De resolutione et compositione mathematica libri quinque. Opus posthumum

THE COPY OF KENELM DIGBY - THE BIRTH OF ANALYTIC GEOMETRY. First edition of the posthumous treatise in which Viète's pupil turned the new symbolic algebra systematically on geometry, the book that 'has been referred to as the first textbook on algebraic geometry' (Boyer), the copy of Sir Kenelm Digby (1603-1665), in the armorial binding made for him in Paris, stamped with the arms of Digby and the cypher of his marriage to Venetia Stanley. On its account Ghetaldi 'has been hailed by various mathematicians as the father of analytic geometry' (Forbes), a title that Forbes himself would divide between Ghetaldi and Viète. The book stands between Viète's In artem analyticem isagoge of 1591, which had introduced letters for known as well as unknown quantities, and Descartes's Géométrie of 1637, which gave curves their equations. Ghetaldi's subject is the ancient method of analysis and synthesis. A problem is assumed solved, an equation is set up in Viète's letters, and the construction is then recovered from the equation and proved. The algebra per species immutabiles, Ghetaldi writes on his second page, leaves vestigia clara, clear traces by which the analysis can be retraced, where the common algebra of numbers confounds them. He was one of a small group, with Alexander Anderson, Willebrord Snell and later Fermat, who were restoring the lost analytical books of the Greeks. Fermat, writing in 1658 to the owner of this copy, set his own treatises beside the works of Viète, Ghetaldi and Snell as that restoration. The five books carry the method through the problems of elementary geometry up to the second degree. They close with a classification of what an equation can tell its author: that a problem is impossible, that it has one solution, or that it has infinitely many. It is in the last class that Ghetaldi came closest to the analytic geometry he never named. The copy passed later to the ducs de Broglie, whose armorial label is on the pastedown. Two copies of the edition have come to auction in the last forty years, and no other in an armorial binding is recorded on the market. Provenance: Sir Kenelm Digby (1603-1665), philosopher, diplomat and founding council member of the Royal Society, with his gilt arms on both covers and the interlaced cypher KVD in six compartments of the spine, the binding made for him in Paris; the Paris library, left there at his death, claimed by the French crown and sold; the house of Broglie, ducs de Broglie and princes of the Holy Roman Empire, with their engraved armorial label, nineteenth-century in style, on the front pastedown. The arms stamp is the second of the four types that Léopold Delisle distinguished in 1892: the quartered coat of Digby, Pakeman, Mulsho and Neville with the Stanley escutcheon of pretence at the centre, the barred helm and the ostrich holding a horseshoe for crest. Delisle's second and third types, both paired with the KVD monogram, are the stamps Digby adopted for his Paris bindings; Émile Chatelain found them on no book printed after 1641 and placed the fourth type, with the plain KD monogram, in the years 1641 to 1665. The V is Venetia's. She had died in 1633, and the cypher kept her name on the spines of books bound years afterwards; Chatelain found the KVD form rarer among the survivors than the plain KD. The tooling is of the Parisian pattern called à la Du Seuil, a double frame of fillets with a pointillé roll and sprays at the inner corners, the pattern in which the Sorbonne keeps Digby's Descartes of 1637 and his Montaigne of 1635. The Paris library, some 3,500 volumes, was left in Paris when Digby returned to England in 1660 and was claimed by the French crown at his death. A printed catalogue of books issued without place or date, which the Bibliothèque nationale assigns to the sale of Digby's Paris library about 1665, lists the work on its page 10; it does not appear in the Bibliotheca Digbeiana, the London sale of 19 April 1680 of the library of Digby's cousin.…