BERNOULLI'S SOLUTION TO THE ISOPERIMETRIC PROBLEM

BERNOULLI, JACOBI (JACOB).

Analysis magni problematis Isoperimetrici.

Leipzig, Gross & Fritsch, 1701. 4to. Contemporary full vellum. Handwritten title on spine. A small stamp to title page and page . Pasted library label to pasted down front free end-paper. In: "Nova Actorum Eruditorum Anno MDCCI". Pp 213-228 + 1 engraved plate. [Entire volume: (2), 581 pp. + 8 engraved plates].

First publication of Jacob Bernoulli influential dissertation in which he published the first correct solution to the isoperimetric problem both Johann Bernoulli and Leibniz had been seeking without success. The paper influenced both Leonhard Euler in writing his first research paper and British mathematician Brook Taylor to begin a dispute which has later been referred to as Taylor versus Continental mathematicians.

"It [the dissertation] was considered as a prodigy of sagacity and invention: and indeed, if the time be considered, it will not be too much to assert, that a more difficult problem never was solved." (Bossut. A general history of mathematics. 341 p.).
The isoperimetric problem is an ancient problem which dates back to antiquity and can be described as which curve, if any, maximizes or minimizes the area of its enclosed region?
Euler, who had been taught by Johann Bernoulli, published his first paper in 1726 which was a note on the construction of isochronous curves in a resistant medium.

DSB II, 48b.

The following papers by Johann Bernoulli are also contained in the present volume:
1. Disquisitio Catoptrico-Dioptrica exhibens Reflexionis et Refractionis naturam ex aequilibrii fundamento deductam. Pp 19-26.
2. Novaratio construendi radios osculi seu curvanturae in Curvis quibusvis etc. Pp. 136-40.
3. Multisectio Anguli vel Arcus, duplici aequatione universali exhibita. Pp. 170-75.

Order-nr.: 44002