New elements of geometry. Paris, Guillaume Desprez, 1683. In-4, brown calf, spine ornamented, roulette on the edges, spotted edges (period binding). Second edition, partly original, of the famous geometry of Port-Royal.
As sought after as the first one published in 1667, it is increased by a preface by de Beaubourg and a new way of treating proportions. The second and third books have been entirely redone by the author.
The illustration includes numerous graphs, tables and geometric figures in the text, as well as 4 plates of magic squares engraved in intaglio.
This work is of great importance, because it contains Pascal's solution to the problem of magic squares. Indeed, Pascal also composed a work on the same subject as this one, but he destroyed his manuscript after seeing the one Arnauld had written. Pascal admired the way in which his friend had remedied the confusion that was blamed on Euclid's geometry, and which he had not unraveled. Here, the great Arnauld presented Euclid's theorems in a new order, taking into account the scientific advances of his time, and in particular Pascal. Solved by Fermat, the problem of the magic squares found in Pascal's research - which reached us indirectly and thanks to this work - an immense progress that he communicated to his friend Arnauld, who published it as an appendix to this work.
The long preface is by Nicole.
Jean Itard, who examines the contents of the work in detail in a famous article ("La Géométrie de Port-Royal", in L'Enseignement mathématique, March 1940), notes that teaching in France was durably affected by it and that, until Legendre, all the authors of geometry textbooks or almost all of them adopted the views of Port-Royal.
Handwritten mathematical calculations of the period, in pen and ink, on the back covers, the verso of the last plate and the endpapers. Handwritten 20th century annotations and diagrams in pencil in the margins.
Fine restorations to headpieces, spines and corners; first flyleaf removed; 2 plates stained, a few small spots and uniform freckles.
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