The Life of Sir Isaac Newton

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1831 edition. Excerpt: ... the composition of which it moves in the direction of a tangent; and had he possessed the method of fluxions, he could, in every case, have determined the relative velocities of these motions, which depend on the nature of the curve, and consequently the direction of the tangent which he assumed to be in the diagonal of a parallelogram whose sides had the same ratio as the velocities. But as he was able to determine these velocities only in the conic sections, &c. his ingenious method had but few applications. " On peut reparder Format," says Lagrange, " comme le premier inventeur des nouveaux calculs;" and Laplace observes, "II paraitque Fermat, le veritable inventeur du calcul differentiel, 1'ait envisage comme un ens particular de cel.ui des diffiert-nces, "fcc. The labours of Peter Fermat, a counsellor of the parliament of Toulouse, approached still nearer to the fluxionary calculus. In his method of determining the maxima and minima of the ordinates of curves, he substitutes x--e for the independent variable x in the function which is to become a maximum, and as these two expressions should be equal when e becomes infinitely small or 0, he frees this equation from surds and radicals, and after dividing the whole by e, e is made = 0, and the equation for the maximum is thus obtained. Upon a similar principle he founded his method of drawing tangents to curves. But though the methods thus used by Fermat are in principle the same with those which connect the theory of tangents and of maxima and minima with the analytical method of exhibiting the differential calculus, yet it is a singular example of national partiality to consider the invcnter of these methods as the inventer of the method of fluxions. " One might be led," says Mr....