A Archimedes: Reception in the watershed. Valla drew knowledge of the person Renaissance as well as his works from Proclus and Pappus, thus integrating the two. Over the century, a Jens Høyrup number of editions also appeared, the Editio Section for Philosophy and Science Studies, princeps in 1544, and a mathematical work Roskilde University, Roskilde, Denmark following the footsteps of Archimedes was made by Maurolico, Commandino, and others. Abstract The Northern Renaissance only discovered With only Apuleius and Augustine as partial Archimedes in the 1530s and for long only exceptions, Latin Antiquity did not know superficially. The first to express a (purely Archimedes as a mathematician but only as ideological) high appreciation is Ramus in an ingenious engineer and astronomer, serving 1569, and the first to make creative use of his his city and killed by fatal distraction when in mathematics was Viète in the 1590s. the end it was taken by ruse. The Latin Middle Ages forgot even much of that, and when Archimedean mathematics was translated in Ancient Latin and Medieval Background the twelfth and thirteenth centuries, almost no integration with the traditional image of the Archimedean mathematics had a certain impact in person took place. late Renaissance thinking, and it was important With the exception of Petrarca, who knew for changes in late Renaissance mathematics; the civically useful engineer and the astrologer, however, much more pervasive, and of much lon- fourteenth-century Humanists show no interest ger duration, was the impact of “Archimedes” as in Archimedes. In the fifteenth century, “higher an almost Protean figure, changing with the con- artisans” with Humanist connections or educa- ditions of the time. tion took interest in Archimedes the technician This figure was known to early Humanists and started identifying with him. In mid- exclusively through Latin sources (detailed in century, a new translation of most works from Høyrup 2017). These tell about the producer of the Greek was made by Jacopo Cremonensis, marvelous military machines used in the defense and Regiomontanus and a few other mathema- of Syracuse and admired by Marcellus; about his ticians began resurrecting the image of the fatal distraction when Syracuse was taken; about geometer, yet without emulating him. his “sphere,” a mechanical model of the heavenly Giorgio Valla’s posthumous De expetendis system or his general mastery of astronomy; et fugiendis rebus from 1501 marks a or, rarely, about his preoccupation with geometry, © Springer Nature Switzerland AG 2019 M. Sgarbi (ed.), Encyclopedia of Renaissance Philosophy, https://doi.org/10.1007/978-3-319-02848-4_892-1 2 Archimedes: Reception in the Renaissance yet without indicating that this is more than a field Murs, Oresme, Henry of Hesse, and Albert of dealing with figures drawn with a radius (Cicero, Saxony (Clagett 1978,3–144) – all linked to the Elder Pliny, Cassiodorus). Vitruvius ascribes Paris University. to Archimedes a number of technical manuals that Outside this restricted circle, only Gerard’s cannot be understood if one does not know natural Measurement of the Circle had repercussions. philosophy and also tells the story of Hieron’s Around 1250, Vincent of Beauvais combined in crown. Archimedes’ overall subtlety was prover- Speculum historiale V. XLIII (1624, 149) quota- bial in Cicero’s time and circle. tions from Orosius (the machines and the defense Only two writers give hints that Archimedes of Syracuse) and Valerius Maximus (the death made advanced geometric theory (yet in a way story) with a reference to Archimedes’s Measure- that can only be understood by readers who know ment of the Circle, “of which Aristotle says that it already): Apuleius, in the Apology, says that can be but is not known” (Categories 7b31–33). Archimedes’ study of convex and concave mirrors A century later, Walter Burley (1487,biiv) added outshines his general admirable subtlety in geom- to this a long verbatim borrowing from Valerius etry, and Augustine, in De utilitate credendi, asks Maximus. On the whole, however, the Arabo- rhetorically who would take Epicurus as his guide Latin as well as Moerbeke’s Greco-Latin trans- to Archimedes’ geometrical writings –“against lations circulated in isolation from interest in which he spoke with much tenacity, in my opinion the person – and information about the person without understanding them.” was drawn from very few sources: Orosius, Medieval Latin culture until 1100 took very Macrobius, and Valerius Maximus. little notice. In the late eighth century, Paulus Diaconus borrowed some lines from Orosius referring to the role of Archimedes’ machines in Humanism from Petrarca to Alberti the defense of Syracuse, and around 810 Dungalus Reclusus took over