PONCELET, J. V. [JEAN-VICTOR].

Application de la méthode des moyennes à la transformation, au calcul numériques et à la détermination des limites du reste des séries.

Berlin, G. Reimer, 1835. 4to. In "Journal für die reine und angewandte Mathematik, 13 Band, 1. Heft, 1835". In the original printed wrappers, without backstrip. Fine and clean. [Poncelet:] 54 pp. [Entire issue: pp. IV, 54 pp.].

First printing of this extensive paper by the French mathematician on number theory and infinite series.

"Poncelet's years of study led to his personal belief that geometry could be founded on a series of fundamental principles as general as those on which algebra was based. He carried this belief forward by suggesting that since every straight line and plane extend to a point of infinity, then any new points on a line would be the same for specific parallel lines (or planes). At this time in mathematical history, it was accepted that all infinite elements of space were supposed to lie on the infinite plane of space, known as the projective plane.
Early on, Poncelet's colleagues were extremely reluctant to accept his ideas and resulting theories. However, as time went on, several prominent German mathematicians not only accepted them but contributed to the emerging new science. Among those who recognized Poncelet's breakthrough in the field were Karl Georg Christian von Staudt, Felix Klein, Georg Cantor, Richard Dedekind, and Moritz Pasch. They were later joined by Otto Stolz of Austria who made his own contributions to the field.
He died on December 22, 1867, in Paris without the recognition he deserved for his brilliant contributions to the world of numbers. His Treatise on the Projective Properties of Figures (1822) is still regarded as the pioneer work in the field." (Schlager, Science and its Times, P. 261).

Order-nr.: 45145