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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.This was a blow which for a time completely prostrated the Prussian monarch. Nothing but the most indomitable spirit and the highest military talent could have saved any man under such circumstances. But Frederick had disciplined both his generals and soldiers to despise reverses, and he relied on their keeping at bay the host of enemies with which he was surrounded till he had tried a last blow. On the field of Rosbach, near the plain of Lützen, where Gustavus Adolphus fell, after having relieved Marshal Keith at Leipsic, Frederick gave battle to the united French and Austrians. The French numbered forty thousand men, the Austrians twenty thousand; yet, with his twenty thousand against sixty thousand, Frederick, on the 5th of November, took the field. His inferior numbers favoured the stratagem which he had planned. After fighting fiercely for awhile, his troops gave way, and appeared to commence a hasty retreat. This, however, was continued only till the French and Austrians were thrown off their guard, when the Prussians suddenly turned, and received the headlong squadrons with a murderous coolness and composure. The Austrians, confounded, fled at once; and Soubise, a general of the princely House of Rohan, who owed his appointment to Madame Pompadour, was totally incapable of coping with the Prussian veterans. He saw his troops flying in wild rout, and galloped off with them, leaving a vast number of slain, seven thousand prisoners, and the greater part of his baggage, artillery, and standards in the hands of the enemy.