Description:

André-Marie Ampère
n.p., n.d.
André-Marie Ampère Mathematical Manuscript Exploring Partial Derivatives! Featuring 20+ Equations, Nearly 400 Words
AM

A 2pp autograph manuscript in French in the hand of mathematician André-Marie Ampère (1775-1836), comprising about 390 words; about 16 inline formulae/equations; and about 6 formulae/equations on separate lines. N.d., n.p. The manuscript represents a draft of one of Ampère's unidentified treatises on calculus. Inscribed on both sides of a single sheet of laid watermarked paper, with scattered contemporaneous edits. Expected wear including even toning and flattened transmittal folds. Scattered ink bleed-through and with isolated instances of ink corrosion. Else near fine and very legible. 8.125" x 12." Provided with a full English translation.

This manuscript provides us with the unique opportunity to examine Ampère's train of thought as he considered complex partial derivatives. Specifically, Ampère studies the interactions of the variables F, d, x, y, u, and c. Particularly fascinating is the adept way that Ampère transitions between words and formulae/equations in the manuscript.

Translated in part:

"As we noted [ ], precisely the same thing as having among the three variables x, y, u, the two relations u=F(x,y), u=0, or by virtue of the latter, all derivatives of u, considered a function of x alone, are null, we'll therefore have these equations…

… by substituting these values dy/dx and d2y/dx2 in the third equation, there will only be one unknown left d3y/ dx3 in this equation which will immediately produce the value thereof, by equating to zero the following derivatives of F(x,y) we'll get, through a similar process, the values of the derivatives of y up to whichever magnitude one desires…"

André-Marie Ampère was a leading French physicist and mathematician of his day. He pioneered the study of electromagnetism, contributing to major theories and laws, and even giving his name to the ampere, a unit of measurement of electricity. Ampère taught chemistry, physics, astronomy, math, and astronomy when he was not producing original scientific work.

This item comes with a Certificate from John Reznikoff, a premier authenticator for both major 3rd party authentication services, PSA and JSA (James Spence Authentications), as well as numerous auction houses.

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  • Dimensions: 8.125" x 12"
  • Medium: AM

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