. 765-772. For a similar rejection of natural science as a moral guide, see Opera, p. 1038.

13 Opera, p. 1045; Petrarch, he Traite De Sui Ipsius et Multorum Ignorantia, ed. L. M. Capelli (Paris, 1906), p. 47. For Archimedes’ reputation as a maker of astronomical instruments see Cicero, De Republica, 1, xIV, 21-22.

14 Petrarch, Rerum Memorandamm Libri, ed. Giuseppe Billanovich (Florence, 1943), pp. 22-24. De Viris Illustribus, ed. Guido Martellotti (Florence, 1964), I, 122-123 15 Opera, p. 913. In his will Petrarch praises the planetarium made by de’ Dondi. See Giovanni de’ Dondi, Tractatus Astrarii (Biblioteca Capilolare di Padova, Cod. D. 39), ed. A. Barzon, E. Morpurgo, A. Petrucci, G. Francescato (Vatican, 1960), pp. 14, 24-25; Silvio A. Bedini and Francis R. Maddison, Mechanical Universe: The Astrarium of Giovanni de' Dondi, Transactions of the American Philosophical Society, n.s., 56 (Philadelphia, 1966), p. 50. Petrarch owned at least one Latin geometrical manuscript, for Salutati in 1392 referred to the poet's ‘Varronis de Mensuris orbis in quo sunt quedam geometrice figure’.

15 See Ullman, B. L., ‘Geometry in the Mediaeval Quadrivium’, in Studi di Biblioorafia e di Storia in Onore di Tammaro de Marinis (Verona, 1964)Google Scholar, IV, 263-285, at pp. 283-284. (Boccaccio may have owned a copy of Euclid [idem., p. 285], as well as a text of Fibonacci [below, n. 48].)

16 Cino Rinuccini, Invettiva contro a cierti Calumniatori di Dante e di Messer Francesco Peirarca, in Giovanni da Prato, II Paradiso degli Alberti, ed. Alessandro Wesselofsky (Bologna, 1867), 1, II, 303-316, at pp. 308-309. Cf. an anonymous Commento sopra Dante dove tratta delle Mathemalice, written in an early sixteenth-century humanist hand, Marciana MS leal. X, 94 (6403).

17 Ullman, B. L., The Humanism of Coluccio Salutati (Padua, 1963), pp. 68–69 Google Scholar, cites the De Laboribus on mathematics.The Tractatus to Dominici (1405-1406) is printed in Coluccio Salutati, Epistolario, ed. Francesco Novati, Fonti per la Storia d'ltalia pubblicati dall'Istituto Storico Italiano, Epistolari, nos. ij-18 (Rome, 1891-1911), IV, 226 ff. For astrology, see ibid., IV, 229-230. For the letter to Petrarch, see ibid., I, 74-75. Cf. Ullman, Salulali, pp. 89-90. On Salutati's mathematical manuscripts see Ullman, Salutali, pp. 170, 174, 186, 239. See also below, n. 26. Cf. Garin, Scienza, pp. xiii-xiv. For doubts that Parisian mechanics were as influential in Italy as Duhem claimed, see Eugenio Garin, La Cultura Filosqfica del Rinascimento Ilaliano (Florence, 1961), pp. 388-401.

18 Bruni, Leonardo, Humanistisch-Philosophische Schriflen, ed. Hans Baron (Leipzig- Berlin, 1928), p. 11 Google Scholar. Translation in Woodward, Vittorino, p. 126.

19 Text in Zippel, G., Niccold Niccoli (Florence, 1890), pp. 84–85 Google Scholar. Sec below, n. 97.

20 For the place of mathematics in Pico's philosophy, see Garin, Eugenio, Giovanni Pico della Mirandola. Vita e Dottrina (Florence, 1937), pp. 69–70 Google Scholar, 221; Paul Oskar Kristeller, ‘Giovanni Pico della Mirandola and his Sources’,in L'Opera e il Pensiero di Giovanni Pico della Mirandola nella Sloria deU'lImanesimo (Florence, 1965), I, 35-142, especially pp. 81- 83. The remarks on Euclid, theology, and mathematics are in Pico, Conclusiones Nongenlae, in his Opera (Basle, 1557), pp. 100-101. While denouncing astrology and defending astronomy Pico, Dispulaliones adversus Astrologiam Divinairicem, ed. Eugenio Garin (Florence, 1946), 1, 60, praises Toscanelli. Related passages are cited in Eugenio Garin, Ritratti di Umanisti (Florence, 1967), pp. 45- 46, n. For Pico's mathematical manuscripts see Kibre, Pearl, The Library of Pico della Mirandola (New York, 1936), nos. 489 Google Scholar (Proclus), 600 (Mechanica), 165, 226, 245, 652, 940, 941, 985,1064 (Euclid). Some of the Euclid items are Latin manuscripts or copies of printed editions, e.g., of Venice, 1482. The manuscript ‘Paulus Florentinus, De Geometria’ (no. 1012) is perhaps by Paolo Dagomar dell'Abbaco, rather than by Toscanelli.

21 Ficino, Marsilio, Opera Omnia (Basle, 1576), 1, 944 Google Scholar. For Ficino's view of Toscanelli, see Paul Oskar Kristeller, Supplementum Ficinianum (Florence, 1937), n, 66, 321.

22 For abundant information on this revival see Sabbadini, Scoperle. Cf. Garin, Cttllura (1967), pp. 19-33, f°r a suIVey. See also Giuseppe Cammelli, I dotti Bizantini e le Origini dell'Umanesimo (Florence, 1941-1954).

23 Vespasiano, Vite, p. 388. Cf. Bolgar, Classical Heritage, pp. 268-272, 403. (A new edition of Vespasiano is being published by the Istituto Nazionale del Rinascimento: Le Vite, ed. Aulo Greco, 1 [Florence, 1970-.] I have not seen the unpublished Ph.D. thesis of C. de la Mare, ‘Vespasiano da Bisticci, Historian and Bookseller’ [London, 1965].

24 Poggio seems not to have pursued mathematical manuscripts although he did own a book, ‘Astronomicon cum multis aliis in papiro copertum corio albo’, and took also an interest in geography. See Walser, Ernst, Poggius Florentinus, Leben und Werke (Berlin, 1914), pp. 421 Google Scholar and 241 respectively. I have not seen Sensburg, W., Poggio Bracciolini und Niccoli de Conti in Hirer Bedeutung für die Ceographie des Renaissancezeitalters (Vienna, 1906)Google Scholar. For humanism and geography see Siegmund Giinther, ‘Der Humanismus in seinem Einflusse auf die Entwicklung der Erdkunde’, in Ceographische Zeitschrift; VI (1900), 65-89. \

25 Salutati, Epistolario, III, 258. Cf. Ullman, Salutati, p. 227.

26 Ullman, Salutati, pp. 170, 174, 186, 248-249. The Almagest is in the Greco-Latin version made at Sicily, circa 1160. The Canones Ptolemei is now in the Biblioteca Naziohale Centrale, Florence (B.N.C.F.), Conv. Soppr. MS J. rx. 39; the Perspediva is MS J. V. 25. See above, n. 17. For astronomical references, see Salutati, Epistolario, 1, 280; n, 348; IV, i,.l2, 86, 226.

27 Salutati, Epistolario, III, 624-627.

28 Ibid., III, 129-132.

29 Ullman, Salutati, pp. 127-129.

30 Rudolf Blum, La Biblioteca della Badia Fiorenlina e i Codici di Antonio Corbinelli, Studi e Testi, 155 (Vatican, 1951), pp. 135-136. The codices are now in the Biblioteca Nazionale, Florence, Conv. Soppr . A. v. 2587; c. VH. 2820; A. V. 2654.

31 Boncompagni, Baldassare, Notizie intorno ad alcune Opere di Leonardo Pisano, Matematico del Secolo decimoterzo (Rome, 1854)Google Scholar, pp. 217-219. The Fibonacci codices are now in B.N.C.F. MSS Conv. Soppr. c. 1. 2626; Magi, xi, 117. The Greek Euclid is now in the Laurenziana, MS Conv. Soppr. 30. See Blum, Corbinelli, pp. 105, 118.

32 Fiocco, Giuseppe, ‘La Biblioteca di Palla Strozzi’, in Studi di Bibliografia e di Sloria in Onore di Tammaro de Marinis (Verona, 1964)Google Scholar, n, 289-310, especially 309-310. This supersedes V. Fanelli, ‘I Libri di Messer Palla Strozzi (1372-1462)’, in Convivium (Turin, 1949), PP- 57-73- For the manuscripts which later came via S. Giustina di Padova to the Bibliothèque Nationale, Paris, see the list by L. Ferrai in Giuseppe Mazzatinti, Inventario dei Manoscritti Italiani delle Biblioteche di Francia (Rome, 1886-1888), n, 549-661.

33 Diller, Aubrey, ‘The Greek Codices of Palla Strozzi and Guarino Veronese’, in Journal of the Warburg and Courtauld Institutes, XXIV (1961), 313–321 CrossRefGoogle Scholar, at pp. 316-317. In his will (printed by Fiocco, ‘Palla’, p. 292) Palla made special provision for this codex as a family heirloom. Vespasiano, Vile, p. 388, gives the impression that Palla had himself ordered it from Constantinople, but see Diller. Cf. G. Mercati, ‘Excursus’, in Claudi Ptolemaei Geographiae Codex Urbinas Graecus 82, ed. Joseph Fischer (Leiden-Leipzig, 1932), Tomus Prodromus, p. 192. Cf. Stevenson, Edward Luther, tr. and ed., The Geography of Claudius Ptolemy (New York, 1932)Google Scholar.

34 Bruni, Schriften, p. 105. Also in Zippel, Niccoli, p. 92.

35 Guarino Guarini, Epistolario, ed. R. Sabbadini, R. Deputazione di Storia Patria per le Venezie: Monumenti Storici, ser. 4, ‘Miscellanea’, ser. 3, vols. 8,11,14 (Venice, 1915- 1919), 1, 106; also pp. 25, 164.

36 Weiss, Roberto, ‘Jacopo Angeli da Scarperia (c. 1360-1410)’, in Medioevo e Rinascitnento: Studi in Onore di Bruno Nardi (Florence, 1955), II, 801–827 Google Scholar, especially pp. 811-812, 824. Many of the manuscript copies of the translation bear a dedication to Gregory XII. For Pal. Gr. 388 (Pico's text of the Geographia edited in 153 3 by Erasmus), see A. De Smet, ‘Erasme et la Cartographie’, in Coppens, J., ed., Scrinium Erasmianum: Melanges historiques (Leiden, 1969), 1, 277–291 Google Scholar.

37 Giovanni Aurispa, Carleggio, ed. R. Sabbadini (Rome, 1931), pp. 12-13. Traversari, Ambrogio, Epistolae et Orationes, ed. Mehus, L. (Florence, 1759)Google Scholar, n, col. 1028.

