Traité d'Algèbre de rolle. 1690.
Remarques de M.Rolle de l'académie royale des sciences, touchant le problême général des tangentes. 1703.
Rare first editions
ROLLE, Michel.
Traité d'Algèbre ou principes généraux pour résoudre les questions de mathématique.
Relié à la suite :
Remarques de M.Rolle de l'académie royale des sciences, touchant le problême général des tangentes. Pour servir de réplique à la réponse que l'on a insérée, sous le nom de M.Saurin dans le Journal des Sçavans du 3 Aoust 1702.
Paris, Estienne Michalet, 1690 [MDCLXC].
3000 €
Two works in one 4to (241x180 mm), (14)-270-(2)-(4)-47-(1) pages and two folding plates.
binding: Contemporary full sheep, spine gilt in six compartments, title in gilt on lettering-piece.
Binding a little worn with some careful repairs.
First edition of two rare works of Rolle.
According to our research, there have been several changes during the printing of the "Traité d'Algèbre".
Copie's with the wrong date (MDCLXC) as our copy, then corrected (M.DC.XC).
An Epistle to Mr. Louvois two sheets was added to some copies (not in ours)
Copie's with the sheets FF and FFII (pages 223-226) replaced as in our copy by a single sheet Ff (paged 267/266 error).
Our copy is after adding the FF leaf, but before changing the wrong date on title page and the addition of the Epistle to Mr. Louvois.
The "Traité d'algèbre" is the most important work of Rolle.
He invented the notation n √ x to the nth root of x, which is still used today.
His most important contribution, however, is the part where he introduced the concept of "cascades". Let the polynomial equation P (x) = 0 with real roots a and b, then built polynmoe P '(x) he calls the first "cascade" as P' (a) = (ba) Q (b) where Q (x) is a polynomial of degree less. Now P '(x) is call the first derivative of P (x).
Rolle then built second cascade, the second derivative, and so forth to find all the roots of the polynomial.
Bound after is the "les remarques de Rolle touchant le problème général des tangentes" relates to the scientific controversy of Rolle against the differential calculus.
Rolle critics the poor new scientific material of novelty of differential calculus: "the fundamental formula of calculus is nothing but the usual form tangents Fermat and that it was public before it has nothing sound of the first projects this calculation "(page 4. transl.).
