argante ciocci
Università degli Studi di Bari, Seminario di Storia della Scienza, Department Member
- Freelanceedit
Questo articolo prende spunto da un brano delle Vite di Vasari in cui Luca Pacioli viene definito "discepolo" di Piero della Francesca, per analizzare il debito intellettuale del primo nei confronti del secondo non soltanto nell'ambito... more
Questo articolo prende spunto da un brano delle Vite di Vasari in cui Luca Pacioli viene definito "discepolo" di Piero della Francesca, per analizzare il debito intellettuale del primo nei confronti del secondo non soltanto nell'ambito della prospettiva ma anche per la geometria dei poliedri. Fino ad ora si è ritenuto che la versione volgare del Libellus edita a stampa nella Divina proportione (1509) sia una ritraduzione in italiano del testo latino tramandatoci dall'Urb. Lat. 632. Dopo aver proposto argomenti a confutazione di questa ipotesi, si prospetta l'idea che il testo volgare edito da Pacioli possa essere l'autografo di Piero o una sua copia, rivista dal Frate di Sansepolcro. Introduzione Giorgio Vasari, nelle sua biografia di Piero della Francesca, elogiava, oltre alle notevoli doti artistiche e prospettiche, le straordinarie competenze geometriche del pittore di Sansepolcro e non esitava ad affermare "che nessuno più di lui fu mirabile nelle cognizioni delle cose di Euclide, e tutti i migliori giri tirati ne' corpi regolari egli meglio ch'altro geometra intese, et i maggiori lumi che di tal cose ci sieno, ci son di man sua; perché Maestro Luca dal Borgo frate di San Francesco che sopra i corpi regolari della geometria scrisse, fu un suo discepolo: et venendo in vecchiezza Pietro, che aveva composto di molti libri, Maestro Luca facendoli stampare tutti gli usurpò per se stesso come già s'è detto di sopra" 2 .
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Federico Commandino’s Latin editions of the mathematical works written by the ancient Greeks constituted an essential reference for the scientific research undertaken by the moderns. In his Latin editions, Commandino cleverly combined his... more
Federico Commandino’s Latin editions of the mathematical works written by the ancient Greeks constituted an essential reference for the scientific research undertaken by the moderns. In his Latin editions, Commandino cleverly combined his philological and mathematical skills. Philology and mathematics, moreover, nurtured each other. In this article, I analyze the Greek and Latin manuscripts and the printed edition of Apollonius’ Conics to highlight in a specific case study the role of the editions of the classics in the renaissance of modern mathematics
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The Latin edition of Archimedes’s works published by Commandino in 1558 constitutes an important exemplar of mathematical humanism. Focusing on the Spirals, this paper aims to perform a comparative analysis between the manuscripts of... more
The Latin edition of Archimedes’s works published by Commandino in 1558 constitutes an important exemplar of mathematical humanism. Focusing on the Spirals, this paper aims to perform a comparative analysis between the manuscripts of Urbino and Los Angeles, the editio princeps of Basel (1544), and the printed edition by Commandino (1558). Such investigation leads to the following conclusions: 1) Commandino’s enterprise began from the Latin version of Iacopo from San Cassiano and, through a progressive work of revision, produced a completely new Latin text; 2) the final edition of the Spirals represents the result of deep mathematical assimilation of Archimedes’s work, which allowed the Urbino scholar to provide modern readers with a text rich in comments and explanations of the implicit and obscure passages that characterized Archimedes’s treatise.
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In the Urbino University Library, a large manuscript documentation is conserved, useful for bringing into focus Commandino's philological and mathematical skills and for shedding light on further developments regarding the school of... more
In the Urbino University Library, a large manuscript documentation is conserved, useful for bringing into focus Commandino's philological and mathematical skills and for shedding light on further developments regarding the school of Urbino after his death. In this article a first survey is made of the manuscript sources preserved in the “buste” 120 and 121 , with the purpose of orienting and stimulating further research on Commandino and his school. By means of this survey it was possible to identify with certainty the autograph manuscripts of Commandino and to date the folios that conserve the preparatory study for the printed editions of the works of Archimedes (1558), Ptolemy (1558, 1562) and Pappus (1588).