38 J. L. Heiberg, ed., Archimedes. Opera Omnia, 2nd ed. (Leipzig, 1910-1915), HI, Ixxxii. The inventory of Aurispa's books, made after his death, numbers some 137 manuscripts, but there is no sign of an Archimedes or a Pappus. See Sabbadini, Remigio, Biografia documentata di Giovanni Aurispa (Noto, 1891), pp. 156–157 Google Scholar.

39 The Pappus is first mentioned in the list of 1533, according to Robert Devreesse, La Fonds Grec de la Bibliothique Vatkane des Origines à Paul V, Studi e Testi, 244 (Vatican, 1965). P- 309.

40 Traversari, Epistolae, u, cols. 1010-1011. Cf. Paul Lawrence Rose, ‘Renaissance Italian Methods of Drawing the Ellipse and Related Cuivs’, in Physis, xn (1970), 371- 404, at pp. 371-372. Fragments suIVive of a medieval translation of ApoUonius, possibly by Gerard of Cremona.

41 Calderini, Aristide, ‘Ricerche intorno alia Biblioteca e alia Cultura Greca di Francesco Filelfo’, in Studi Italiani di Filologia Classica, xx (1913), 204–404 Google Scholar, at pp. 257, 260- 261, 344, and 385-387. A new life of Filelfo is needed. The best treatment remains Carlo de’ Rosmini, Vita di Francesco Filelfo, 3 vols. (Milan, 1808).

42 Rose and Drake, ‘Questions of Mechanics’, pp. 74-75.

43 Ibid., p. 75. In the 1420s Filelfo had left some of his books with his Venetian friends Marco Lippomano, Francesco Barbaro, and Leonardo Giustinian. See Francesco Filelfo, Epistolarum Fatniliarium Libri XXXVII (Venice, 1502), f. 1, and f. 9.

44 Filelfo, Epistolae, fs. 26^v, 26, 29. See below, p. 84.

45 Ibid., fs. 91V-92. See below, n. 133.

46 Ibid., f. 82. ‘Leonardus Theologus, idemque mathematicus duo non tamen eloqucnter, quam subtiliter, opera in mathematicis elucubravit, annis superioribus, alterum in geometria, quod artis metricae nomine appellavit… alterum in Arithmetica….’ For the Franciscan Fra Leonardo de’ Antonii Cremonese (d. after 1438), see Antonio Favaro, ‘Nuove Ricerche sul Matematico Leonardo Cremonese’, in Bibliotheca Mathemalica, ser. in, v (1904), 326-341. (Filelfo's description of Leonardo as ‘Theologus’ confirms Favaro’s identification.) This Leonardo should not be confused with Leonardo Mainardi of Cremona, nor with Leonardo Fibonacci of Pisa. Fra Leonardo's Artis Metrice Pratice Compilatio has been published (under Mainardi's name) by Maximilian Curtze, ‘Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance. 11. Die Practica Geometriae des Leonardo Mainardi aus Cremona’, in Abhandlungen zur Geschichte der mathematischen Wissenschaften, xm (1902), 337-434. Among Fra Leonardo's manuscripts are some notes on Campanus, in Laurenziana, MS San Marco 212.

47 Boncompagni, Alcune Opere di Leonardo Pisano, pp. 161 (Ser Filippo), 187-195 (Santo Spirito and Santa Maria Novella), 209-237 (Badia). The two from the Badia are now in B.N.C.F. MSS Conv. Soppr. c. 1. 2616 (ex-Corbinelli 73) and Magi, xi, 117 (ex- Corbinelli 74).

48 Boccaccio, Genealogie Deorum Gentilium Libri, ed. Vincenzo Romano, new ed., Scrittori d'ltalia, 200-201 (Bari, 1951), n, 762. For a Euclid and a Witelo at Santo Spirito possibly owned formerly by Boccaccio see above, n. 15. Also A. Mazza, ‘L'Inventorio della PaIVa Libraria di Santo Spirito e la Biblioteca del Boccaccio’, in Italia Medioevale e Umanistica, rx (1966), 1-75, esp. pp. 24-25, 61. Cf. O. Hecker, ‘Die Schicksale der Bibliothek Boccaccios’, in Zeitschrift fur Biicherfreunde, 1 (1897), 33-41. For testimonies of Paolo by Matteo Palmieri and others see Boncompagni, Alcune Opere Leonardo Pisano, pp. 276-399, passim. See Boffito, G., Paolo dell'Abbaco e Fabrizio Mordente, II Facsimile, 6 (Florence, 1931)Google Scholar.

49 References are in de’ Rosmini, Filelfo, III, 75-76.

50 Filelfo, Convivia Mediolanensia (? Milan, ? 1478), sig. g 6v. A manuscript version is in the Biblioteca Trivulziana, Milan. See Aristide Calderini, ‘I Codici Milanesi delle Opere di Francesco Filelfo’, in Archivio Storico Lombardo, xm (1915), 335-411, at p. 354

51 Vespasiano, Vile, pp. 355-356. Traversari, Epistolae, n, col. 381. See Gustavo Uzielli, La Vila e i Tempi di Paolo dal Pozzo Toscanelli (Rome, 1894). Cf. the short reassessments by Eugenio Garin, ‘Ritratto di Paolo dal Pozzo Toscanelli’, in his Ritratti, pp. 41-67; de Santillana, Giorgio, ‘Paolo Toscanelli and His Friends’, in his Reflections on Men and Ideas (Cambridge, Mass., 1968), pp. 33–47 Google Scholar. For a Renaissance biography see Gustavo Uzielli, ‘Ricerche intorno Paolo dal Pozzo Toscanelli: Della Biografia di Paolo dal Pozzo Toscanelli, scritto inedito di Bartolomeo [.sic] Baldi’, in Bolletlino della Society Ceografica Italiana, ser. n, ix (1884), 129-133.‘

52 Pico, Dispulationes adversus Aslrologiam, ed. Garin, 1,60. Garin, ‘Toscanelli’, pp. 45-46, notes. A treatise by ‘Paulus Florentinus’, De Geometria, is listed in Pico's library, but may well be the work of Paolo Dagomari dell'Abbaco instead. Kibre, Library of Pico, p. 100. Landino was acquainted with Toscanelli, as appears from Landino, Cristoforo, Comento sopra la Comedia di Danthe Alighieri (Florence, 1487)Google Scholar, sig. & iiiv. For Ficino's opinion of Toscanelli, see above, n. 21.

53 Regiomontanus, Printing Programme (Nuremberg, 1474 [copy in British Museum]).

54 In addition to those of Paolo's writings noted by Uzielli, Toscanelli, there is a treatise Della Prospettiva, in Biblioteca Riccardiana, Florence, Ms 2118, previously assigned to Alberti but now attributed to Toscanelli by Alessandro Parronchi, Studi su la ‘Dolce’ Prospettiva (Milan, 1964), p. 585. Conceivably, too, there might be added the De Geometria mentioned in n. 52 above. 55 Giorgio Vasari, Le Opere, ed. G. Milanesi (Florence, 1878-1885), n, 333. Cf. Antonio di Tuccio Manetti, The Life of Brunelleschi, ed. and tr. Howard Saalman and Catherine Enggass (University Park, Pa., 1970), p. 55. Uzielli, Toscanelli, pp. 37-40.

56 Renaissance lives of Brunelleschi are in Manetti, Brunelleschi (1485) and Vasari, Opere, n, 327-394. See Leonardo S. Olschki, Ceschichle der neusprachlichett wissenschaftlichen Literatur, reprint (Vaduz, 1965), I, 39-44. Frank D. Prager and Scaglia, Gustina, Brunelleschi: Studies of His Technology and Inventions (Cambridge, Mass., 1970 Google Scholar), give an excellent account of Brunelleschi's mechanical technology.

57 A forthcoming paper of mine deals with this problem.

58 For inconclusive but informative discussions see P. Sanpaolesi, ‘Ipotesi sulle Conoscenze mathematichc, statiche e meccaniche del Brunelleschi’, in Belle Arti (1951), pp. 25-54.

59 E. H. Gombrich, ‘From the Revival of Letters to the Reform of the Arts: Niccolò Niccoli and Filippo Brunelleschi’, in Essays in the History of Art Presented to Rudolf Wittkower, ed. Fraser, D. et al. (London, 1967)Google Scholar, pp. 71-82. Uzielli, Toscanelli, passim. Vespasiano, Vile, p. 441. Renaissance architects often point out that their art required the most eclectic education.

60 Lorenzo Ghiberti, J Commentari, ed. Ottavio Morisani (Naples, 1947).

61 Gombrich, E. H., ‘The Renaissance Conception of Artistic Progress and its Consequences’, in his Norm and Form (London, 1966), pp. 1–10 Google Scholar, especially p. 5. Cf. John White, The Rebirth of Pictorial Space, 2d ed. (London, 1967), pp. 126-130.

The letters from Aurispa to Traversari regarding Ghiberti's desire to have the Athenaeus are in Aurispa, Carteggio, ed. Sabbadini, pp. 67, 69, 70. The deal seems to have fallen through, for later in the same year Aurispa was thinking of exchanging the manuscript for Niccoli's Sallust (Aurispa, Carteggio, p. 72); and a letter of 1444 to King Alfonso of Naples refers to the translation of texts from a volume which included Athenaeus (Aurispa, Carteggio, pp. 109, 168). Vat. Gr. 1164—the Aurispa Athenaeus—was later owned by Angelo Colocci.

62 Euclid is cited in the Commentari, at pp. 50, 107, 159. Cf. White, Rebirth, pp. 121, 134; G. Federici Vescovini, ‘Contributo per la Storia della Fortuna di Alhazen in Italia: il Volgarizzamento del MS Vat. Lat. 4595 e il Commentario Terzo del Ghiberti’, in Rinascimento, ser. n, v (1965), 17-49.

63 Ghiberti, Commentari, pp. 3-4, 49.

64 Giuseppe Saitta, Nicolo Cusano e l'Umanesimo Italiano (Bologna, 1957), pp. 145-174, gives an account of Cusanus in Italy. For many recent references see Paul Oskar Kristeller, ‘A Latin Translation of Gemistus Plethon's De Fato by Johannes Sophianos Dedicated to Nicholas of Cusa’, in Nicolo Cusano agli Inizi del Mondo Moderno (Florence, 1970), pp. 175-193. Cf. Garin, ‘Toscanelli’, pp. 57-59. Uzielli, Toscanelli, p. 265.

65 Dates according to Joseph E. Hofmann, introduction to Nikolaus von Kues, Die mathematischen Schrifien, Heidelberg Übersetzung, 11 (Hamburg, 1952), pp. xlvi-xlix. The relevant texts are to be found translated therein. Cf. Uzielli, Toscanelli, pp. 265 rf., 279 ff. Garin, ‘Toscanelli’, pp. 57-59.

