356 PHILOSOPHICAL TRANSACTIONS. [aNNO 17 J 8. 



to it, that a sentinel on the top of Beachy, not 2 miles from it, in a clear day, 

 without turning his body, might see the Isle of Wight, the hills in France 

 near Bologne, and the Ness in Kent; so that from the Ness to Selsey it must 

 have been a small sail that could escape his eye. 



On the Construction and Measure of Curves: by which many Infinite Series 

 of Curves are either measured or reduced to Simpler Curves. By Colin 

 Maclaurin,* Professor of Mathematics^ in the New College at Aberdeen. 

 N° 356, p. 803. Translated from the Latin. 



Since in every curve line there is a certain regularity of curvature, though 

 perhaps intricate, according to which the figure is described; therefore geome- 

 tricians define the various characters of curves by an equation, expressing the 

 relation of the ordinates to the abscisses of any axis or diameter. But as the 

 same may be done from considering the curves in respect to one given centre, 

 nay the very simple uniformity of nature often requires that this method be 



* Mr. Maclaurin, a most eminent mathematician and philosopher, was the son of a clergyman, 

 and born at Kilmoddan in Scotland, in the year 1698. He studied at the university of Glasgow, 

 whither he was sent at eleven years of age, and where he remained 5 years, with the most intense 

 application to learning, particularly the mathematics, and to such good purpose, that it is said in his 

 l6"th year he had invented many of the propositions in his Geometria Organica, aftei-wards published, 

 and when also it is probable he wrote the paper on curves here printed in the Philos. Transactions. 

 In his 15th year he took tlie degree of M, A, on which occasion he composed, and publicly de- 

 fended, a tliesis on the power of gravity, with great applause. In 1717, at 19 years of age, he 

 was appointed professor of Mathematics at the New or Marischal College at Aberdeen ; and 2 years 

 after he visited London, when he was chosen a fellow of the Royal Society, to which he proved 

 afterwards so. useful and honourable a member. In 1724 he gained the prize of the Royal Aca- 

 demy of Sciences, for a memoir on the percussion of bodies; and in 1725 he was chosen Professor of 

 Mathematics at Edinburgh, which he enjoyed to the time of his death in 1746, at 48 years of age. 

 After the publication of Bp. Berkley's Analyst, Mr. Maclaurin began to write an answer to it, 

 which he gradually extended to a complete treatise on the doctrine of Fluxions, which was pub- 

 lished at Edinburgh in 1742, 2 vols. 4to. Mr. Maclaurin lent his advice profitably in several public 

 and private works. Thus, he was consulted by the government on the passage by the north pole to 

 the south seas ; and on settling the geography of the Orkney and Shetland isles; on constructing 

 various machines, the conveying of water, &c. : he settled rules for the Commissioners of Excise, 

 to regulate the gauging of vessels at Glasgow; made calculations for the societies and funds for the 

 widows and children of the Scotch clergy, and for the university professors, &c. Besides his publi- 

 cations before-mentioned, viz. the G«ometria Organica and his Fluxions, and the piece which gained 

 the Academical prize in 1724, he wrote many other valuable works, particularly in the Phil. Trans, 

 from vol. 30 to vol. 42, and in the Edinburgh Medical Essays. In 1740 he shared tlie prize of the 

 Paris Academy with Messrs. Dan. Bernoulli and Euler, for a paper on the motion of the tides, which 

 he drew up in ten days; afterwards inserted in his treatise on Fluxions. Besides these, two posthu- 

 mous works have been published by his friends, viz. the treatise on Algebra in 1 vol. 8vo. and the 

 account of Sir I. Newton's discoveries, in 1 vol. 4to. 



