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3 vols large folio, mm. 430 x 310. Contemporary binding full brown, double ornamental frame on the covers, six bands on spine with gilt titles and dentelles; 6 unnumbered leaves, pp. [2], 3-418, [18 Index], 2 bl., with numbering errors; pp. [6], 3-528, i.e. 437, [30 Index], the numbers jump from 309 to 400; pp. [6], 3-490, [9, Index], 1 bl. Text within linear frame,

The work, beautifully illustrated, especially in the sections devoted to the practical geometry and military architecture, is of great importance for the history of mathematics. Giordano Vitale held the mathematics course at the Academy of France, a position achieved in 1667 also thanks to the favor of Christine of France; in 1672 he was also named Engineer of Castel Sant'Angelo; in those years he was working on his famous Euclide restituto, also born as a course of lectures. There are known unpublished manuscripts of the mathematician of Bitonto, in particular some volumes that are part of a planned course in mathematics, which never saw the light. We have confirmation of this project in the preface of Mattei to Euclide Restituto [1680]: ?E però il Signor Vitale Giordano, Autore di quest?Opera, Geometra celebre fra i migliori della nostra età, dopo lunghe fatiche fatte nello spatio di ventiquattr?anni, havendo aggiustato un Corso Matematico, ove pienamente si tratta non solo la parte Teorica, però anche la prattica utilissima alle indigenze della vita humana, gli parve in questo primo Tomo degli Elementi seguitare il bell?ordine d?Euclide?? Taken together, these three volumes are a first-rate document for the study of encyclopaedic mathematical knowledge of Giordano and the Roman academic world around which he revolved, in the period when he was teaching at the Academy of France, where it occupied the chair of mathematics up to 1685.In addition to substantial sections devoted to practical geometry and military architecture, disciplines in which Giordano was very competent by virtue of his experience in the fleet and the army of the Papal State, the manuscript is of special importance for the history of seventeenth-century mathematics. It's light on the multifaceted scientific training of Giordano and its relations with the most innovative mathematical research of his time: in particular, the vastness and complexity of this ?Studio di Matematica? explicitly calls looking for a Mathesis Universalis, according to the intention of Viète. First, the Proemio is, as already indicated, the first draft of the text which opens the best-known work by Giordano, the Euclide restituto; then the third volume represents the transmission in Italy of the new algebra opened by F. Viète, which pays tribute from the title; finally, it seems of particular interest to note that emerges an unusual connection between Giordano and the French mathematician Pierre Hérigone found it has ever been reported. In the second volume, in fact, the Tattioni Apollonius, i.e. the Apollonius Contacts, are exposed in the reconstruction of Viète as they are illustrated in 16 Problems to Pierre Hérigone in his Cursus mathematicus of 1634; the Inclinations of Apollonius are exposed in the version that provides Marino Ghetaldi, the Dalmatian mathematician Marin GetaldiÄ?, published in the book of Hérigone.The last part of the volume, starting from ?Tattioni?, resumes the Treaty of Pierre Hèrigone, here called Origonio and Irigonio, but develops it in an original manner, with different exposure of the demonstrations and with additions. This section of the manuscript is particularly important, because just working on the problems of Apollonius and Theone, Viète axiomatizes his algebraic formalism in his Isagoge of 1591. Viète distinguishes between ?algebra numerosa?, in which the data are numbers, and ?algebra speciosa?, " in which the data are quantity of any kind, objects that are not expressed in numerical terms, but through letters that make it possible to treat a variety of situations in a numerical or geometric manner. In this way it is proposed a relationship between geometry and algebra, in which the letters are the bridge between numbers and quantities: geometric reading of algebraic formulas and, conversely, the algebraic expression of the geometric relationships. It goes like this way the generator concept of analytical geometry, which constitutes a general algebraic method to solve geometric problems.

wed 19 February 2020

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