(1775 – 1836) French physicist and mathematician, one of the founders of the science of classical electromagnetism, which he referred to as electrodynamics, also making important contributions in chemistry and philosophy. Ampere invented numerous applications, including the solenoid and the electrical telegraph, and theorized atomic magnetism. Very rare A.Ms. (unsigned), 2pp. 4to. [France, n.d.], approx. 390 words in Ampere's hand including 16 inline formulae/equations and about six formulae/equations on separate lines, most likely a draft of one of Ampere's treatises on calculus with contemporaneous edits. A fine insight into the French mathematician's thought processes as he considered complex partial derivatives, transitioning between text and calculations in the manuscript. 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...' Boldly penned and near fine condition, with a full transcript. With COA from John Reznikoff / University Archives as well as our own.