THREE:In 1720 Colin Maclaurin, the successor of James Gregory in the mathematical chair at Edinburgh, published his "Geometrical Organica," a treatise on curves; in 1742 his admirable treatise on Fluxions; and in 1748 his treatise on Algebra. Dr. Robert Simson, professor of mathematics at Glasgow, published a restoration of the "Loci" of Apollonius, and an English translation of Euclid, which continued down to a late period in use, both in Scotland and England. In 1717 James Stirling published a Latin treatise on lines of the third order, and another on Fluxions, called "Methodus Differentialis," in 1730. William Emerson, a mathematician and mechanist, wrote on fluxions, trigonometry, mechanics, navigation, algebra, optics, astronomy, geography, dialling, etc., but a considerable portion was only in part published during this period. Thomas Simpson, a weaver, of Market Bosworth, at the age of seven-and-twenty suddenly discovered himself as an extraordinary mathematician, and went on till his death, in 1761, publishing works on fluxions, the nature and laws of chance, on mixed mathematics, on the doctrine of annuities and reversions, on algebra, elementary geometry, trigonometry, etc. James Ferguson, also, the son of a day-labourer, in Banffshire, studied mathematics whilst tending sheep, and published a number of works on the phenomena of the harvest moon, astronomy, mechanics, hydrostatics,[154] pneumatics, and optics. Ferguson had a remarkably lucid and demonstrative style, both in writing and lecturing, and his example excited a keen spirit of inquiry amongst the working classes, so that he is said to have diffused the knowledge of physical science amongst the class from which he sprang more than any other man.The King of Spain hoped, by the dismissal of Alberoni, to obtain more advantageous terms of peace from France and England; but they still stood firmly to the conditions of the Quadruple Alliance. On the 19th of January, 1720, the plenipotentiaries of England, France, and Holland signed an engagement at Paris not to admit of any conditions of peace from Spain contrary to those of the alliance. Stanhope despatched his secretary, Schaub, to Madrid, to endeavour to bring over the queen to this agreement, and Dubois sent instructions to the Marquis Scotti, Father d'Aubenton, and others in the French interest to press the same point. She stood out firmly for some time, but eventually gave way, and the mind of the king was soon influenced by her. Some difficulties which could not be overcome were referred to a congress to be held at Cambray. On the 26th of January Philip announced his accession to the Quadruple Alliance, declaring that he gave up his rights and possessions to secure the peace of Europe. He renewed his renunciation of the French Crown, and promised to evacuate Sicily and Sardinia within six months, which he faithfully performed.
