Manuscript of Mathematics. GIORDANO, SPINOLA.

Manuscript of Mathematics. GIORDANO, Vitale, SPINOLA, Giacomo. Studio di Matematica fatto da Giacomo Spinola sotto la direzione del Sig.r Vitale Giordano Ingegniero di Castel S. Angelo e Lettore di Matematica nellAccademia Reale della Maesta Cristianissima in Roma. Tomo primo [– terzo]. Manoscritto Codice manoscritto cartaceo, Roma, lAnno del Giubileo, 1675

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, hundreds of geometric figures accurately traced with a pen in the text with the use of the compass, many architectural drawings and perspectives. Clear and legible writing, very spaced.In total 1,426 pages of text, including titles and indices.Waterstain on many pages of the first volume, the second volume with some pages browned, the third volume in good condition.
Condition Report: Important manuscript of an unpublished work of the great mathematician of the seventeenth century Vitale Giordano. The student Giacomo Spinola transcribes the lessons that Giordano took at the Academy of France in 1675. The three volumes bear the following titles: Tomo Primo continente lAritmetica la Geometria Pratica la Gniomonica; Tomo Secondo continente la Trigonometria piana il misurare in lontananza lArchitettura militare il moto eqabile naturalmente accelerato, e de proietti, le speculationi dApollonio sopra le tattioni, linclinationi, la determinata settione, la settione della proportione, e la settione dello Spatio; Tomo terzo Algebra speciosa o vero Analitica Universale. The first volume opens with a preface that bears the same title of the first chapter of Euclide Restituto, "Che cosa sia la Matematica e quali sieno le sue parti" [What is Mathematics and what its parts], leaves 4,6; the text is almost identical to that of the printed work from page 1 to page 3, but has some minor variations. Follow the treaties mentioned in the title: Arithmetic, up to p. 103 [unnumbered]; Geometry Practice, p. 99; Sundials, p. 345.The second volume is divided into the following chapters: Trigonometry, up to p. 34; Del misurare in lontananza [About measure from a distance], p. 35; Military architecture, p. 59; Del Moto Equabile [About uniform motion], p. 129; Del moto dei gravi naturalmente accelerato [About naturally accelerated motion of heavy], p. 147; Del moto dei proietti [About motion of projectiles], p. 243; Tattioni di Apollonio investigate da Franco Vieta [Contacts of Apollonius investigated by Franco Vieta, i.e. Francois Viete] p. 467; Inclinationi di Apollonio investigate da Mario Chetaldo [Inclinations of Apollonius investigated by Mario Chetaldo, i.e. Marino Ghetaldi], p. 489; Della determinata Settione [About the determined Section], p. 509; Della Settione della Proportione [About the Section of proportion], p. 517; Della Settione dello Spatio [About the section of the space], p. 521. The third volume is divided into: Algorithm, up to p. 110; DellEquatione [About the Equation], p. 110; DellEquatione Amfibale, p. 227; DellEstrarre le Radici semplici e affette dei Numeri [About the extraction of simple roots and with numbers], p. 265.

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 SantAngelo; 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 pero il Signor Vitale Giordano, Autore di questOpera, Geometra celebre fra i migliori della nostra eta, dopo lunghe fatiche fatte nello spatio di ventiquattranni, havendo aggiustato un Corso Matematico, ove pienamente si tratta non solo la parte Teorica, pero anche la prattica utilissima alle indigenze della vita humana, gli parve in questo primo Tomo degli Elementi seguitare il bellordine dEuclide." 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. Its 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 Viete. 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. Viete, 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 Herigone 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 Viete as they are illustrated in 16 Problems to Pierre Herigone in his Cursus mathematicus of 1634; the Inclinations of Apollonius are exposed in the version that provides Marino Ghetaldi, the Dalmatian mathematician Marin Getaldi", published in the book of Herigone.The last part of the volume, starting from "Tattioni", resumes the Treaty of Pierre Herigone, 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, Viete axiomatizes his algebraic formalism in his Isagoge of 1591. Viete 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.