#### “Raphson’s Method”; Not “Newton’s Method” or,

Maybe, the “Newton–Raphson Method”

# Analysis Aequationum Universalis, seu ad Aequationes Algebraicas resolvendas Methodus generalis, & expedita, ex nova infinitarum serierum methodo, deducta ac demonstrata. Editio secunda cui accessit Appendix de Infinito Infinitarum Serierum progressu ad Equationum Algebraicarum Radices eliciendas. Cui etiam Annexum est; De Spatio reali, seu Ente Infinito Conamen Mathematico-Metaphysicum.

Woodcut diagrams in the text. 3 p.l., 5-55, [9], 95, [1] pp. Small 4to, 18th-cent. calf (rebacked & recornered), red morocco lettering piece on spine. London: Typis TB. for A. & I. Churchill et al., 1702.

Third edition; the first edition appeared in 1690 and the second in 1697. Raphson (d. 1715 or 1716), also wrote the important History of Fluxions (1715) and translated Newton’s Arithmetica Universalis into English (1720). He was a fellow of the Royal Society.

“In 1690, Joseph Raphson…published a tract, Analysis aequationum universalis. His method closely resembles that of Newton. The only difference is this, that Newton derives each successive step, p, q, r, of approach to the root, from a new equation, while Raphson finds it each time by substitution in the original equation…Raphson does not mention Newton; he evidently considered the difference sufficient for his method to be classed independently. To be emphasized is the fact that the process which in modern texts goes by the name of ‘Newton’s method of approximation,’ is really not Newton’s method, but Raphson’s modification of it…It is doubtful, whether this method should be named after Newton alone…Raphson’s version of the process represents what J. Lagrange recognized as an advance on the scheme of Newton…Perhaps the name ‘Newton-Raphson method’ would be a designation more nearly representing the facts of history.”–Cajori, A History of Mathematics, p. 203.

The first edition is very rare. The Appendix appears for the first time in the second edition of 1697 along with the separately paginated second part De Spatio reali.

Fine fresh copy. 19th-century bookplate of P. Duncan.

Price: $4,500.00

Item ID: 3504