# De speculo ustorio, ignem ad propositam distantiam generante, liber unicus. Ex quo duarum linearum semper appropinquantium, & numquam currurrentium colligitur demonstratio **Autore:** Finé Oronce **Dati editoriali:** Paris, Michel Vascosan, 1551 **Codice archivio:** 164 **Prezzo:** 2500.00 USD **Stato commerciale:** Disponibile **Link ufficiale:** https://www.govirarebooks.com/products/oronce-fine-de-speculo-ustorio-1551 --- ## Descrizione accademica e analisi 4to (199x139 mm). 25, [1 blank] leaves. Collation: A-E4 F6. The final leaf F6 is a blank. Roman and italic types. With several woodcut diagrams and illustrations in text. Modern stiff vellum. Some pale foxing and browning, but a good copy. Rare first edition of this treatise on burning glasses or concave mirrors, which includes mathematical analysis and methods of their construction. Such mirrors were used in metallurgy and in assaying. The edition is dedicated by the author to the English ambassador to France, Sir John Mason (dated Paris, October 1551). The dedication is followed by a poem by Antoine Mizault in praise of the work. As evidenced by a partial manuscript version of the treatise (Bibliothèque Nationale, Ms Lat. 7415, 10-17), which predates the printed edition by three years, the De speculo ustorio had in fact already been completed around 1548. The reason why Fine waited another three years before publishing it remains a mystery. The date of the manuscript, however, rules out any possibility that Fine’s work was derived from that of Antonius Gogava, a mathematician in the circle of Gemma Frisius, who published a treatise on burning mirrors in Leuven in 1548 as an appendix to an edition of Ptolemy’s Tetrabiblos that he had edited. On that occasion, Gogava also published Alhazen’s De speculis comburentibus and a treatise of uncertain authorship (Speculi almukesi compositio) datable between 1250 and 1350, which Gogava attributes to Roger Bacon, while Fine considers it of Arabic origin; since it had been widely circulated in manuscript form, it is likely that Fine was familiar with the Speculi almukesi compositio (one of his primary sources) well before the printed edition of 1548. The De speculo ustorio consists of two parts: one geometric, dealing with the parabola, and the other, more “mechanical,” dealing with the construction of a parabolic mirror. Fine also places his mathematical discussion of the parabola within an optical context, setting forth four optical postulates at the beginning of the volume. The inclusion of optics within a work dedicated to burning mirrors, while it may seem obvious today, was by no means so in the mid-sixteenth century. Thanks to an Italian translation, the De speculo ustorio exerted great influence in Italy, especially through the work of Giovanni Battista della Porta, who drew heavily on Fine’s treatise. “Oronce Fine set out to revive mathematics in Renaissance France, specifically in the curriculum at the Collège de France. De Speculo Ustorio and other books were his effort to provide the necessary awareness of mathematic and provide students textbooks. This is the origin of and intention for his textbook on mathematical optics and parabolic burring mirrors, which included mathematical analyses and methods of construction. As Fine stats in the preface, his most important optical source for De Speculo Ustorio was Witelo’s Perspectiva. Though Fine likely had access to the Perspectiva’s printing in 1535, it is known that he worked from a manuscript copy before the 1535 printing. His other optical source was an edited version of Alhazen’s De Speculis Comburentibus which had been printed in 1548. Fine’s parabolic geometry comes from Georgius Valla’s De Expetendis et Fugiendis Rebus Opus of 1501 and from Johann Werner’s Libellus of 1522. Though not of original material, the De Speculo Ustorio was a carefully crafted compilation of sections of select texts, comprising a much-need textbook on catoptrics. It was the first such book printed in France and like his other books was widely popular, esteemed for its careful presentation, straightforward Latin, and the excellence of its figures. De Speculo Ustorio, along with several other of his books, became widely used throughout Europe at universities in need of up-to-date textbooks. In this, Fine took advantage not only of his knowledge of optics and geometry, but also of the need and ability of students. An Italian translation of De Speculo Ustorio appeared in 1587 as an appendix to a translation of another of Fine’s books, Protomathesis. Fine’s Propositions 8 and 9 were repeated nearly verbatim in Giovanni Battista Della Porta’s Magiae Naturalis of 1558 […] Fine’s textbook has the intention of exercising mathematical analysis in catoptrics, of showing the superior nature of paraboloids as burring mirrors, and to show practical methods to make such mirrors. First, there are 12 definitions involving conic sections, then four postulates involving the laws of reflection. There follow propositions, proved using Euclid’s Elements, culminating in Proposition 7, showing that incoming rays parallel to the axis of the parabola are all reflected to the same point, the focus. Proposition 8 shows a way to draw a parabola and Proposition 9 demonstrates a way to construct a parabolic burning mirror using the method in Proposition 8. Proposition 10 involves the hyperbolic conic section, though it is not named as such” (D.L. DiLaura, Bibliotheca opticoria 1475-1925, Boulder, CO, 2019, pp. 23-24). “In 1551 Oronce Fine published De speculo ustorio. It was one of the first works on optics to be published in France. At this point the only optical treatise widely available in print in France was – if we exclude Jean Pélerin Viator’s De artificiali perspectiva – the Introductio in scientiam perspectivam of the French humanist, Charles de Bovelles. First printed in 1503 in Paris, its availability was enhanced by Fine’s reprint of the work as an appendix to his edition of Gregor Reisch’s Margarita Philosophica of 1535. Bovelles’ treatise was, however, quite unlike Fine’s own work on burning mirrors. Bovelles’ treatise was a basic introduction to the science of optics, structured around definitions of