CRAIG, John, a Scottish mathematician of the age of Newton, and one of the earliest writers on the fluxionary or differential calculus in this country. Newton no doubt had long been in possession of the principles of this calculus before his modesty allowed him to give his discoveries to the world, and he even revised1 one of Craig's treatises previously to publication in 1685, the year after Leibnitz had announced his discovery in the Leipsic Transactions. During his residence at Cambridge, similarity of pursuit had made Craig acquainted with that truly great man; and on his return to Scotland he enjoyed the intimate friendship of the accomplished Dr Pitcairn, and of David Gregory,2 professor of mathematics in the University of Edinburgh, and afterwards Savilian professor of astronomy at Oxford. His investigations, however, with the new calculus, subjected him to the severe strictures of the distinguished John Bernoulli, but obtained for him the support of Leibnitz, whose approbation may be considered as exempt at least from that national partiality with which he himself charges Craig.3 But whatever praise may be due to Craig for his mathematical inquiries, it must be allowed that his Principia of the Christian religion, by a misapplication of the doctrine of probability to human testimony, rest on premises which lead to conclusions alike dangerous and absurd. Having assumed the position that human testimony can only amount to probability, and that this probability diminishes as the distance of time from the event increases; he readily obtains the startling and fallacious, though calculated, result of a period when faith would become evanescent, and disappear from the earth. If, however, it may be allowed to form an opinion of Craig's character from a letter to Dr Cheyne,4 there may perhaps be some justice in attributing the erroneous principles of this work rather to theoretical mistake than to wrong intention. He seems ultimately to have been a Fellow of the Royal Society, and vicar of Gillingham, Dorsetshire,5 but for some years he resided in London, where he died in 1731.
Besides communications to the Leipsic Acta Eruditorum, his contributions to the London Philosophical Transactions from 1697 to 1712 embrace essays on quadratures, length of curve lines, logarithmic curve and construction of logarithms, solutions of the problems of the solid of least resistance and of the line of swiftest descent, as well as of the problem of John Bernoulli. His separately published writings, now chiefly interesting with reference to the progress of mathematical science, are, 1. Methodus figurarum lineis rectis et curvis quadraturas determinandi, London, 1658, 4to. 2. Tractatus Mathematicus de figurarum cur-
vilinarum quadraturis et locis geometricis, London, 1693, 4to. 3. Theologia Christianæ Principia Mathematica, London, 1699 (reprinted, with a refutation, at Leipsic, 1755). 4. De Calculo Fluentialium Libri duo, quibus subjunguntur libri duo de Optica Analytica, 1718. (T. A.)