560 Mathematics. 



the application of geometry to many probleiTis, td 

 the solution of which the Algebraic Calculus had 

 been alone supposed adequate. 



About the year 1758 the invention of a new 

 branch of the analytic art, under the name of the 

 Besidnal Anahjsis, was published by Mr. Landen, 

 of Great-Britain. By means of this new operation 

 he enabled the mathematician to solve a variety of 

 problems, to which the method of fluxions had 

 usually been applied, in a way entirely original, 

 and by a process more simple, natural, and elegant, 

 than formerly. He applied this method to draw- 

 ing tangents, and finding the properties of curve 

 lines, and to the solution of many curious and dif- 

 ficult problems, both in mechanics and physics. 



The invention of the Antecedental Calcidiis, a 

 new method of geometrical reasoning, first pub- 

 lished in 1793, by James Glenie, Esq. of Norths 

 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 undergo by composition and decomposition. 

 This method proceeds without any consideration 

 of motion or of time, but is, notwithstanding, 

 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 Be- 

 verslonary Payments, were first reduced to system, 

 and brought into use in the eighteenth century. 

 Dr. Halle Y, of Great-Britain, and De Moivre, 

 of France, were among the earliest cultivators of 

 this department of mathematical science. It was 

 afterwards much improved and extended by the 

 successive labours of Simpson, Price, Webster, 