66 Letter of 1471 to Christian Roder of Erfurt, printed in Regiomontanus, ‘Der Briefwechsel Regiomontans mit Giovanni Bianchini, Jacob von Speier und Christian Roder’, in M. Curtze, ed., Abhandlungen zur Ceschichle der mathematischen Wissenschaften, xii (1902), 185-336, at p. 329.

67 Regiomontanus, De Triangulis (Nuremberg, 1533), ‘Quadrature’, f. 56. Uzielli, Toscanelli, p. 268. E. Zinner, Leben und Wirken desJohannes Müller von Königsberggenannt Regiomontanus, 2d ed. (Osnabrück, 1968), pp. 121-124, 321.

68 Uzielli, Toscanelli, pp. 200-207. Joan Gadol, Leon Battista Alberti, Universal Man of the Early Renaissance (Chicago, 1969), pp. 27, 195-197. Garin, ‘Toscanelli’, p. 46 n.

69 In 1439 Alberti dedicated his Intercoenales to Toscanelli.

70 Regiomontanus, ‘Briefwechsel’, p. 264, letter of February 1464 (exact date uncertain) to Bianchini.

71 Ficino, Opera (1576), n, ii, f. 1464, commentary on the Timaeus, cap. 41.

72 Printed in Angelo Fabroni, Laurentii Medicis Vita (Pisa, 1784), n, 281-282.

73 For Albcrti's mathematics and mechanics, see Gadol, Alberti; Uzielli, Toscanelli, pp. 204-205. A manuscript treatise on machines, Laurenziana MS Ashburnham 361, has been attributed to Alberti by Girolamo Mancini, Giorgio Vasari: Vite Cinque annotate (Florence, 1917). It is, in fact, the work of Francesco di Giorgio Martini. The crown problem appears in Ludi Matematici, printed in A. Bonucci, ed., Leon Battista Alberti, Opere Volgari (Florence, 1843-1849), IV, 438-439.

Alberti's manuscript of Euclid is extant, Marciana MS Lat. vm, 39 (3271). See J. Valentinelli, Bibliotheca Manuscripta ad S. Marci Venetiarum (Venice, 1868-1873), IV, 217; J. Morelli, Codices Manuscripti Latini Bibliothecae Nanianae (Venice, 1776), pp. 30-31.

74 Leon Battista Alberti, L'Arcliitcttura: De Re Aedificatoria, ed. G. Orlandi and P. Portoghesi (Milan, 1966), n, 767.

75 Uzielli, Toscanelli, pp. 242-243, 284. Although there is no definite proof that Alberti and Cusanus knew each other, their mutual friendship with Toscanelli, their common ideas, and their proximity on several occasions suggest that they were personally acquainted. See Gadol, Alberti, pp. 196-197.

There is little direct evidence of the acquaintance of Toscanelli and Bessarion, but Regiomontanus was a mutual friend when they were all at Rome in 1461. Moreover, Bessarion owned a map which was probably the joint work of Regiomontanus and Toscanelli. See Uzielli, Toscanelli, p. 529.

76 For Regiomontanus’ copy see Zinner, Regiomontanus (1968), pp. 91, 322-323.

77 Heiberg, Archimedes, III, pp. lxx-bcxii. Unfortunately I have not seen a list of sixteen Greek manuscripts supposed to have been owned by Toscanelli at his death. Uzielli, Toscanelli, pp. 543, 6$6, refers to his projected publication of this list and associated documents, but apparently nothing came of his intention.

78 Accounts of this episode appear in Heiberg, Archimedes, ra, pp. lxxx-lxxxiii, and in Sabbadini's notes to Aurispa, Carteggio, pp. 161-162. Sabbadini prints relevant excerpts from the Traversari-Niccoli correspondence on the affair. See also Lockwood, D. P., ‘De Rinucio Amino Graecarum Litterarum Interprete’, in HaIVard Srudies in Classical Philology, XXIV (1913), 51–109 CrossRefGoogle Scholar; Ambrogio Dini-Traversari, Ambrogio Traversari e 1 51(01 Tempi (Borgo S. Lorenzo, n.d.), pp. 104-105.

79 Letters of 18 and 27 December 1423 from Traversari to Niccoli, in Traversari, Epistolae, 11, cols. 361 and 365 respectively.

80 Traversari, Epistolae, n, cols. 376 and 370 (sic), letters to Niccoli of 26 February and 25 May 1424, the first mentioning Parentucelli, the second Barbaro.

81 Traversari, Epistolae, n, col. 386, letter to Niccoli, 26 July 1424.

82 Traversari, Epistolae, n, col. 388, letter to Niccoli, 29 August 1424.

83 Aurispa, Carteggio, p. 13, letter to Traversari, 27 August 1424.

84 Angelo Decembrio, Politia Litteraria, 2d ed. (Basle, 1562), p. 44. (First edition, 1540.) Affirmed also by Conrad Gesner, Bibliotheca Universalis (Zurich, 1545), f. 386V. For details on Decembrio see Anita della Guardia, La Politia Letteraria di Angelo Decembrio e l’ Umanesimo a Ferrara nella prima metà del secolo XV (Modena, 1910). In the late sixteenth century, Baldi too reports that Aurispa had translated Archimedes.

85 Aurispa, Carteggio, p. 109, letter of July 1444. Cf. Sabbadini's notes at p. 168.

86 Sabbadini, note to Aurispa, Carteggio, p. 162.

87 Heiberg, Archimedes, in, p. lxxxii, n. 2.

88 Ibid., p. lxxxiii.

89 Traversari, Epistolae, n, col. 386, says that Rinuccio ‘Archimcdem se habere de instrumentis bellicis et aquaticis cum pictura confessus est’.

90 Traversari, Epistolae, n, col. 365, letter to Niccoli, 27 December 1423. Heiberg's claim (Archimedes, va, p. lxxxiii) that Ser Filippo had seen with his own eyes the Archimedes manuscript rests on a mistranslation of the following passage: ‘Philippus noster ante plures dies profectus ad me, adseruit, esse exploratissimum Archimedem ilium Bononiae apud Ranutium seIVari; didicisse se id ab eo, qui volumen ipsum viderat’ (my italics).

91 Fabroni, Lauremii Vita, u, 285.

92 Heiberg, Archimedes, III, p. xii.

93 For San Marco see now B. L. Ullman and Philip A. Stadter, The Public Library of Florence: Niccolò Niccoli, Cosimo de’ Medici and the Library of San Marco (Padua, 1972).

94 Vespasiano, Vite, pp. 434-444. Zippel, Niccoli.

95 Vespasiano, Vite, pp. 423-436, 441.

96 Gombrich, ‘Revival of Letters’, p. 78. However, there is scarcely a mathematical title in the list of codices desiderali given by Niccoli circa 1431 to Cardinals Cesarini and Albergati prior to departing from Italy (copy now in the Pierpont Morgan Library, MS Morgan 497, f. 2 59v-27i; published by Robinson, Rodney, ‘The Inventory of Niccol6 Niccoló ’, Classical Philology, xvi [1921], 251–255)CrossRefGoogle Scholar. See now N. Rubenstein, ‘An Unknown Letter by Jacopo di Poggio Bracciolini on Discoveries of Classical Texts’, in Italia Medioeuale e Umanistica, 1 (1958), 383-400; T. FofFano, ‘Niccoli, Cosimo e le Ricerche di Poggio nelle Biblioteche Francesi’, ibid., XII (1969), 113-128.

97 Leonardo Bruni, Oratio in Nebulonem Maledicum, in Zippel, Niccoli, p. 84. Guarino, Epistolario, 1, 37.

98 Although Ullman and Stadter, San Marco, p. 88, identify only one astronomical work belonging to Niccoli (B.N.C.F. MS Conv. Soppr. j . v. 4), three others are extant (B.N.C.F. MSS Conv. Soppr. j . IX. 39; j . x. 20; and Laurenziana MS San Marco 190). These are all medieval compilations. For Hero's Pneumatica see Ullman and Stadter, San Marco, p. 84; and for a Greek text of the Geographia of Ptolemy, see ibid., p. 74.

99 A partial reconstruction of Niccoli's library, with many present identifications, is given by Ullman and Stadter, San Marco, chap. 2. Cf. Vespasiano, Vite, pp. 411-412; Zippel, Niccoli, pp. 66-70.

100 Vespasiano, Vile, pp. 444-454, at p. 445. The books were sold by Ser Filippo's heirs to Cosimo de’ Medici who presented them to San Marco. Ullman and Stadter, San Marco, p. 26.

101 A. A. Bjornbo, ‘Die mathematischen San Marco Handschriften in Florenz’, in Bibliotheca Mathematica, ser. m, IV (1903), 238-245; vi (1905), 230-238; xn (1911-1912), 97-132,193-224. Ullman and Stadter, San Marco, pp. 26-27, 213, list the fourteen manuscripts catalogued by Bjornbo, and add a fifteenth of which only the flyleaf can be identified (no. 770 in the list compiled around 1500, now in Modena; printed by Ullman and Stadter, San Marco). For the mathematical manuscripts lost or outside the Biblioteca Nazionale and Laurenziana see Ullman and Stadter, San Marco, pp. 208 ff.

102 The San Marco catalogue of 1500 lists two Greek texts of the Mechanica (Ullman and Stadter, San Marco, pp. 255, 321); one of Hero (p. 256); and codices of Theon and Euclid (p. 257). These may well now be in the Laurenziana although no identification has been made.

103 Luca Pacioli, Summa (Venice, 1494), 1, f. 79. For the identification see Boncompagni, Baldassare, ‘Intorno ad un Manoscritto de WOtlica di Vitellione citato da fra Luca Pacioli’, in Bulkltino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche, IV (1871), 78–81 Google Scholar, at p. 79; listed but not identified in Ullman and Stadter, San Marco, p. 215. In 1451 another manuscript of Witelo was said to be at Santo Spirito in Florence, according to A. Goldmann, ‘Drei italienische Handschriftenkataloge s. XII-XV’, in Zentralblatt für Bibliothekswesen, iv (1887), 137-155, at p. 147. Witelo was first printed in 1535 at Nuremberg.

104 Leoniceno, letter to Valla, in J. L. Heiberg, Bciiräge zur Geschichte Georg Valla's unci seiner Bibliothek, Zentralblatt für Bibliothekswesen, Beiheft 16 (Leipzig, 1896), p. 71. Ceivini's letters of 1533 to Angelo Colocci are cited in Pierre de Nolhac, La Bibliolhèque de Fulvio Orsini, Bibliothèque de l'Ecole des Hautes Etudes, 74 (Paris, 1887), p. 182. The San Marco catalogue of 1500 lists a Practica Geometriae of Fibonacci (Ullman and Stadter, San Marco, p. 215).

