THE FINAL SOLUTION TO THE BALLISTIC CURVE

BERNOULLI, JOANNES [JOHANN].

Responsio ad nonneminis provocationem eiusque solutio quaestionis ipsi ad eodem proposititae de invenienda linea curva, quam describit proiectile in medio resistente (+) Problema Analyticum, quod omnibus Geometris non-Anglis proposuit.

Leipzig, Grosse & Gleditsch, 1719. 4to. In: "Acta Eruditorum Anno MDCCXIX". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 256-270. [Entire volume: (4), 539, four engraved plates.].

First printing of Bernoulli's exceedingly important paper in which he presented the final (and correct) solution to the ballistic curve. Newton had also occupied himself with the problem but had only solved the law of resistance.

In 1718, English mathematician Keill had given Bernoulli the following challenge: "Find the curve which a projectile describes through the air on the simplest hypothesis of uniform gravity and density in the medium, the resistance varying as the square of the velocity". The challenge was more an attempt to humiliate Bernoulli, since it was supposed to be unsolvable, than it was an attempt to advance mathematics.

"It was therefore natural the Bernoulli, when he published his solution of Keill's problem and an account of his conduct, should dwell at greater length upon his triumph over the English mathematician than upon his very considerable achievement in mathematics." (Hall, Ballistics in the seventeenth century, Pp. 155).

"Bernoulli's criticism of Taylor's Methodus incrementorum was simultaneously an attack upon the method of fluxions, for in 1713 Bernoulli had become involved in the priority dispute between Leibniz and Newton. Following publication of the Royal Society's Commercium epistolicum in 1712, Leibniz had no choice but to present his case in public. He released-without naming names-a letter by Bernoulli (dated 7 June 1713) in which Newton was charged with errors stemming from a misinterpretation of the higher differential. Thereupon Newton's followers raised complicated analytical problems, such as the determination of trajectories and the problem of finding the ballistic curve, which Newton had solved only for the law of resistance R = av (R = resistance, a = constant, v = velocity). Bernoulli solved this problem (AE, 1719) for the general case (R = avn), thus demonstrating the superiority of Leibniz' differential calculus." (DSB)

Order-nr.: 45321