De resolutione et compositione mathematica libri quinque. Opus posthumum

THE COPY OF KENELM DIGBY - THE BIRTH OF ANALYTIC GEOMETRY. First edition, extremely rare, and a magnificent copy from the library of Kenelm Digby, of the most important work of the great Croatian mathematician Marino Ghetaldi (or Marin Getaldi?) who, while he did not introduce coordinates, is regarded by many scholars, on the basis of the present work, as the founder of analytic geometry - Descartes' Géométrie was not published until seven years later. De resolutione is the first comprehensive work devoted to the application of the methods of symbolic algebra introduced in François Viète's epoch-making In artem analyticam isagoge (1591) (a work of only 9 pages). "The final stage in the embryonic evolution of analytic geometry was to transfer the purpose of Viète's analysis away from geometrical constructions to the solution of algebraic equations, and towards the application of the already well-known algebraic techniques to the solution of geometrical problems. This transformation was first effected by Viète's contemporary and one-time pupil Marino Ghetaldi, in his posthumously published De resolutione et compositione mathematica (Rome, 1630). Here, the status of symbolic algebra was raised from a 'means to an end' to a method in its own right, with a wider scope and application than it had hitherto possessed . Ghetaldi has been hailed by various mathematicians as the father of analytic geometry . perhaps an acceptable compromise is to regard this science as having been conceived jointly by both of them . One might tentatively date the moment of conception as Ghetaldi's first meetings with Viète in Paris, and the time of birth as shortly before [Ghetaldi's] death when he is known to have composed this treatise . two things follow from the proposed interpretation of the birth of analytic geometry: one is that it did not require the adoption of the coordinate principle; and the other is that it occurred prior to the publication of Descartes' Géométrie" (Forbes, pp. 147-8). "Getaldi?'s mathematical works can be divided into two essentially different groups. The first group consists of the five works published while he was alive, the second consists of the posthumously published work [De resolutione]. In the first group of works, Getaldi? solved geometrical problems by Greek methods, while in the last mentioned work he used algebraic analysis" (Dadi? 1984, p. 208). De resolutione is divided into five books, the last being the most important. The third chapter in the fifth book deals with algebraic problems with infinitely many solutions, which Ghetaldi calls 'Problemata Vana et Nugatoria'. Of these, the solution to the fourth problem is represented by a point which traces out a hyperbola when a certain length is varied; in the fifth problem a similar construction leads to an ellipse. These are regarded as the first descriptions of curves by means of algebraic equations. "Due to the fact that Getaldi? came very close to the realization that all points that satisfy an indeterminate problem are on some curve, . [it] was argued that Getaldi?, through his major work, indirectly participated in the preparation and creation of the synthesis of the arithmetic continuum of numbers and the geometric continuum of points, realized in Descartes' analytical geometry, on the basis of which infinitesimal analysis later developed" (Bori?, pp. 69-70). Ghetaldi met and corresponded with the Jesuit mathematicians Christopher Clavius, Christopher Grienberger and Paul Guldin, and also with Galileo, whose influence can be seen in Ghetaldi's use in the present work of the terms analysis (resolutio) and synthesis (compositio), rather than Viète's exegetics, poristics and zetetics. ABPC/RBH list only the Macclesfield copy in the last 35 years, and only one copy in the quarter-century before that. OCLC lists Brown, Columbia, Huntington, Kansas, Temple, and Yale in the US. Provenance: Sir Kenelm Digby (1603-65), philosopher (gilt arms on covers and his wife.…