105 Ser Filippo is known to have had a book by, or derived from, Fibonacci; see Boncompagni, Alcune Opere di Leonardo Pisano, p. 161.

106 Vespasiano, Vite, pp. 413-415. The canon was also used, according to Vespasiano, pp. 27-28, for the San Marco library. The document is printed in Enea Piccolomini, 'Delle Condizioni e delle Vicende della Libreria Medicea Privata dal 1494 al 1508’, in Archivio Storico Italiano, ser. m, xrx (1874), 101-129,254-281; x x (1875), 51-94; xxi (1876), 102-112, 282-296, at 102-106. Also in Sforza, loc. cit. below in n. 130, pp. 385-392. For further comments see below, section on Rome. I have not seen F. Pintor, ‘La Libreria di Cosimo de’ Medici nel 1418’, in Nozze Delia Torre Guidoiti (Florence, 1902).

107 For the inventories and history of the Medicea Privata, see Piccolomini, ‘Medicea’; Fortunato Pintor, ‘Per la Scoria della Libreria Medicea nel Rinascimento: Appunti d' Archivio’, in Italia Medioevale e Umanislica, in (1960), 189-210. By the death of Lorenzo there were about 1000 codices.

108 Inventory printed in Piccolomini, ‘Medicea’, xx, 51-94.

109 For a selection of Privata manuscripts, with their present Laurenziana identifications, see Mostra della Biblioteca di Lorenzo nella Biblioteca Medicea-Laurenziana (Florence, 1949).

110 ‘Horonis [sic] Pneumatica et quaedam alia in 4. to folio’, listed in Piccolomini, ‘Medicea’, XIX, 279 (cf. ibid., pp. 128-129).

111 For Lorenzo's patronage of books and Poliziano see Fabroni, Laurentii Vita, 1,151- 157; 11, 284-288; Leoniceno's undated letter to Poliziano in Poliziano, Omnia Opera (Venice, 1498), sigs. b.viii v-c.i v; Janus Lascaris, Anthologia Craeca (Florence, 1494), dedication.

112 Börje Knös, Un Ambassadeur de V Hellénisme: Janus Lascaris et la Tradition Greco- Byzantine dans rHumanisme François (Upsala-Paris, 1945), p. 57 and passim.

113 K. K. Müller, ‘Neuc Mittheilungen iiber Janus Lascaris und die Mediceiische Bibliothek’, in Zentralblatl für Bibliothekswesen, 1 (1884), 333-412, at pp. 382-385. See below, section on Venice.

114 Müller, ‘Lascaris’, p. 383 (Hero), pp. 383-384 (Archimedes). Lascaris himself owned a Greek text of the Pneumatica of Hero, and an Almagest. See Pierre de Nolhac, ‘Inventaire des Manuscrits grecs de Jean Lascaris’, in Mélanges a” Archéologie de d'Histoire, VI (1886) 251-274, at pp. 259 and 256 respectively. I have not been able to ascertain whether these are presently among the Lascaris-Ridolfi manuscripts in the Bibliothèque Nationale at Paris. Cf. R. Ridolfi, ‘La Biblioteca del Cardinale Niccold Ridolfi (1501- 1550)’, in La Bibliofilia, XXXI (1929), 173-193.

115 Printed in Fabroni, Laurentii Vita, n, 284-286, at p. 285. The original letter is in Archivio di Stato, Florence, M.A.P., Filza 43 (42). See Heiberg, Archimedes, in, xii. ‘Pappa Janni’ is John Rhosos, but the hand of the Laurenziana copy (XXVIII, 4) is that of John Scutariota, to whom the copying was probably delegated. For manuscripts associated with Poliziano see Mostra del Poliziano nella Biblioteca Medicea-Laurenziana (Florence, 1954). Most of Poliziano's manuscripts are listed in Piccolomini, ‘Medicea’, xx, 92. Cf. A. Campana, ‘Contributi alia Biblioteca del Poliziano’, in // Poliziano ed il suo Tempo (AttidellVConvegnoInternazionalediStudisulRinascimento) (Florence, 1957),pp. 173-229.

116 Heiberg, Archimedes, III, p. xii. Misdated by A. M. Bandini, Catalogus Codicum Latinorum Bibliothecae Mediceae Laurentianae (Florence, 1774-1778), n, 14, to the thirteenth century.

117 J. L. Heiberg, ‘Praefatio’, in Wilhelm Schmidt, ed., Heronis Alexandrini Opera quae Supersunt Omnia (Leipzig, 1899-1914), v, v. Poliziano specifically requested a copy of the De Mensuris; see the letters in Heiberg, Valla's Bibliothek, pp. 71-72.

118 Schmidt, Heronis Opera, Supplementum to vol. 1, p. 19.

119 Piccolomini, ‘Medicea’, XXI, 286, register of loans. For Theon see Mostra Poliziano, pp. 59-60. A. Rome, ‘Un Manuscrit de la Bibliothèque de Boniface VIII à la Médicéenne de Florence’, L’ Antiquiti Classique, vn (1938), 261-270.

120 Poliziano, Opusculum, quod Panepistemon Inscribilur (Florence, 1496), sig. a iv: ‘… ut Heron Pappusque declarant [on mechanics]… docet in Pneumaticis Heron … idem in Automatis… in Ochumenis Archimedis Est in eadem mechanicae serie; quae centrobarica … dicitur … et Sphaeropoeia … ’. For Poliziano's encyclopaedism see Ida Maier, ‘Un Inedit de Politien: La Classification des Arts’, in Bibliothèque d’ Humanisme et Renaissance, XXII (1960), 338-355 (from Riccardiana MS 2723, fs. 73V-74).

121 Correspondence in Heiberg, Valla's Bibliothek, pp. 71-72.

122 Poliziano, letter of 8 August 1484 to Francesco della Casa, in Opera (1498), sig. f. i. iv. Cf. Carlo Maccagni, ‘The Florentine Clock and Instrument Makers of the Delia Volpaia Family,’ in Acles du Xlle Congrès International a“Histoire des Sciences, Paris, 1968, (Paris, 1968-1971), x A, 65-73.

123 Fabroni, Laurentii Vita, a, 281-282.

124 Pacioli, Summa, u, f. 74V. The book was compiled by an unnamed ultramontane bishop. Could the bishop have been Cusanus, and the book Vaticana MS Ottoboni Lat. 1870? See below. Pier Leone's manuscript of Manilius was seen at Padua by Poliziano (letter of 20 June 1491 to Lorenzo).

125 José Ruysschaert, ‘Nouvelles Recherches au sujet de la Bibliothèque de Pier Leoni, medicin de Laurent la Magnifique’, in Académie Royale de Belgique, Bulletin de la Classe des Lettres, set. v, XLVI (1960), 37-65, at pp. 50-51. For the De Mensura Circuli see Marshall Clagett, Archimedes in the Middle Ages (Madison, Wise), 1964,1, 92-93.

126 Ficino, Opera (1571), n, 1464. Cf. Arnaldo della Torre, Storia dell'Accademia Platonica di Firenze (Florence, 1902), pp. 783-788.

127 For contemporary notes on the cultural patronage of Nicholas V, see Vespasiano, Vite, pp. 38 ff.; Giannozzo Manetti, Vila Nicolai V, in Muratori, L., Rerum Italicarum Scrip/ores (Milan, 1734)Google Scholar, in, pt. 2, cols. 905-960. The two best secondary accounts are Domenico Zanelli, Il Ponlefice Nicolò V ed il Risorgimento delle Lellere, delle Arti e delle Scienze in Italia (Rome, 1855) and Costantino Cipolla, L'Azione letteraria di Niccold V nel Rinascimento (Frosinone, 1900). Cf. Georg Voigt, Die Wiederbelebung des classischen Allerthums, 2d ed. (Berlin, 1880), 11, 53-102, 138-148, 177-212. There is little in Valentino Ferrando, Vita del Papa Niccolò V (Sarzana, 1929). A useful sketch is in Cesare Vasoli, Studi sulla Cultura del Rinascimento (Manduria, 1968), ‘Profilo di una Papa Umanista: Tommaso Parentucelli’, at pp. 69-121.

128 Vespasiano, Vite, pp. 27-28, 414.

129 Ibid., p. 28. On the last named library see Cecil H. Clough, ‘A Note of Purchase of 1467 for Alessandro Sforza's Library at Pesaro’, Studia Oliveriana, XIII-XIV (1965-1966), 171-178.

130 Piccolomini, ‘Medicea’, XXI, 102-106 (madiematical titles at p. 105), prints a fifteenth- century copy of the Inventarium now in B.N.C.F., MS j . VII. 30, fs. 193-198. The autograph's location is not known. The canon is also printed in Piccolomini, ‘Medicea’, XXI, 102-106. See also Sforza, Giovanni, ‘La Famiglia, la Patria e la Giovinezza di Papa Niccolò V: Ricerche Storiche’, Atti della Reale Accademia Lucchese, XXIII (1884), 1–400 Google Scholar. at Pp. 359-381.

131 For Fournival see Leopold Delisle, Le Cabinet des Manuscrits de la Bibliothique Nationale (Paris, 1868-1881), n, 518-535 (mathematical titles at pp. 526-527). B. L. Ullman, ‘The Sorbonne Library and the Italian Renaissance’, in his Studies in the Italian Renaissance (Rome, 1955), pp. 41-53. Aleksander Birkenmajer, Bibljoteka Ryszarda de Fournival (Cracow, 1922), pp. 49-61.

132 Vespasiano, Vite, pp. 38-41. Manetti, Vita Nicolai, cols. 925-926. Eugène Müntz and Paul Fabre, La Bibliothèque Vaticane au XVe Siècle d'apèh des documents intdits, Bibliothèque des Ecoles Franchises d'Athènes et de Rome, 48 (Paris, 1887), pp. 39 ff. Cf. G. Mancini, ‘Giovanni Tortelli, Cooperatore di Niccolò V nel Fondare la Biblioteca Vaticana’, Archivio Storico Italiano, ucxvm (1920), 161-282, at p. 269, for a mathematical codex connected with Tortelli (MS Vat. Gr. 1411). Studies on Tortelli have been appearing in Italia Medioevale e Umanistica since 1966.

133 Filelfo, Epistolae (1502), fs. 91 v-92. Niccolò Perotto, in a letter of 5 December 1453, to Tortelli (quoted by Mancini, ‘Giovanni Tortelli’, pp. 212-213, from MS Vat. Lat. 3908, f. 236), states that ‘grammatici, rètori,'poeti, oratori, storici, matematici, filosofi, teologi, in ogni luogo abbondano uomini dottissimi perchè … favoriti dal papa’.