sight, light, shadow, colour, rays and mirrors, without demonstrations and with simple, even crude small diagrams […] The audience which Bovelles envisaged for his practical optics, and Fine for De speculo ustorio, did not consist of the mirror-makers themselves. Even if mirror-makers would have been trained in a ‘school’ (and there is only one known example of such a training outside the master-apprentice-relation in France), Fine’s work on burning mirrors was in Latin. It did, however, fit the model of the text-book promoted at the Collège Royal, where Fine held the royal chair in mathematics, and where the whole field of mathematics, the old quadrivium and also ‘new’ branches, such as perspective, or optics and catoptrics, were taught. The Collège Royal favored the spreading of mathematical knowledge through ‘practical’ approaches, and Fine published several mathematical text-books in which instruments were central. The Collège Royal also was, however, strongly attached to humanism, and the kind of knowledge which Fine offered in De speculo ustorio was ‘bookish’ knowledge. It was based on Fine’s reading of manuscripts and books on burning mirrors rather than on visits to workshops […] Thus, the manuscript version of 1548 shows that Fine’s knowledge of burning mirrors was, first, of a practical geometrical kind, and second, bookish, since Fine’s De speculo ustorio was a re-working of older manuscript material. The additions of 1551 alter little to this image of Fine’s knowledge. Fine added proposition 9, in which he discussed the fabrica of a burning mirror. However, the first part of the proposition was only a substantially shortened paraphrase of the section on the ‘conditions of good steel’ which he had found in the Speculi almukesi compositio. It is indicative of the distance between Fine’s De speculo ustorio and workshop practice that Fine borrowed from a thirteenth or fourteenth-century text a section on the making of a mirror of steel, while the important technical development in mirror-making of his own time was the diffusion of techniques to make glass cristallo mirrors. Fine also added an alternative procedure for making a burning mirror. This method consisted of casting the mirror instead of grinding it. The procedure was, however, mathematised. Fine was most concerned with the preservation of the parabolic curve. His alternative procedure for making a mirror testifies more strongly of Bovelles’ call for the mathematisation of the art of mirror-makers than of any familiarity with workshop practice. Fine also briefly mentioned techniques and products, which were used for polishing in contemporary workshops, not included in the Speculi almukesi compositio. The inclusion of this material knowledge assumes some familiarity with contemporary mirror-making practices, but Fine’s brief notes on this hardly function as a practical guide for making mirrors (nor are they intended as such). Finally, Fine also added a short note on the annular or ring mirror type, but again the addition is bookish […] Fine included four optical postulates at the beginning of De speculo ustorio. The first postulate defined a solar ray as a mathematical line; the second stated the law of equal angles for plane mirrors; the third expanded this law to convex and concave mirrors; and the fourth stated that a burning mirror which will reflect the incident solar rays to one point of combustion produces the quickest and most intense combustion of all burning mirrors, and that the parabolic burning mirror is such a mirror. These postulates place the otherwise strictly geometrical discussion of the parabola in an overtly optical context […] In 1587 Fine’s De speculo ustorio was published as an appendix to Cosimo Bartoli’s translation of Fine’s Protomathesis, in an Italian translation by Ercole Bottrigaro, a Bolognese humanist who had also edited Ptolemy’s Geographia. Bottrigaro frequented the circle of Gian Vincenzo Pinelli, one of Europe’s most important collectors of books and manuscripts at the time. To Pinelli’s circle also belonged Filippo Pigafetta and Guidobaldo del Monte. Around 1597 Pigafetta discussed the idea of a museum of military architecture, to which the Medici collection of drawing and measuring instruments would be added, with the Grand Duke of Tuscany Ferdinando I. The project never materialized, but the Stanza delle Matematiche of the Uffizi, housing a collection of mathematical instruments, was decorated around 1600 by Giulio Parigi with ancient war instruments, which were, in the original proposal, meant to be actually present in the collection. One of these instruments was Archimedes’ burning mirror. Bartoli’s and Bottrigaro’s Italian translation of Fine’s works was dedicated to Guidobaldo del Monte» (S. Dupré, Printing Practical Mathematics. Oronce Fine’s De speculo ustorio between Paper and Craft, in: “The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France”, A. Marr, ed., Donington, 2009, pp. 1-2, 8-9, 10-11, 14, 15, 20-21). Oronce Fine (or Finé), known in the academic world by his Latinized name Orontius Finaeus, was an important figure of the French Renaissance. Appointed by King Francis I as the first Chair of Mathematics at the Collège Royal in 1531, he revolutionized how the exact sciences were taught and perceived. From 1515 Fine edited astronomical and mathematical writings for printers in Paris and abroad, such as Peuerbach’s Theoricae planetarum and Sacrobosco’s De sphaera, as well as a tract on the plague written by his grandfather Michel Finé. In his first printed book (1526) and other unpublished works, Fine focused intensely on the equatorium - a complex instrument used to determine the true positions of planets without tedious calculation. His primarly interest in astronomy soon extended to astrology, even tough he only wrote minor works. Fine was a polymath artisan: he did not merely write academic prose, but personally designed the intricate woodcut illustrations, mathematical diagrams, and world maps that populated his books (cf. A. Marr, Op. cit., passim). --- ## Bibliografia di riferimento Adams, F-474; DiLaura, no. 21. --- *Documento generato automaticamente dall'Archivio Govi Rare Books per finalità di ricerca e catalogazione.*