314 Intelligence and Miscellaneous Articles* 



Vos lecteurs, pour sen assurer, peuvent recourir aux Memoires de 

 FAcademie de Berlin, annee 1781. Fayolle. 



on varignon's method of solving equations of the 

 second degree. by m. fayolle. 

 To the Editors of the Philosophical Magazine and Annals. 

 Messieurs, 

 La methode que vous avez inseree dans votre dernier numero, 

 pour la resolution des Equations du second degre, m'en a rappelle 

 une de Varignon qui est encore plus simple, et qui s'applique aux 

 equations du troisieme degre. Elle est si facile (disait Fontenelle), 

 qu'on est tout surpris que Varignon l'ait trouvee le premier. 

 La voici en peu de inots : 



Soitz*+p z + q = 0. 

 Faisons z = x— y ; alors 



z % — x % — 2xy+y* = x*— 2xy + 2y*— y* 



= x i —2yz—y*; 

 Et par consequent, z°--\-2yz-{-y* \ _ n 



—x* > ~" 

 Laquelle comparee terme a terme avec la proposee, donnera 

 1°. pz = 2yz, ou y = %p, 

 2°. q=y q -x*> ou q = ±p* — x\ 

 D'ou resulte x — + x/^p* — q 



Done z = x — y = — ip ± V \p % — q. 

 Si Ton avait z 1 — pz~\-q = 0, 

 II faudrait prendre z = x + y. 



Cette methode s'applique avec la meme facilite a l'equation du 

 troisieme degre z 3 + p z + q = 0, 



Laquelle est degagee du second terme. 



Ce 16 Aug. 1828. Fayolle. 



MINERALOGICAL LITERATURE. 



1. Dr.Naumann, professor in the Mining Academy of Freiberg, 

 has published Lehrbuch der Mineralogie ( Treatise on Mineralogy), 

 Berlin, 1828, by A. Rucker, in 8vo. This treatise, by a scholar of 

 the celebrated Professor Mohs of Vienna, is one of the best on that 

 science. The crystallographic method of Professor Naumann is 

 eclectic in reference to those of Mohs and Weiss, and is very good ; 

 the system is established according to the physical and chemical 

 characters of minerals. He describes a multitude of varieties of 

 crystals with the assistance of 556 figures. In general the work is 

 very classical, and deserves to be recommended to mineralogists. 



"2. Dr. Charles Hartmann, Mining-officer in the service of his 

 Highness the Duke of Brunswick, has published Worterbuch der 

 Mineralogie und Geognosie y (Dictionary of Mineralogy and Geology), 

 Leipsic, by Brockhaus, 8vo. This work gives a description of all 

 known minerals and rocks in alphabetical order, and contains an 



introduction 