134 Franz Ehrle, Historia Bibliothecae Ronianorum Pontificum turn Bonifationae turn Avenionensis (Rome, 1890), 1,95-99; Robert Devreesse, Le Fonds Crec de la Bibliothèque Vaticane des Origines à Paul V, Studi e Testi, 244 (Vatican, 165), pp. 2-3.

135 Ehrle, Historia, p. 97, no. 612. A. Pelzer, Addenda et Corrigenda ad Francisci Ehrlc Historia Bibliothccae Romanorum Pontificum (Rome, 1947), I, 95. Heiberg, Archimedes, III, pp. lvii-lviii.

136 Ehrle, Historia, p. 96, no. 604, ‘librum de ingeneis’. Identified as Hero, Pneumatica, by Pelzer, Addenda, p. 94. Alexander Birkenmajer, Vermischle Untersuchungen zur Geschichte der mittelalterlichen Pliilosopliie, Beiträge zur Geschichte der Philosophie des Mittelalters, 20 (Münster, 1922), pp. 22-32. Martin Grabmann, Cuglielmo di Moerbeke, O.P., il Tradultore delle Opere di Aristotele (Rome, 1946), pp. 164-165.

137 William Thomson and Gustav Junge, The Commentary of Pappus on Book X of Euclid's Elements. Arabic Text and Translation, HaIVard Semitic Series, 8 (Cambridge, Mass., 193°)) from Bibliothèque Nationale, Paris, Ms Arab. 2457. A partial Latin translation, possibly by Gerard of Cremona, is in B.N.P., MS Lat. 7377A. See Marjorie Boyer, ‘Pappus’, in Catalogus Translationum et Commentariorum, ed. Paul Oskar Kristeller and F. Edward Cranz (Washington, D.C., 1960-1971), 11, 205-213, at pp. 211-212.

138 Theon's commentary on the Almagest has been identified with Laurenziana MS xxvin, 18. See Devreesse, Fonds Crec, p. 3. Cf. A. Maier, Codices Burghesiani Bibliothecae Vaticanae, Studi e Testi, 170 (Vatican, 1952).

139 To the Archivio di San Pietro, i.e., the Biblioteca Capitolare, was bequeathed the library of Cardinal Giordano Orsini in 1439. The Orsini bequest numbered 241 manuscripts, including copies of Boethius, Euclid, and Vitruvius. See the catalogues printed by Francesco Cancellieri, De Secreiariis Basilicae Vaticanae (Rome, 1780), n, 906-914; Paul Canart, Catalogue des Manuscrits Grecs de l'Archivio di San Pietro, Studi e Testi, 246 (Vatican, 1966); O. Rossbach, ‘Zu Ammian und den Codices Petrini’, Philologus, u (1892), 512-518. See also G. Mercati, Codici Latini Pico, Grimani, Pio …, Studi e Testi, 75 (Vatican, 1928), pp. 144-168. For Traversari's remarks on the Orsini manuscripts see ibid., pp. 21-22. Cf. Erich König, Kardinal Giordano Orsini (f 1438): ein Lebensbild aus der Zeit der grossen Konzilien und des Humanismus (Freiburg in Breisgau, 1906), for a short biography.

140 Müntz and Fabre, Bibliothèque, pp. 9-32

141 Müntz and Fabre, pp. 39 and 42, give the total as 1177, but Joseph Hilgers, ‘Zur Bibliothek Nikolaus V, Zentralblatt für Bibliothekswesen, xix (1902), 1-11, at p. 6, emends this to 1209. The inventory (now in Vich Cathedral, Spain) is printed in Müntz and Fabre, Bibliothe'que, pp. 48-113, with the Greek manuscripts at pp. 316-343. The Greek list is summarily reprinted with present-day identifications by Devreesse, Fonds Crec, pp. 9-43. For the dispersed manuscripts see Maria Bertòla, ‘Codici Latini di Niccolò V, perduti o dispersi’, in Mélanges Eugène Tisserant, Studi e Testi, 236 (Vatican, 1964), VI, 129-140.

142 Müntz and Fabre, Bibliothèque, pp. 141, 307; Devreesse, Fonds Grec, pp. 121-151.

143 Müntz and Fabre, Bibliothèque, pp. 39-40, 42.

144 Vespasiano, Vite, p. 352; Manetti, Vita Nicolai, col. 926, puts the number at 5000.

145 Devreesse, Fonds Grec, p. 36, gives the identifications adopted here. Cf. Müntz and Fabre, Bibliothèque, p. 339. For bibliographies of individual manuscripts see Paul Canart and Vittorio Peri, Sussidi Bibliografici per i Manoscritli Greci delta Biblioteca Vaticana, Studi e Testi, 261 (Vatican, 1970).

146 Devreesse, Fonds Grec, p. 3.

147 Müntz and Fabre, Bibliothe'que, p. 342; Devreesse, Fonds Grec, p. 41.

148 Heiberg, Archimedes, in, p. lxxix.

149 Ibid. Cf. Devreesse, Fonds Crec, pp. 40-41 n.; Müntz and Fabre, Bibliothèque, pp. 342-343-

150 Paul Fabre, ‘La Vaticane de Sixte I V , Mélanges d'Archéologie et d'Hisloire, xv (1895), 455-483; Müntz and Fabre, Bibliothèque, pp. 135-146.

151 The 1475 inventory (Vatican MS Vat. Lat. 3954) is printed in Müntz and Fabre, Bibliothèque, pp. 159-250. The Greek section of this list and of the 1481 and 1484 lists (MSS Vat. Lat. 3947 and 3949 respectively) are printed with identifications by Devreesse, Fonds Grec, pp. 44-151.

152 Müntz and Fabre, Bibliothèque, p. 217.

153 Vat. Gr. 206 (Apollonius) first appears in the 1475 inventory (Devreesse, Fonds Grec, p. 60) and seems to be different from the codex of Apollonius loaned earlier to Bessarion (ibid., p. 41).

154 Vat. Gr. 200 (Diophantus) first appears in the 1481 inventory (Devreesse, Fonds Grec, p. 93). For Vat. Gr. 304 see the 1455 list (ibid., p. 36). Vat. Gr. 191 appears in 1475 (ibid., p. 68).

155 The first four Aristarchus codices seem to appear in the 1475 inventory according to Devreesse, Fonds Grec, pp. 60-61. For the last two see ibid., pp. 163 and 465.

156 Most are codices of the Elementa. Of these Vat. Gr. 1041 is perhaps included in the 1455 list (Devreesse, Fonds Crec, p. 40), as well as in the 1484 list (ibid., p. 139). The following codices appear first in the 1475 Sistine list (the page references are from Devreesse, Fonds Crec, the first in each case being of the 1475 list, the second to the 1484 list): Vat. Gr. 190 (pp. 59, 131); V. G. 193 (pp. 60, 131); V. G. 1051 (pp. 59, 140).

A manuscript of the Elementa with Nicomachus, ‘de papiro, in nigro’, figures in the 1455 list and is identified by Devreesse, Fonds Grec, p. 36, as Vat. Gr. 1040. However, Vat. Gr. 1040 is elsewhere described as an incomplete Euclid, ‘in gilbo’ (Devreesse, pp. 37, 219); it was possibly rebound circa 1516 (ibid., p. 180).

The 1475 list includes Vat. Gr. 192, a volume bound in green, comprising the Elementa, Catoptrica, and Perspectiva. This was rebound in black under Julius II (Devreesse, p. 183). Another Catoptrica is in Vat. Gr. 191 (Devreesse, pp. 60, 130).

The Phenomena is represented by Vat. Gr. 204 (Devreesse, pp. 60,131). Another codex listed at p. 139 has not been identified.

157 Thomas L. Heath, The Thirteen Books of Euclid's Elements, 2d ed. (Cambridge, 1908), 1, 46-47, 103.

158 For the Biblioteca Vaticana in the sixteenth century see Devreesse, Fonds Grec; Eugène Müntz, La Bibliothique du Vatican au XVIe Siecle. Notes et Documents (Paris, 1886).

159 For loans from the Vatican see Maria Bertola, I Due Primi Registri di Prestito della Biblioteca Aposlolica Vaticana: Codici Vatican Latini 3964, 3966 (Vatican, 1942). ApoUonius (Vat. Gr. 206) was borrowed in 1535 (Bertò1a, p. 39). One codex of Diophantus (Vat. Gr. 304) was borrowed in 1522, another (Vat. Gr. 191) in 1518,1522, and 1531 (Bertòla, PP- 34. 55. 50. 109 respectively). Pappus (Vat. Gr. 218) was lent out in 1547 (Bertòla, p. 114).

160 Vespasiano, Vite, p. 39. For Nicholas’ circle see Zanelli, Niccolò V, pp. 17 ff.

161 For a list of the translations made under the aegis of Nicholas see Cipolla, L'Azione, pp. 31-32. Cipolla omits the Jacobus Cremonensis translation of Archimedes, while, following Voigt's lead, he mistakenly includes a translation of the Mechanica by Aristotle, by Theodor Gaza. The translation in question is actually of the Problemata. Connections between Florence and Rome are described in G. A. Holmes, The Florentine Enlightenment 1400-1450 (London, 1969).

162 paul Oskar Kristeller, ‘Music and Learning in the Early Italian Renaissance’, in his Studies in Renaissance Thought and Letters (Rome, 1956), pp. 451-470, at p. 456. Nicholas entrusted to Bessarion the reform of Bologna University.

163 Filelfo, Epistolae, f. 80, letter to Trapezuntius. Cf. f. 175. At the time of writing, I have not seen the unpublished thesis of John Monfasani on Trapezuntius (Columbia University, 1972).

164 See above, notes 40-50.

165 For Alberti's mathematical learning see Gadol, Alberti, and above, notes 78-80. The Ludi Matematici are accessible in their Italian version in Alberti, Opuscoli Morali (Venice, 1568), pp. 225-255, as well as in the Bonucci edition of Alberti, Opere Volgari, iv. The Latin version has not yet been published.

166 Books 1-5 were written in 1443-1445, Books 6-10 in 1447-1452. See Cecil Grayson, ‘The Composition of L. B. Alberti's Decern Libri de Re Aedificatoria’, Miinchenerjahrbuch der bildenden Kunst, ser. III, XI (1960), 152-161. See also the introduction to the recent edition cited above, n. 74. 167 Letter in Giuseppe Cagni, Vespasiano da Bisticci e il suo Epistolario (Rome, 1969), p. 132. In general see H. W. Wittschier, Giannozzo Manetti (Cologne-Graz, 1968).