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The manuscript Urb. Lat. 1329 from the Vatican Library is a luxury parchment codex of 67 folios, copied in 1458 by Michael Foresius and commissioned by Francesco Cereo dal Borgo. Folios 1r-19r contain a treatise entitled Euclidis de... more
The manuscript Urb. Lat. 1329 from the Vatican Library is a luxury parchment codex of 67 folios, copied in 1458 by Michael Foresius and commissioned by Francesco Cereo dal Borgo. Folios 1r-19r contain a treatise entitled Euclidis de aspectuum diversitate libellus. So far, no transcripts or critical editions of De aspectuum diversitate have been published. Yet, the references to this title contained in the De prospectiva pingendi by Piero della Francesca suggests the importance of this Latin version of Euclid's Optics known to scholars for a long time. Until now, we had believed that the only manuscript containing the Euclidean Optics under the title De aspectuum diversitate was Urb. Lat. 1329. However, I have discovered a second manuscript with the same title that is currently found in the Milan Ambrosiana Library under the shelf mark P 81 sup. At the review stage, the following conclusions have been drawn: 1) The Ambrosiana codex is an apograph of Urb. Lat. 1329 and was therefore written after 1458; 2) Urb. Lat. 1329 contains a Latin version of Optics B that Heiberg called Recensio Theonis; 3) Contrary to what has been thought so far, the Latin translation of the De aspectuum diversitate was made directly from the Greek and not from Arabic; 4) Several clues suggest the codex Vat.gr. 204 as being the Greek manuscript translated into Latin in the sixth decade of the XVth century.
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The Latin translations of two works by Euclid, Optica and Phaenomena, constitute the first two treatises of the Urb. Lat. 1329 preserved in the Biblioteca Apostolica Vaticana. The study of Phaenomena Latin edition led to the following... more
The Latin translations of two works by Euclid, Optica and Phaenomena, constitute the first two treatises of the Urb. Lat. 1329 preserved in the Biblioteca Apostolica Vaticana. The study of Phaenomena Latin edition led to the following results: 1) its text derives from what Menge, in his critical edition, defined «version b»; 2) the Greek manuscript, from which the Latin edition of both Phaenomena and Optica comes from, is Vat. Gr. 204; 3) by means of the collation of the manuscripts Urb. Lat. 1329 and Par. Nouv. Acq. Lat. 1538, in which is contained the autograph of the Latin Archimedes by Iacopo from San Cassiano, three important clues emerge that indicate Iacopo as the possible author of Euclid’s Latin translations copied by Foresius in Urb. Lat. 1329
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Since his early works, Galileo never hid his admiration for the divine Archimedes. Galileo’s praise is not only evident in the apologetic adjectives that he reserved to the Syracusan mathematician; it is especially in the epistemological... more
Since his early works, Galileo never hid his admiration for the divine Archimedes. Galileo’s praise is not only evident in the apologetic adjectives that he reserved to the Syracusan mathematician; it is especially in the epistemological approach that Archimedes guided the Pisan mathematician in the foundation of the new science of motion. The study of the wonderful Spirals of Archimedes was for Galileo an important source of inspiration not only for the principle of composition of the motions illustrated in the Dialogo but also for the attempt to revise the Euclidean definition of proportionality contained in the fifth day of Discorsi. The comparison between the sheets 138r-v of the manuscript Gal.72 and the Latin translation of Archimedes’ works, published by Commandino in 1558, shows that Galileo used Commandino’s edition of the Spirals to elaborate the first of his theorems on uniform motion.
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1. Pacioli e la teoria vitruviana delle proporzioni nel primo Rinascimento Nel corso del primo Rinascimento le teorie architettoniche vitruviane, dopo la riscoperta umanistica del De architectura, trovarono ampio spazio nella... more
1. Pacioli e la teoria vitruviana delle proporzioni nel primo Rinascimento Nel corso del primo Rinascimento le teorie architettoniche vitruviane, dopo la riscoperta umanistica del De architectura, trovarono ampio spazio nella trattatistica del XV secolo. Della mastodontica opera di Vitruvio, tuttavia, fu soprattutto un tema a catturare l'attenzione di artisti e teorici rinascimentali: la teoria delle proporzioni del corpo umano.
In Pacioli's Compendium de divina proportione, the author showed to his readers Leonardo da Vinci's illustrations of the regular solids. The graphic style of these illustrations differed radically from both the manuscript tradition of... more
In Pacioli's Compendium de divina proportione, the author showed to his readers Leonardo da Vinci's illustrations of the regular solids. The graphic style of these illustrations differed radically from both the manuscript tradition of drawing the solids in Euclid's Elements and the innovative solutions presented by Piero della Francesca in his Libellus de quinque corporibus regularibus. Pacioli's Platonic solids, which represented the divine proportion, became real and measurable entities. The relationship between the geometrical text and the figures is reversed: Leonardo's illustrations, in fact, were not anymore necessary tools to develop the deductive passages of a demonstration-as it was for the geometrical figures in the manuscript tradition of Euclid's Elements.
Game theory is a formal way to analyze the interactions among groups of subjects who behave each other. It has historically been of great interest in the economic fields in which decisions are made in a competitive environment. Game... more
Game theory is a formal way to analyze the interactions among groups of subjects who behave each other. It has historically been of great interest in the economic fields in which decisions are made in a competitive environment. Game theory has fascinating potential if applied in the medical science. Few papers have been written about the application of game theory in surgery. The majority of scenarios of game theory in surgery fall into two main groups: cooperative and no cooperative games.