from Macrobius that Cicero As a rule, fourteenth-century Humanists were and Archimedes agree about the order of the interested in neither the works nor the person heavenly spheres. (attitudes to Archimedes are dealt with under dif- The twelfth century brought translation from ferent but compatible perspectives in Laird 1991 the Arabic of a few Archimedean works (and of and Høyrup 1992). Petrarca was, however, though works drawing on Archimedes). Two translations only in the person. To judge from his letters, of the Measurement of the Circle were made (one Archimedes was admittedly not central to him – possibly by Plato of Tivoli and the other by Gerard he is mentioned only twice. Nonetheless, Petrarca of Cremona). The latter circulated well among did produce two biographical notices. In De viris mathematically active university scholars – illustribus vitae (1338), within the biography of witness the production of at least nine revised Marcellus (Petrarca 1874, I, 280–282), he narrates versions from the twelfth through the fourteenth in his own words Valerius Maximus’ stories about century (Clagett 1964). Archimedean material Archimedes’ powerful war machines and his was contained in the Verba filiorum of the Banū death, with his own observations, twists, and addi- Mūsā, similarly translated by Gerard. The well- tions: that even though Firmicus Maternus dispar- circulated De curvis superficiebus compiled in the ages Archimedes as a mechanic, he was late twelfth or earlier thirteenth century by John of formidable both as an astrologer and a geometer; Tynemouth contained material in Archimedean that the figures he was drawing were astrological style; Roger Bacon ascribes it to Archimedes, or geometrical; and, finally, that Cicero found while he never refers to the genuine works. Archimedes’ grave. In Rerum memorandarum In 1269, William of Moerbeke made an almost libri I.23 (1343) (Petrarca 1943,22–24), an arrival complete translation of the Archimedean corpus in Syracuse offers the occasion to expand Livy’s from the Greek (ed. Clagett 1976). Only Witelo single line about Archimedes’ unique observation appears to have used it in the thirteenth century, of the heavens and the stars into a general praise of but in the fourteenth it was drawn upon by Jean de Archimedes’ study of nature and of his sphere Archimedes: Reception in the Renaissance 3 which allows understanding of the celestial insistence that Archimedes considered mechani- motions not only by the mind but also by our cal work and even mechanical treatises improper eyes. Even more praiseworthy were his terrestrial is not argued against; it goes unmentioned – it mechanical feats; his fatal distraction, on the other would indeed disparage Alberti’s own undertak- hand, is slightly censured as “immoderate.” On ing. Neoplatonism and esoteric Platonism remain both accounts, Platonizing celebration of the pure unthinkable. Further, Alberti declares not to intellect is outside the perspective. The value scale intend to be Zeuxis in painting, Nicomachus in is that of Cicero and the Roman elite, and Archi- the manipulation of numbers, or Archimedes medes is almost perfect when measured thus. when dealing with angles and lines; he will Archimedes was part of the legitimate ancient stick to the basic principles and that which gives heritage, respected because of his sophisticated honor and fame to the architect. Admitting that machines, his planetary model as well as those Archimedes had been the supreme geometer that could serve efficiently in war. Even Petrarca’s (Plutarch says so), Vitruvius distances himself aversion for astrology only induces him to com- from this aspect of the hero. pare modern astrologers unfavorably to Ptolemy, Archimedes, and Firmicus Maternus, not to den- igrate this aspect of his “Archimedes.” Return of Archimedes the Other fourteenth-century Humanists were not Mathematician interested in the Archimedes figure at all. That changed to some extent in the fifteenth century, Even among Humanists with no direct links to as “higher artisans” (architects, painters, military architecture and engineering, there seems to engineers, etc.) and their ambience began to have have been some interest in Archimedes, probably intercourse with Humanists. Engineer artists like because of what the Latin sources tell about Mariano Taccola and Filippo Brunelleschi were him. In 1423–1424, rumors circulated that an known, respectively, as the “Archimedes of Archimedes manuscript had been brought back Siena” and a “second Archimedes.” None of from Byzantium. However, nobody ever saw it, them were mathematicians. What they had in and some 25 years passed before more happened common with the “Archimedes” known at the among Humanists. Around 1450, however, time was to be skilled