168 Complementum Theologicutn, in Cusanus, Opera (Paris, 1514), n, f. xcn v. For his relations with Italian humanism see Saitta, Cusano, pp. 145-174; Kristeller, ‘Plethon's De Fato Dedicated to Nicholas of Cusa’, he. cit. in n. 64. An inventory of Cusanus’ library has been published by Mantese, Giovanni, ‘Ein notarielles Inventar von Buchern und Wertgegenständen aus dem Nachlass des Nikolaus von Kues’, Mitteilungen und Forschungenbeiträge der Cusanus-Gesellschaft, II (1962)Google Scholar, 85-116, but there is little of Greek mathematics. Cf. Paolo Rotta, ‘La Biblioteca del Cusano’, Rivista di Filosqfia Neo-Scolastica, XIX (1927), 22- 47, which I have not been able to see. At Kues there are preseIVed thirteen medieval mathematical manuscripts formerly owned by Cusanus. See Xavier Kraus, ‘Die Handschriften- Sammlung des Cardinals Nicolaus von Cusa’, Serapeum, XXV-XXVI (1864-1866), passim, at XXVI, 85-89. J. Marx, Verzeichnis der Handschriftcn-Sammlung des Hospitals zu Cues bei Bernkastel a. Mosel (Trier, 1905).

169 Cusanus, Opera (Paris, 1514, repr. Frankfurt am Main, 1962), 11, ‘De Mathematicis Complementis’, sig. Hh. iii (f. ux).

170 Heiberg, Archimedes, III, pp. lxx-lxxix; Clagett, Archimedes, l, 12. For Ottoboni Lat. 1157 see Paul Oskar Kristeller, Iter Italicum (Leiden-London, 1964-1967), n, 427-428. I am grateful to Professor Clagett for his kind advice on the Marciana manuscript, as well as other Archimedean matters.

171 Heiberg, Archimedes, III, pp. Ixxiii-lXXIV, followed by Marshall Clagett, ‘Leonardo da Vinci and the Medieval Archimedes’, Physis, xi (1969), 100-151, at p. 102, conjectures that Urb. Lat. 261 is the codex referred to in the following remark by Leonardo: ‘Archimenide e intero appresso al fratel di monsignore di Sant'Augusta in Roma; disse averlo dato al fratello che sta in Sardigna; era prima nella libraria del duca d'Urbino; fu tolto al tempo del duca Valentino’ (Codice Atlantico, f. 349v). On the other hand, neither the old indices of the Urbino library nor the codex itself indicate that Urb. Lat. 261 ever left Urbino. The identification is therefore open to doubt at present.

172 Heiberg, Valla's Bibliolhek, p. 85.

173 Heiberg, Archimedes, III, p. lxxix. But according to the list of codices in Müntz and Fabre, Bibliothique, p. 342, the borrowed Vatican manuscript consisted of ‘Quintemiones aliqui in Latino de Geometria Archimedis et certi in pergameno versu’. On the otherhand, Marciana Z. Lat. 327 is written on paper. For other codices of Nicholas that disappearedfrom the Vatican see Bertola, ‘Codici di Niccolò perduti’, where there is no mention of an Archimedes.

174 Heiberg, Archimedes, III, pp. lxxv, lxxix.

175 See ibid., III, lxxv, for the use of Codex A. For the use of Moerbeke see J. L. Heiberg, ‘Neue Studien zu Archimedes’, Abhandlungen zur Geschichte der malhematischen Wissenschaften, v (1890), 3-84, at p. 83. For Valla see below.

176 Most of the known details of Jacobus’ life are in Francesco Prendilacqua, Dialogo iniorno alia Vila di Vittorino da Feltre, tr. Giuseppe Brambilla (Como, 1871), pp. 44, 56; Carlo de’ Rosmini, Idea deU'Ottimo Precettore nella Vita e Disciplina di Vittorino da Feltre (Bassano, 1801), pp. 380-388; Bartolomeo Platina, ‘Commentariolus de Vita Victorini Feltrensis’, in Tommaso Agostino Vairani, Cremonensium Monumenta Romae extantia (Rome, 1728), p. 25. Bartolomeo Fazio, De Viris Illustrious (Cologne, n.d.), p. 27. Cf. Heiberg, Archimedes, III, p. lxxv. See also Sesto Prete, Two Humanistic Anthologies, Studi e Testi, 230 (Vatican, 1964).

177 Alfred Armand, Les Medailleurs Italiens des Quinziéme et Seizième Siècles, 2d ed. (Paris, 1883-1887), 1, 8. For recent accounts of Vittorino see G. P. Marchi, ‘Un nuovo Documento su Vittorino da Feltre’, in Italia Medioevale e Umanistica, vra (1965), 341-350; Bruno Nardi, ‘Contributi alia Biografia di Vittorino da Feltre’, in Mantuanitas Vergiliana (Rome, 1963), pp. 167-198. We find Niccolò Perotti, a pupil of Vittorino and a friend of Bessarion, requesting an ‘Archimedem grecum et latinum’ from Rome in 1454. See G. Mercati, Per la Cronologia delta Vita e degli Scritti di Niccold Perotti, Arcivescovo de Siponto, Studi e Testi, 44 (Vatican, 1925), p. 39, note

178 Aurispa, Carteggio, p. 128.

179 Heiberg, Archimedes, III, p. lxxv.

180 Traversari, Epistolae, n, col. 376.

181 Heiberg, Archimedes, III, pp. lxxx-lxxxiii. See above, text at n. 90.

182 For Trapezuntius see Vespasiano, Vile, pp. 297-299; Voigt, Wiederbelebung, s.v.

183 Quoted by de’ Rosmini, Vittorino, pp. 386-387. The letter was then in the Canonici collection at Venice; it is now in the Bodleian Library, Oxford, MS Canon. Misc. 169, f. 47V. Another copy is at the end of Trapezuntius’ commentary on the Almagest, Bodleian, MS Laud. Lat. 111, fs. 152V-153. Andreas Trapezuntius dedicated a copy of his father's translation to Sixtus IV; this was printed at Venice in 1528.

184 Biblioteca Ambrosiana, Milan, MS A. 143 inf., quoted by F. Argellati, Bibliolheca Scriptorum Mediolanensium (Milan, 1745), 1, clvii. The allegation against Jacobus is presented in a letter to the bishop of Perugia, now in the Bodleian, MS Canon. Misc. 169, f. 47. For Vittorino's mathematical teaching see Sassolo Pratese, Lettere intorno alia Vita e aWInsegnamento di Vittorino da Feltre, ed. and tr. Cesarc Guasti (Florence, 1869),pp. 38-40, 44-45, 64-66, 70.

185 The manuscript of Regiomontanus’ Theonis Defensio is now in the Archive of the Academy of Sciences, Leningrad. See E. Zinner, ‘Einige Handschriften des Johann Regiomontan (aus Konigsberg in Franken)’, Historischer Verein, Bamberg, Berichte, c (1964), 315-323.

186 The following list has been supplied by Professor John Monfasani who is preparing a study of Trapezuntius: Biblioteca Nazionale, Turin, MS G. n. 36; University Library, Basle, MS F.V. 22; University Library, Lund, MS Math. Fol. 1; Real Academia de la Historia, Madrid, Ms 22; Ambrosiana, MS A. 143 inf.; Bodleian, MS Laud. Lat. 111; B.N.P., MS Lat. 7265; Landesbibliothek, Stuttgart, MS Math. 24; Vaticana, MS Vat. Lat. 2058; Nationalbibliothek, Vienna, MSS Lat. 3106 and 10903.

187 W. Norlind, ‘Georgius Trapezuntius och hans Almagest-Kommentar’, Nordisk Tidskrift för Bok och Bibliotheksväsen, LIII (1966), 19-24 (reference supplied by Prof. Monfasani).

188 Francesco Barbaro, Frattcisci Barbari et Aliorum ad Ipsum Epistolae, ed. Angelo Maria Quirini (Brescia, 1743), p. 290.

189 Clagett, Archimedes, 1, 11-12; idem, ‘The Use of the Moerbeke Translations of Archimedes in the Works ofjohannes de Muris’, Isis, XLIII (1952), 236-242; Henri Bosnians, ‘Guillaume de Moerbeke et le Traitd des Corps Flottants d'Archimède’, Revue des Questions Scientifiques, set. IV, 1 (1922), 370-388; Grabmann, Guglielmo di Moerbeke. Since finishing this article, two useful papers by Marshall Clagett have come to my attention: ‘Archimedes’, in Dictionary of Scientific Biography (New York, 1970-), 1, 213-231, and ‘Archimedes in the Late Middle Ages’, in Duane H. D. Roller, Perspectives in the History of Science and Technology (Norman, Okla., 1971), pp. 239-259.

190 Heiberg, ‘Neue Studien zu Archimedes’, he. cit. in n. 173, p. 83. Cf. Clagett, Archimedes, 1,12. Professor Clagett is preparing an edition of Moerbeke's version for the second volume of his Archimedes in the Middle Ages.

191 T. Ashby, Jr., Sixteenth-Century Drawings of Roman Buildings Attributed to Andreas Coner, Papers of the British School at Rome, 2 (London, 1904), pp. 3-4. The sketchbook is now in Sir John Soane's Museum, London. Doubts are raised concerning the attribution of the sketchbook by Giovanni Mercati, ‘A Proposito di Andrea Coner …’, in his Note per la Storia di alcune Biblioteche Romane dei Secoli XVI-XIX, Studi e Testi, 164 (Vatican, 1952), pp. 131-146.

192 Vat. Gr. 196, according to Bertòla, Registri, pp. 43-44.

193 The inventory is printed by Ashby, Coner, pp. 75-79, from a volume in the Archivio di Stato, Rome, and reprinted with identifications by Mercati, ‘Coner’, pp. 142- 146.

194 The holograph is listed in the inventory of CeIVini's books, Vaticana, MS Vat. Lat. 8185, f. 286. Commandino, Liber de Centro Gravitatis Solidorum (Bologna, 1565), sig. +2, says that CeIVini gave him as a gift ('dono dedit’) the Latin version of On Floating Bodies. It would seem, therefore, that Commandino may have received a copy, rather than the original which remained in the library of CeIVini. On CeIVini's collection see Robert Devreesse, ‘Les Manuscripts Grecs de CeIVini’, Scriptorium, xxn (1968), 249-270. I am grateful to Mme Jeanne Bignami-Odier for information on the CeIVini codices.

195 Heiberg, Archimedes, III, pp. lix-brii. For the only printed notice of Barb. Lat. 304, see Kristeller, Iter, n, 443. From the mathematics lectures which it contains, this anonymous codex was written by a professor of mathematics at the Collegio Romano, circa 1558. He was probably Balthasar Torres who taught mathematics in the Collegio Romano from 1553 to 1561. Torres’ frequent references to a ‘Messer Federico’ most likely pertain to Federico Commandino, then in Rome.

196 In the Renaissance the Moerbeke translation was known to Jacobus Cremonensis, Leonardo da Vinci, Luca Gaurico, Tartaglia, Commandino, and Maurolico, among others. See Clagett, Archimedes, 1, 12-14; idem, ‘Leonardo and Archimedes’.

