Chap. VI.] Mathematics. 71 



plication of geometry to many problems, to the 

 solution of which the Algebraic Calculus had been 

 alone supposed adequate. 



About the year 17-^8 the invention of a new 

 branch of the analytic art, under tlie name of the 

 Residual Analysis, was published l.)y Mr. Landen, 

 of Great Britain. By means of this new operation, 

 he enabled the mathematician to solve a variety of 

 problems, tO which the metliod of fluxions had 

 usually been applied, in a way entirely original, 

 and by a process apparently more simple and na- 

 tural than formerly. He applied this method to 

 drawing tangents, and fmding the properties of 

 curve lines, and to the solution of many curious and 

 difficult problems, both in mechanics and physics. 



The invention of the Antecedcnial CalculuSy a 

 new method of geometrical reasoning, first pub- 

 lished in 1793, by James Glenie,* esq., of North 

 Britain, also deserves some notice. This is a branch 

 of general geometrical proportion, or universal 

 comparison, derived from an examination of the 

 antecedents of ratios, having consequents, and a 

 standard of comparison given, in the various de- 

 grees of augmentation and diminution which they un- 

 dergo by composition and decomposition. This me- 

 thod proceeds without any consideration of motion 

 or of time ; and is, in the opinion of the inventor, 

 applicable to every purpose to which the celebrated 

 doctrine of fluxions has been, or can be, applied. 



The doctrines of Tontines, Annuities, and lie- 

 versionajy Payments, were first reduccfl to system, 

 and brouo'ht into use in the eiditeenth centurv. 

 Dr. Halley, of Great Britain, and de Moivre, a 

 native of France, but resident in England, were 



