Sphinx Geometra, seu quaesita geometrica proposita, et soluta. Rursus prodeunt sub auspiciis, serenissimi principis Francisci Farnesii.

Excudebant Parmae, Alberttus Pazzonus et Paulus Montius Socii, 1694. 12mo. 112 pages. 13 out-of-text engraved plates, of which 8 are folding. Contemporary full vellum, spine with nerves. First Collective Edition, printed in Parma, of this valuable collection of geometric problems solved by the Sicilian mathematician Ruggero Ventimiglia (1670-1698) and his correspondent Girolamo Saccheri (1667-1733), the famous precursor of non-Euclidean geometry, respectively aged twenty-four and twenty-seven. Coming from a prominent Sicilian family that had maintained links with renowned mathematicians Francesco Maurolico (1494-1575) and Giovanni Borelli (1608-1679), Ventimiglia had published in 1690, at the age of twenty, the solutions to twelve geometric problems that an anonymous Dutch geometer "hidden behind the blackboard" ("geometra post tabulam latens") had published around 1675 as an academic challenge. These solutions ("Enodationes duodecim problematum a Geometra post tabulam latente propositorum") were accompanied by a new problem that he submitted to his peers, under the title "Unum ad Omnes". As the problem remained unanswered, he republished it in 1692 ("Geometram Quaero", a book now lost), along with six new problems. It was then that another young prodigy, the Jesuit Girolamo Saccheri, decided to respond by publishing his first book, titled "Quaesita Geometrica" (1693). This work gathers, under the evocative title "Sphinx Geometra", all the texts published by the two young mathematicians on these geometric problems and their solutions: the statements of the initial twelve problems and their solution by Ventimiglia, the new problems he subsequently posed, and finally the complete text of Saccheri's response. No one seems to know who is behind the publication of this almost unknown work, dedicated by the printer to Prince Francesco Farnese, but everything seems to suggest that it is Saccheri himself or his circle. Indeed, in addition to the proximity of Parma to Milan where Saccheri resided and where he published most of his works (far from Ventimiglia's Sicily), it is interesting to note that eight of the thirteen plates in the work are actually the same eight original plates from his "Quaesita Geometrica" of 1693. In a lengthy article of forty pages published in 1983, Aldo Brogaglia and Pietro Nastasi shed light on the interest of Saccheri's first work, which notably highlighted his interest in projective geometry as well as the organic sources of his mathematical thought. This article also outlined the scientific career of Ruggero Ventimiglia, a brilliant but fleeting figure in Italian mathematics of the 17th century, who died at the age of twenty-eight and whose works only survive through a few publications like this one, practically impossible to obtain. Only four copies of this work are listed in public libraries in Italy (Biblioteca Nazionale Napoli, Biblioteca Universitaria Pavia, Collegio Nazareno Roma, and Biblioteca Grosso, Turin). We have only located one copy in American collections (Huntington Library), two copies in Great Britain (Trinity College, Cambridge, and University College London), and one copy in Bergen, Norway. There are no copies in French public collections. Important copy from the library of Alberto Pascal (1894-1918), who, despite his young age, was one of the first biographers of Saccheri and who died prematurely during the First World War. This copy, mentioned in his article dedicated to Saccheri ("raro libretto di cui ho potuto acquistare recentemente una copia"), bears his discreet initials "A.P." in the upper corner of the title page and, after his death, ended up in the hands of his brother Mario Pascal (1896-1949), also a mathematician, who stamped his triangular exlibris on the title page. Clear angular dampstain discreetly affecting the first two gatherings. Fine copy printed on strong paper and bound in its original vellum, containing 13 folding plates instead of the 11 described in all the collations we have found. See Brigaglia and Nastasi, "Le soluzioni di Girolamo Saccheri e Giovanni Ceva al 'Geometram quaero' di Ruggero Ventimiglia: Geometria proiettiva italiana nel tardo seicento" in: Arch. Hist. Exact Sci. 30, 7–44 (1984). See also Brigaglia "Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique" in: Bulletins de l'Académie Royale de Belgique (2010), n°21, pp.83-104. Catalogue of the Libri sale, 1413. See also Alberto Pascal, "Girolamo Saccheri nella rita e nelle opere" in: Giornale di Battaglini v . 52 , 1914.