197 Bibliography and biography are in Lotte Labowsky, ‘Bessarione’, in Dizionario Biografico degli Italiani (Rome, 1967), IX, 686-696; Carlo Frati, Dizionario Bio-Bibliografico dei Bibliolecari e BibliofiU Italiani, Biblioteca di Bibliografia Italiana, 13 (Florence, 1933), pp. 76-94; Marino Parenti, Aggiunle al Dizionario … di Carlo Frati (Florence, 1952), 1, 129-130; Ludwig Mohler, Kardinal Bessarion als Theologe, Humanist und Staatsman (Paderborn, 1923-1942), particularly I, 325-335; Vespasiano, Vile, pp. 95-98.

198 For Urbino see Cecil H. Clough, ‘Cardinal Bessarion and Greek at the Court of Urbino’, Manuscripta, vm (1964), 160-171, and below.

199 Omont, Charles, ‘Inventaire des Manuscrits Grecs et Latins donnes a Saint-Marc de Venise par le cardinal Bessarion (1468)’, Revue des Bibliothèques, IV (1894), 129–187 Google Scholar. For recent work on the early inventories see Lotte Labowsky, ‘Il Cardinale Bessarione e gli- Inizi della Biblioteca Marciana’, in Venezia e l'Orientefra Tardo Medioevo e Rinascitnento, ed. Agostino Pertusi (Florence-Venice, 1966), pp. 159-182. Manuscripts coming from Bessarion form the bulk of the Fondo Antico Greco (Z. Graeci); catalogued in A. M. Zanetti, Graeca D. Marci Bibliotheca Codicum Manuscriptorum (Venice, 1740); idem, Lalina et Italica D. Marci Bibliotheca Mant4scriptorum (Venice, 1741).

200 See Bessarion's letter to the Doge (1468), printed in Omont, ‘Inventaire’, pp. 138-140. Cf. Vespasiano, Vite, p. 96; and the two studies by Deno J. Geanakoplos, Greek Scholars in Venice (Cambridge, Mass., 1962); Byzantine East and Latin West (Oxford, 1966).

201 Edited by Mohler, Bessarion, n, 75-79.

202 Müntz and Fabre, Bibliothèque, pp. 342-343. But see above, n. 173.

203 Marciana MS Z. Lat. 491. Printed in Mohlet, Bessarion, III, 546-548. For the astrolabe made in 1462 by Regiomontanus for Bessarion see Derek de S. Price, “The First Scientific Instrument of the Renaissance’, Physis, 1 (1959), 26-30.

For the astronomical clock see A. Rubbiani, ‘L'Orologio del Comune di Bologna e la Sfera del 1451’, Alii e Memorie della Reale Depulazione di Storia Palria per le Provincie di Rotnagna, ser.III, XXVI (1908), 349-366.1 am grateful for this reference to Professor Bruce Chandler.

204 Most of the mathematical codices are listed by Zanetti, Graeca, pp. 142-155 (MSS Z. Gr. 300-336).

205 J. Morelli, Bibliotheca Manuscripta Graeca et Latina (Bassano, 1802), 1, 185

206 Giovanni Mercati, Ultimi Conlributi alia Storia degli Umanisti: I. Traversariana, Studi e Testi, 90 (Vatican, 1939). Morelli, Bibliotheca Manuscripta, p. 178.

207 Ibid., p. 148. Bolgar, Classical Heritage, p. 476, lists it as the Mechanics.

208 Rose and Drake, ‘Questions of Mechanics’, p. 76. On Sophianus see now Kristeller, 'Plethon's De Fato Dedicated to Nicholas of Cusa’.

209 For fuller descriptions see Zanetti, Latina; Valentinelli, Bibliotheca S. Marci.

210 Zanetti, Latina, p. 141. Valentinelli, Bibliotheca S. Marci, IV, 218.

211 For loans see Castellani, Carlo, ‘II Prestito dei Codici Manoscritti della Biblioteca di San Marco in Venezia ne’ suoi primi tempi e le conseguenti perdite de’ codici stessi', Atti del Reale Institute Veneto di Scienze, Lettere ed Arti, LV, I (1896-1897), 311–377 Google Scholar; Coggiola, G., 'II Prestito di Manoscritti della Marciana dal 1474 al 1527', Zenlralblatt für Bibliothekswesen, xxv (1908), 47–70 Google Scholar; Volpati, C., ‘Per la Storia e il Prestito di Codici della Marciana nel secolo xvi', ibid., XXVII (1910), 35–61 Google Scholar.

212 Niccoló Tartaglia, Quesiti et Inventioni Diverse (Venice, 1546), fs. 76 ff. Cf. Rose and Drake, ‘Questions of Mechanics’, pp. 85-87; Palencia, Angel Gonzalez and Mele, Eugenio, Vida y Obras de Don Diego Hurtado de Mendoza (Madrid, 1941-1943)Google Scholar; Spivakovsky, Erika, Son of the Alhambra: Don Diego Hurtado de Mendoza (1504-75) (Austin, Tex., 1970)Google Scholar.

213 Castellani, ‘Prestito’, pp. 330, 332. 214 The list is in Vaticana MS Vat. Lat. 3958, fs. 232-234V. For Mendoza's Greek manuscripts see Rose and Drake, ‘Questions of Mechanics’, pp. 85-87; Palencia and Mele, Mendoza, III, 482.

Mendoza's humanist interest in mathematics may be compared with that of Giambattista Rasario (1517-1578) who taught Greek and Latin at Venice for twenty-two years. Rasario's loans from the Marciana in 1555 included Greek codices of Apollonius (Z. Gr. 518), Hero (Z. Gr. 263), and Theon, On the Use of Plato for the Study of Mathematics (Z. Gr. 307).

214 See Castellani, ‘Prestito’, p. 358.

215 Castellani, ‘Prestito’, pp. 350-351.

216 For biographical notes see Heiberg, Valla's Bibliothek.

217 Inventories are printed in Müller, ‘Lascaris und die Mediceiische …’, pp. 382-385.

Heiberg, Valla's Bibliothek, pp. 107-129. Giovanni Mercati, Codici Lalini Pico, Crimani, Pio …el Codici Greci Pio di Modena, Studi e Testi, 75 (Vatican, 1928), pp. 203-245. The main list, which appears in Heiberg, is Vaticana MS Barberini Lat. 3108, compiled in 1564. An unnoted list, dating from circa 1558, of Greek mathematical codices in the Valla- Pio da Carpi library is to be found in Vaticana MS Barberini Lat. 304, f. 163.

218 Mercati, Codici Pio, pp. 203-245, supplies concordances for the various catalogues and also for the codices now in the Biblioteca Estense. Descriptions of the Estense manuscripts are in Anon., Cenni Storici della Rcale Biblioteca Estense in Modena (Modena, 1873); V. Puntoni, ‘Indice dei Codici Greci della Biblioteca Estense di Modena’, Studi Italiani di Filologia Classica, IV (1896), 379-536.

219 For Est. Gr. 56, see Cenni, p. 11; Puntoni, ‘Indice’, p. 421; Mercati, Cociici, p. 211. Est. Gr. 149, containing Euclid's Data, is attributed to Valla's library by Cenni, p. 22, and Puntoni, ‘Indice’, p. 481. Mercati, Codici, p. 211, also describes its provenance as the Valla collection. But at p. 62, ri. 5, Mercati lists it among the manuscripts probably written by Alberto Pio's friend, Musurus, after the death of Valla.

220 Puntoni, ‘Indice’, p. 413; Mercati, Codici, p. 217.

221 Cenni, p. 17, Puntoni, ‘Indice’, p. 451, and Mercati, Codici, p. 217, all trace the manuscript to Valla's possession. But Mercati, Codici, p. 62, lists it among the codices written by Musurus after Valla's death.

222 Credited to Valla by Cenni, p. 17. Mercati, Codici, p. 62, n. 5, assigns it to the Musurus group instead.

223 Cenni, p. 23; Puntoni, ‘Indice’, p. 494; Mercati, Codici, pp. 205, 231.

224 Giuseppe Ceredi, Tre Discorsi sopra il Modo d'alzar Acque da'Luoghi bassi (Parma, 1567). P- 6: ‘Avenga che quasi a sorte mi fur venduti da chi lor non conosceva, certi scritti di Herone, di Pappo e di Dionisidoro tolti dalla libraria, che fu gia del dottissimo Giorgio Valla, nostro Piacentino’. The ‘Pappo’ is probably the De Musica, listed in the pre-1531 catalogue (Mercati, Codici, p. 204). Mercati notes that this item is missing from the 1564 catalogue, nor is it presently at Modena. The De Musica could thus have been acquired by Ceredi between 1531 and 1567. Heiberg, Valla's Bibliolhek, p. 128, believes that the work by Hero is the Pneumalica.

225 Heiberg, Valla's Bibliothek, p. 108, n. 2, conjectures that Codex A might have been bought with the other manuscripts by Ceredi. Mercati, Codici, pp. 206, 233, 235, believes that the Archimedes was still in the Pio da Carpi library in 1564, and was lost some time thereafter.

226 Müller, ‘Lascaris und die Mediceiische Bibliothck’, pp. 383-385. This list comes from Vaticana MS Vat. Gr. 1412.

227 Ibid., p. 356. The letter is printed in Fabroni, Laurentii Vita, n, 284-286. The autograph is in the Archivio di Stato, Florence, M.A.P. Filza 43, no. 42 (ex-78). The Hero text mentioned was probably the De Mensuris, rather than the Pneumatica. The De Mensuris, along with Archimedes, forms part of Codex A. See notes above on the Laurenziana.

228 Heiberg, Archimedes, III, xii.

229 Letter printed in Heiberg, Valla's Bibliothek, p. 71 (from Vaticana MS Vat. Lat. 3537).

230 Ibid., p. 72.

231 Letter printed in Giulio Bertoni, La Biblioteca Estense e la Coltura Ferrarese ai Tempi del Duca Ercole I (1471-1505) (Turin, 1903), pp. 119-120, from the original in the Archivio di Stato, Modena.

232 Cf. Antonio Rotondo, ‘Pellegrino Prisciani (c. 1435-1518)’, Rinascimento, xi (1960), 69-110, at p. 75.

233 Letter to Pietro Barozzi (1495?), printed in Heiberg, Valla's Bibliothek, p. 85.

234 For the projected translation see the correspondence with Barozzi and Antiquarius, printed in Heiberg, Valla's Bibliothek, pp. 69-70, 85, 87-88; also, at p. 47.

235 For the manuscript sources of the De Rebus Expetendis see J. L. Heiberg, ‘Die Handschriften Georg Valla's von griechischen Mathematikern’, Jahrbücherfür classische Philologie, Supplement, xn (1881), 375-402. The Aristarchus translation was first published in the volume Nicephori Logica … (Venice, 1498).

