I will now extract Beaulieu's treatise on algebra, entire. "L'Algebre est la science curieuse des Scavans et specialement d'un General d'Armee ou Capitaine, pour promptement ranger une Armee en bataille, et nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a 5 figures particulieres en cette sorte. P signifie _plus_ au commerce, et a l'Armee _Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons. [It is quite true that P and M were used for _plus_ and _minus_ in a great many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armee _rang_. Q signifie _quare_ en l'un et l'autre usage. C signifie _cube_ en la mesure, et _Cavallerie_ en la composition des bataillons et escadrons. Quant a l'operation de cette science, c'est {122} d'additionner un _plus_ d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait le moindre du _plus_, et la reste est la somme requise ou nombre trouve. Je dis seulement cecy en passant pour ceux qui n'en scavent rien du tout."[240] This is the algebra of the Royal Household, seventy-three years after the death of Vieta. Quaere, is it possible that the fame of Vieta, who himself held very high stations in the household all his life, could have given people the notion that when such an officer chose to declare himself an algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu, and all the _beaux_. Beaugrand--not only secretary to the king, but "mathematician" to the Duke of Orleans--I wonder what his "fool" could have been like, if indeed he kept the offices separate,--would have been in my list if I had possessed his _Geostatique_, published about 1638.[241] He makes bodies diminish in weight as they approach the earth, because the effect of a weight on a lever is less as it approaches the fulcrum. {123} SIR MATTHEW HALE. Remarks upon two late ingenious discourses.... By Dr. Henry More.[242] London, 1676, 8vo. In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two tracts, an "Essay touching Gravitation," and "Difficiles Nugae" on the Torricellian experiment. Here are the answers by the learned and voluminous Henry More. The whole would be useful to any one engaged in research about ante-Newtonian notions of gravitation. Observations touching the principles of natural motions; and especially touching rarefaction and condensation.... By the author of _Difficiles Nugae_. London, 1677, 8vo.