312 Reviezv of the Cambridge Course of Malhematics. 



certainly been too much neglected both in this country 

 and in Great-Britain. This is best accounted for, perhaps, 

 from the circumstance, that Sir Isaac Newton, from par- 

 tiality to the ancient writers, delivered his splendid dis- 

 coveries by the synthetic method,* and that his authority 

 has influenced The greatest part of mathematicians who 

 have written in his native language. The essential char- 

 acter of the synthetic method, is, that it always proceeds 

 from the simple to the more complex, and is on that ac- 

 count well adapted to the communicatiorj of truth when 

 once discovered. But it fails almost entirely in commurii- 

 cating to the mathematical reader, that spirit of invention, 

 which may enable him, after perusing what is most valua- 

 ble in the writings of others, to open a new track for him- 

 self. It seems particularly appropriate, that Algebra 

 which is scarcely more than another name for Analysis,! 

 should be communicated by the analytic, and not as has 

 usually been done among us, by the synthetic method. 



5. The treatises in question are so composed as to be 

 preparatory and introductory to the higher and more diffi- 

 cult physical, astronomical and mathematical treatises. 

 This circumstance can be no disadvantage to him who does 

 not expect to pass the limits of the elementary part of the 

 science, w^hile it is of the utmost value to evev)' one who 

 designs to devote a considerable part of his life to mathe- 

 matical learning. Such an ojie, is anxious to press forward 

 to the works of the great masters of the science, and ulti- 

 mately, if possible, to an acquaintance with the " Meca- 



* Sir Isaac Newloa appears originally to have made his discoveries by 

 analysis, and afterwards, in commiinicatiog them to the world, to have 

 clothed them with a synthetic demonstration, with a view to render them 

 more fit to meet the public eye ; he thas expresses himself in his treatise 

 of Fluxions : Pcstquam area curvae alicujus ita (analytic^^ reperta est et 

 construota, indaganda est demoastratio constructionis, ut omisso, quatetius 

 fieri potest, calculo algebraico, theorema fiatconcinnum et cleans ac lu- 

 men publicum sustinere valeat.'* Newtoni opuscula, vol. I. p. 170. 



M. Laplace thinks that Newtoa had found the greatest part of his theo- 

 rems by analysis, bot that his predilection for synthesis, and his great es- 

 teem for the geometry of the ancients, made him deliver, under a synthet- 

 ic form, his theorems and even his method effluxions. Exposit, du Syst- 

 du Monde 4th edit. p. 422. 



t Some writers on mathematics make a distinction between analysis and 

 algebra, Bezout defines analysis to be the metho<] of determining those 

 genenil rule; which assist the nnderstandinar in all mathematical investiga- 

 tions, and by Algebra, the instrument whicli this method employ? for ac- 

 complishing that end* Euler's Alg. 2d edit. London, p. 3. 



