76 Stand 21 Antiquariaat Papyrus (Rita Colognola) Sir Winston Churchilllaan 733, NL- 2287 AN Rijswijk, Niederlande Telefon +31-(0)6-4 81 540 24 e-mail: colog19@hetnet.nl, www.papyrusrarebooks.com Old and rare books Carlo Renaldini  Opus  mathematicum  in  quo  utraque algebra, vetus scilicet, & nova a se in opere. hac de re pridem editio, pertractata novis preceptis & novisq(ue) demonstrationibus illustratur. Bononiae, ex typographia H.  H.  Ducii,  1655.  4to.  12  unn.  ll.,  475  pages.  With several woodcut schemes and diagrams. Contemporary Italian vellum, edges mottled in blue. Little foxing and browning in a few places (as usual with the Bolognese editions  of  the  XVII  century),  otherwise  a  fine  copy. € 6.000,- First  edition,  reprinted  in  1677.  The  section  on  resolution  and composition  of  equations  was  separately  printed  in  1667.  Carlo Renaldini (Ancona 1615 - 1698) descended from a noble family of Ancona. After a career as engineer in the papal army he was appointed to lecturer in philosophy at the University of Pisa in 1644. He was one of the most active members of the Accademia del Cimento. Renaldini was an ambiguous figure, tempted to adopt the innovative Galilean philosophical-scientific approach, yet still imbued with the attitudes and prejudices of Aristotelianism. During his academic spell in Pisa he often clashed with Giovanni Alfonso Borelli (1608-1679). He carried out astronomical observations with Toscanelli‘s gnomon in the basilica of Santa Maria del Fiore in Florence. He tutored Prince Cosimo III (1642-1723). In 1667, he obtained the chair of philosophy at the University of Padua. He composed several works of mathematical and philosophical subject, such as Opis algebricum (Bologna 1648), Ars analytica mathematicum (Florence-Padua, 1665-1669), De resolutione et compositione mathematica (Padua, 1668) and Philosophia rationalis , naturalis atque moralis (Padua, 1681) and contributed to the famous volume  containing  the  experiments  carried  out  in  the  Accademia del  Cimento  (1666). „In  this  almost  unknown  work  Renaldini  ... relates  the  discoveries  of Vieta  and  Girard,  and  use  new  curious notations“(Libri, cited in Riccardi). „Includes, among other problems, an approximate rectification of the circle by trigonometrical means.“ (Sotheran). This is thus one of the first books to use the new algebric notations of Viète and Girard in Italy, which had already set firm foot in the rest of Europe. A complete edition of Viète‘s works had appeared by Elzevier in 1646, thus witnessing some delay in the Italian reception of the new symbolism. The book is divided in 19 chapters, dealing with different types of equations and proposing new method to solve them, and discussing the methods proposed by previous scientists, including Diophantus, which Renaldini must have read in the edition of 1621, Stevin and Coignet. The whole book is essentially intended for practical applications as stated in the introductory dedication to the Grand Duke of Florence. Riccardi I/2, 347: „Raro“; Sotheran 14028; Honeyman 2625. This copy appears to be the first appeared on the marked after the Honeyman copy. René Ouvrard L’art et la science des nombres en françois et en latin ou l’arithmétique pratique et speculative … A Paris,  chez  Lambert  Roulland  et  Christophe  Ballard, 1677. 4to. 16 unn. ll. (including additional engraved title and half-title), 338 pages, 3 unn. ll. With one unnumbered leaf containing music scores between pages 122-123 and several  woodcut  diagrams  in  the  text.  Contemporary French calf, spine gilt. Front free endpaper detaching but still solid, an occasional spot, stamp of the “Bibliothéque d’artillerie” on half-title and title, otherwise a very good copy. € 4.500,- Only edition. “René Ouvrard (Chinon 1624 – Tours 1694) (was) a French theorist, musician, ecclesiastic and man of letters. As a youth Ouvrard  trained  in  theology  and  music  in Tours.  About  1657  he was maître de chapelle at Bordeaux cathedral, about 1660 chef de la maîtrise at the St. Just cathedral, Narbonne and from 1663 at the latest  maître  de  musique  at  the  Sainte-Chapelle  until  in  1679  he retired to Tours as canon at the church of St. Gatien. Ouvrard wrote widely on theology and on arts and science. He was active both in academic and musical circles, especially in Paris, and corresponded with leading church and lay figures. Although his compositions seem not to have survived, he is known to have favored the Italian style (especially motets and oratorios in the style of Carissimi), for which he developed a taste while visiting Italy in 1655. His writings contain significant contributions to a knowledge of music theory, through both his comprehensive presentation of it and his attempts to relate it to other intellectual pursuits of his day.” (Grove). “En 1679, alors qu’ il était maître de chapelle à la Sainte Chapelle de Paris, Ouvrard faisait publier chez La Caille un ouvrage intitulé Architecture harmonique … Ouvrard n’était pas à son premier essai sur les proportions puisque, deux ans auparavant, il avait présenté un ouvrage sur l’Art et la Science des nombres … où déjà il envisageait les connivances entre proportions harmoniques et speculations mathématiques. Il prévient d’ailleurs le lecteur ‘qu’il faut supposer la doctrine des proportions, établie dans le livre entitulé L’art et la science des nombres, principalement dans le sixième  livre  de  l’Arithmétique  harmonique,  pour  bien  entendre  sa demonstration … Ces quelques elements permettent de situer René Ouvrard dans le courant néo-platonicien qui animait une partie des théoriciens et penseurs francais de la fin du XVIIe siècle. En effet, il part du principe que, grâce aux mathématiques, on arrive à saisir les structures intimes de la réalité. N’avait-il pas écrit dans la preface de L’Art et la science des nombres que ‘l’arithmétique est comme la clef de toutes les autres sciences’ et que, dans cet ordre d’idées, Platon peut être pris comme modèle car, en insistant sur les arts et sur les sciences, il transformait ‘en Dieu les autres hommes’. Il s’agit d’un néoplatonisme dans  la  mesure  où,  bien  que  l’homme  soit  déjà  en  possession  des vrais  principes  de  la  nature  du  monde  physique,  il  n’en  demeure pas moins que le seul raisonnement ne suffit pas. Ouvrard use donc une dialectique dont l’un des poles est la raison et l’autre la pratique expérimentale sous forme d’observations bien conçues.” (Vendrix). Cioranescu 51683; Wellcome II, page 275; The New Grove (1980) XIV, page 32; P. Vendrix (Proportions harmoniques et proportions architecturales dans la théorie française des XVII et XVIIIe siècle, International Review of the Aesthetics and Sociology of Music 20(1), June 1989) pages 3-10.