Traitté du Triangle Arithmetique

Edition

Excerpt of the Traitté du Triangle Arithmetique, the first piece of Traité du triangle arithmétique, avec quelques autres petits traitez sur la mesme matiere, par Monsieur Pascal (Paris, Guillaume Desprez, 1665). Kept, complete: the heading “Definitions” and all its paragraphs (pp. 1-2, “I’Appelle Triangle Arithmetique” to “conuiendra à tous les autres”), and the Consequence premiere with its proof and its four lines of examples (pp. 2-3); left out: the Consequences seconde to dixneufiesme, the Definition of the cells of the dividend, the Problesme and the other treatises of the volume. The hero image is the folding plate “Triangle Arithmetique” of the BnF copy (Réserve des livres rares, RES-V-860, Gallica view 6), cropped to the triangle and its legends, turned to greyscale and its paper whitened; the library stamp in its lowest cell is kept. The text was read line by line on the BnF scan (views 7 to 9) and on the Internet Archive scan of the Lausanne copy (bub_gb_UqgUAAAAQAAJ), whose OCR served as the working base: that OCR garbles nearly all the italic, so most lines were set from the page images. The definitions are set in italics with the defined terms in roman, as printed; the statement of the consequence is set as printed, in larger type with a hanging indent. Spelling, accents and punctuation are those of the print, including “tinües”, “cettte methode”, “ou E, est” and “ou ie considere”; the dagger that the print uses as a plus sign (“3 † 4”, “G † zero”) is kept. The letter printed like a cross between cells φ and θ is set as ψ, the letter it has on the plate; the second axis of the definitions is set “Gζ”. Normalizations: the long s is set as a round s and the ct and st ligatures as two letters; u and v, i and j are kept as printed; the drop cap I of “I’Appelle” is set as a capital; the apostrophes are set as typographic apostrophes; running heads, page numbers and signature marks are dropped, and words hyphenated at line ends are rejoined.

Rights

Blaise Pascal died on 19 August 1662 (Wikidata Q1290) and the treatise was published in 1665: it is in the public domain in France, where the author died before 1 January 1956, and in the United States, where it was published before 1 January 1931. Gallica gives the scan the rights statement “domaine public” (OAI record of ark:/12148/btv1b86262012); the Internet Archive marks the Lausanne scan with the Public Domain Mark 1.0.

The plate is reproduced from the Gallica scan. The conditions of use of Gallica (https://gallica.bnf.fr/html/und/conditions-dutilisation-des-contenus-de-gallica, the license link of the IIIF manifest) make non-commercial reuse free with the credit “Source gallica.bnf.fr / BnF”, which the footer gives, and commercial reuse subject to a license. The Lausanne copy scanned by the Internet Archive does not show the face of the plate, which is folded in it. A faithful reproduction of a public domain work of visual art is not protected in the European Union (article 14 of Directive (EU) 2019/790), and Gallica itself gives the scan the rights statement “domaine public”.