FORE:As this rout was taking place, Bulow, who had beaten back the French battalions from Frischermont and Planchenoit, was approaching La Belle Alliance, and Blucher with the main army soon after appeared following him. At a farmhouse called Maison Rouge, or Maison du Roi, behind La Belle Alliance, the Duke of Wellington and Blucher met and felicitated each other. Blucher, in the Continental manner, embraced and kissed the victorious Duke; and it was agreed that, as the army of Wellington had been fighting hard for eight hours, the Prussians should make the pursuit. Blucher swore that he would follow the French whilst a horse or a man could move, and, with three cheers from the British, he set forward with his troops in chase. So far from "the Guards dying, but not surrendering," these brave men flew now before the stern old Prussian, and immediately in the narrow passage at Genappe they abandoned to him sixty pieces of their cannon. Amongst other spoil they captured the carriage of Napoleon, and found in it, amongst other curious papers, a proclamation for publication the next day at Brussels. As it was moonlight, the Prussians continued the chase till late into the night, slaughtering the fugitives like sheep. Numbers quitted the road and fled across the country, seeking shelter in the woods, where many of them were afterwards found dead or severely wounded. The highway, according to General Gneisenau, was covered with cannon, caissons, carriages, baggage, arms, and property of every kind. The wounded were humanely sent to Brussels, but those who could continue their flight did so till they had reached France, where they sold their horses and arms, and dispersed themselves to their homes. The grand army was no more, with the exception of the division of Grouchy, who made good his retreat to Paris, only to be upbraided by Buonaparte as the cause of his defeat. In this battle and retreat the French lost more men than at Leipsic, the killed and wounded exceeding thirty thousand.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.