London: Printed for the Author; and sold by L. Hawes…[et al.], 1764. First edition. Five engraved folding plates. With list of subscribers. A little light foxing. A very good copy of a scarce book. Recent tan calf over marbled boards, Gilt-ruled spine with crimson morocco label. Quarto. viii, "218" [i.e., 128] pp. Item #15500
John Landen (1719-1790) was the most notable British mathematician in the second half of the eighteenth century. At the time when British mathematics was held back by inadequate notation, an unfortunate consequence of the Newton-Leibniz dispute, he was the only Englishman to score major advances in mathematics and in the art of computation.
In this, his most important work, he attempted to replace the fluxional calculus with an analytic method "founded entirely on the anciently received principles of algebra." A second volume was planned, but it never appeared. According to Lacroix, this was the first attempt to reduce the infinitesimal calculus to "purely mathematical notions" (Oxford DNB). Landen's writings served as the starting point for investigations by Euler, Lagrange, and Legendre. He also developed the theorem known by his name for expressing the length of a hyperbolic arc in terms of the lengths of arcs in two ellipses.
ESTC lists nine copies in North America. Wallis, Biobibliography of British Mathematics 754LAN64. Smith, History of Mathematics, p. 459. Cf. DSB.