Most of the works of Archimedes were first printed in Latin in 1543, and in Greek in 1544; the De Quadrature! Circuli and De Quadratura Parabolae had earlier appeared in 1503. The first complete printed work of Apollonius was the Latin translation of 1537. For the anticipation by Valla of Tycho Brahe's cosmology see McColley, Grant, 'George Valla: An Unnoted Advocate of the Geo-Heliocentric Theory', Isis, XXXIII (1941), 312–315 CrossRefGoogle Scholar.

236 Letter to Antiquarius, 1492, printed in Heiberg, Valla's Bibliothek, pp. 87-88. The importance of Valla's mathematical labors is attested by the humanist Juan Luis Vives (writing in 1531), Opera Omnia (Basle, 1555), 1, 498.

237 Gaurico printed the De Qtiadratura Circuli and the De Quadratura Parabolae from the Moerbcke translation in Madrid, Biblioteca Nacional, MS 9119, according to Clagett, 'Leonardo and Archimedes’, p. 103.

In Gaurico's Opera Omnia (Basle, 1575), 1, 9; n, 1833, there are carmina by Jo. Bapt. Gabius, ‘Poeta Veronensis’. This connection is important in view of Gabius’ own translating activity; his version of Hero's Pneumalica is in the Vaticana, MS Vat. Lat. 4575; that of Proclus’ Commentary on Euclid is in the Ambrosiana, Ms P. 51. sup. For Gaurico see Ferdinando Gabotto, ‘Alcuni Appunti per la Cronologia della Vita dell'Astrologo Luca Gaurico’, Archivio Storico per le Provincie Napoletane, xvn (1892), 278-298; Pèrcopo, Erasmo, ‘Luca Gaurico, Ultimo degli Astrologi: Notizie biografiche e bibliografiche', Società Reale di Napoli, Atti della R. Accademia di Archeologia, Lettere e Belle Arti, XVII, ii (1896), 3–49 Google Scholar.

238 For Zamberti see Hermann Weissenborn, Die Übersclzungen des Etiklid dutch Compano und Zamberti (Halle, 1882), pp. 12 (T.; Heath, Euclid's Elements, 1, 98-100; Catalogus Translationum, I, 89-90. An early sixteenth-century manuscript of the Euclid translation is now in the Vaticana, MS Barberini Lat. 3.

239 For Memmo's appointment to the public professorship of mathematics in 1530 see E. A. Cicogna, Delle Iscrizioni Veneziane (Venice, 1824-1842), IV, 507-510. Cicogna, IV, 510, errs in saying that Zamberti translated Apollonius.

240 Francesco Maurolico, Cosmographia (Venice, 1543), sig. a ii, dedication to Bembo, chastises the ignorance of Zamberti. Bernardino Baldi, Cronica de’ Matematici (Urbino, 1707), P- 99, says that Commandino attributed Zamberti's errors rather to the poor Greek texts from which he had worked.

241 Apart from corresponding with Maurolico, Bembo took into his own home for several years the Paduan professor of mathematics Federico Delfino. The Cardinal was friendly too with Memmo, the Venetian professor of mathematics. See Bembo's letter of 19 October 1530, in Tommaso Porcacchi, Let’.cre di XIII Huomini illustri raccolte (Venice, 1586), f. 304.

One might also mention that Aldus dedicated his collection of Astronomici Veteres (Venice, 1499), to Alberto Pio da Carpi: ‘Opusculum ad te legendum mittimus, quod iam peripateticus, mathematicis disciplinis navare operam coeperis’. It was Alberto who later acquired Valla's manuscripts; and it was Aldus who published Valla's De Rebus Expetendis.

Cf. Paul Lawrence Rose, ‘The Accademia Venetiana: Science and Culture in Renaissance Venice’, Studi Veneziani, XI (1969), 191-242; Bruno Nardi, ‘La Scuola di Rialto e l'Umanesimo Veneziano’, in Umanesimo Europeo e Umanesimo Veneziano, ed. V. Branca (Florence-Venice, 1963), pp. 93-139, reprinted in his Saggi sulla Cultura Veneta del Quattro e Cinquecento (Padua, 1971), pp. 45-98.

242 Aubrey Diller, ‘The Library of Francesco and Ermolao Barbaro’, Italia Medioevale e Umanistica, vi (1963), 254-262, shows that items 1148-1697 in the inventory printed by Kibre, Library of Pico, are actually the books of the Barbaro. Ermolao's manuscript of the Geographia of Ptolemy is now in the Newberry Library, Chicago, MS 39. The ample correspondence between Pico and Ermolao includes a letter asking for the return of a codex of Ptolemy, Musica (Pico, Opera [Venice, 1498], sig. X, xv v. Cf. Ermolao Barbaro, Epistolae, Orationes et Carmina, ed. Vittore Branca [Florence, 1943], n, 85).

243 E. Barbaro, Epistolae, ed. Branca, n, 22-23. Cf. Quirinus Breen, ‘Giovanni Pico della Mirandola and the Conflict of Philosophy and Rhetoric’, Journal of the History of Ideas, xm (1952), 384-412; A. Ferriguto, Almorò Barbaro, Miscellanea di Storia Veneta della R. Dep. di Storia Patria Veneta, ser. m, vol. 15 (Venice, 1922), pp. 34-35; P. Paschini, Tre Illustri Prelati del Rinascimento, Lateranum, N.S. 23 (Rome, 1957); Carlo Dionisotti, 'Ermolao Barbaro e la Fortuna di Suiseth’, Medioevo e Rinascimento: Studi in Onore di Bruno Nardi (Florence, 1955), I, 217-253, at p. 219.

244 Ermolao Barbaro, Libri Paraphraseos Themistii (Venice, 1499), f. 102V.

245 Ibid., f. lv, reprinted in E. Barbaro, Epistolae, ed. Branca, 1, 9.

246 Correspondence with Valla is printed in Barbaro, Epistolae, n, 15, 21, 52. Cf. Ferriguto, Almorò, pp. 281-284.

247 ‘Video magnitudinem operis [translation of Aristotle] instituti, perterreo et horresco. … Quid, quod post Aristotelem mathematicos libros interpretari cogito?’ (letter printed in Barbaro, Epistolae, I, 91-93, especially p. 92; Ferriguto, Almorò, pp. 380-381; Epistolae Clarorum Virorum Selectae [Venice, Guerrei, 1568], fs. 116-117V). For Barbara's advice on the study of mathematics see Ermolao Barbaro, De Coelibatu. De Officio Legati. Con un Appendice alle Epistolae, Orationes et Carmina, ed. V. Branca (Florence, 1969), pp. 136-137.

248 Barbaro, Epistolae, n, 37-38.

249 Gerardus Joannes Vossius, De Universae Mathesios Nalura et Constilutione (Amsterdam, 1650), pp. 63 and 368. The dates are in the edition in Vossius, Opera (Amsterdam, 1695-1701), in, cols. 81 and 186. The writer cites as evidence his own De Hisloricis Latinis Libri III, 2d ed. (Leiden, 1651), lib. in, cap. 8, but this section (pp. 620-623) does not mention the De Convenientia nor the Quaestiones Geometricae. Cf. Apostolo Zeno, Dissertazioni Vossiane (Venice, 1752-1753), n, 387.

250 Vespasiano, Vile, pp. 213-214. In fact, many of the codices were copied from unsatisfactory manuscripts. See Cecil H. Clough, “The Library of the Dukes of Urbino”, Librarium (Zurich), IX (1966), 101-104; Gino Franceschini, ‘Per la Storia della Biblioteca di Federico da Montefeltro’, in his Figure del Rinascimento Urbinate (Urbino, 1959), pp. 109-147. A full study of Vespasiano, clarifying these and other matters, is awaited from A. C. de la Mare.

251 Franceschini, Figure, pp. 13-14, dates these studies to 1435-1437. Federico kept at Urbino a portrait of Vittorino inscribed: ‘praeceptor sanctissimus … humanitatis litteris exemplisque tradita’, according to G. Calo, ‘Vittorino da Feltre’, in Vittorino da Feltre (Brescia, 1947). A testimony to Federico's wide learning is the set of portraits of famous men and allegories of the seven liberal arts which was commissioned for his study. See Cecil H. Clough, ‘Federigo da Montefeltro's Private Study in his Ducal Palace of Gubbio\ Apollo, ixxxvi (1967), 278-287.

252 Clough, ‘Bessarion and Greek’, pp. 164-165

253 Vespasiano, Vite, p. 208.

254 Ibid., p. 211.

255 Ibid., p. 213.

256 Printed by Cesare Guasti, ‘Inventario della Libreria Urbinate, compilato nel secolo XV da Federico Veterano, Bibliotecario di Federigo I da Montefeltro, duca d'Urbino’, Giomale Storicodegli Archivi Toscani,vt (1862), 127-147; vn (1863),46-55,130-154 (from a manuscript in the Archivio delle Domenicane di San Vincenzo, Prato). For Federico's librarians, see Clough, ‘Bessarion and Greek’, pp. 167-169.

257 Printed in C. Stornajolo, Codices Urbinates Graeci (Vatican, 1895), pp. lv ff. A new edition of the Index Vetus is being prepared by Luigi Michelini-Tocci. Cf. Clough,'Bessarion and Greek’, pp. 167-169.

258 A concordance for the Index Vetus, the Guasti inventario and the present shelfmarks of the fondo Urbinate Latino is given by C. Stornajolo, Codices Urbinates Latini (Vatican, 1902-1921), m.

259 For the Greek section of the Index Vetus see Stornajolo, Urbinates Graeci, pp. clx ff. A concordance of the Index Vetus and the fondo Urbinate Greco is at p. lxxvii.

260 Heiberg, Archimedes, III, lxxiii-lXXIV, identifies Urb. Lat.

261 as the codex cited by Leonardo da Vinci as having being removed from the ducal library of Urbino (see above, n. 171). As far as I know this manuscript did not leave Urbino before 1657. Nor is there another Archimedes manuscript listed in the old Urbino catalogue.

261 Baldi, Cronica de’ Malematici, p. 89. The Practica Geometriae, Urb. Lat. 292, was eventually published by Baldassare Boncompagni, Scritti di Leonardo Pisano, Matematico del Secolo decimoterzo (Rome, 1857-1862), n.

262 Tammaro de Marinis, La Biblioteca Napoletana dei Re d'Aragona (Milan, 1952), 1, 198,203. A Supplement was published at Verona in 1969.

263 Ibid., n, 197-198.

264 Ibid., n, 190.

265 Elisabeth Pellegrin, La Bibliothèque des Visconti el des Sforza (Paris, 1955; with Supplement, Florence, 1969), prints the inventories and identifies many of the manuscripts.

266 Cf. Maccagni, in Atti del Primo Convegno di Ricognizione (cited above in n. 3), p. 176.