Jakob Bernouilli (1 results)

Leipzig, Grosse & Gleditsch, 1694. 4to. Contemp. full vellum. Faint handwritten title on spine. a small stamp on titlepage. In: "Acta Eruditorum Anno MDCXCIV". (2),518 pp. and 11 folded engraved plates. As usual with various browning to leaves and plates. The entire volume offered. Leibniz's papers: pp. 311-316, pp. 364-375. - Johann Bernoulli's papers: pp. 200-206, pp. 394-99, pp. 435-437, pp. 437-441. - Huygen's papers: pp. 338, pp. 339-41. - Jakob Bernoulli's papers: pp. 262-276, pp. 276-280, pp. 336-338, pp. 391-400. Some mispaginations. All papers first appearance, dealing with, and clarifying the problems and the new applications of Leibniz' inventions of the differential- and integral calculus.In the papers Leibniz shows how to reduce linear first order ordinary differential equations to quadratures. I the other paper he gives a general method of finding the envelope of a family of curves, which helped to spread the theory of plane curves.In the groundbreaking paper offered here, Jakob Bernoulli introduces THE LEMNISCATE, a symmetric self-intersecting curve resembling a figure eight and defined by the condition that the product of the distance of anay point on the curve from two fixed points is (d/2)2, where d is the distance between the fixed points."Jacob Bernoulli was fascinated by curves and the calculus, and one curve bears his name - the "lemniscate of Bernoulli", given by the polar equation r2=a cos 2"0". The curve was described in the Acta Eruditorum of 1694 as resembling a figure eight or a knotted ribbon (lemniscus). However the curve that most caught his fancy was the logarithmic spiral.he swowed that it had several strioking properties not noted before.it is easy to appreciate the feeling that led Bernoulli to request that the "spira mirabils" be engraved on his tombstone together with the inscription "Eadem mutata resurgo" (Though changed, I arise again the same)." (Boyer in his History of Mathematics).