484 SIMSOX. 



to suppose that either he or his celebrated pupil 

 Stewart disliked or undervalued. That application 

 forms the most valuable service which modern analysis 

 has rendered to science. But they did object, and 

 most reasonably and consistently, to the introduction 

 of algebraic reasoning wherever the investigation 

 could, though less easily, yet far more satisfactorily, 

 be performed geometrically. They saw, too, that in 

 many instances the algebraic solution leads to con- 

 structions of the most complex, clumsy, unmanage- 

 able kind, and therefore must be, in all these instances, 

 reckoned more difficult, and even more prolix than 

 the geometrical, from the former being confined to the 

 expression of all the relations of space and position, 

 by magnitudes, by quantity and number, (even after 

 the arithmetic of sines had been introduced,) while 

 the latter could avail itself of circles and angles 

 directly. They would have equally objected to car- 

 rying geometrical reasoning into the fields peculiarly 

 appropriate to modern analysis ; and if one of them, 

 Stewart, did endeavour to investigate by the ancient 

 geometry physical problems supposed to be placed 

 beyond its reach as the sun's distance, in which he 

 failed, and Kepler's problem, in which he marvel- 

 lously succeeded, that of dividing the elliptical area in 

 a given ratio by a straight line drawn from one focus 

 this is to be taken only as an homage to the undervalued 

 potency of the Greek analysis, or at most, as a feat of 

 geometrical force, and by no means as an indication of 

 any wish to substitute so imperfect, however beautiful, 

 an instrument, for the more powerful, though more 

 ordinary one of the calculus which " alone can work 



