122 Mr. Woophouse ora the Independence of the 
The question, then, concerning the respective advantages of 
the ancient geometry and modern analysis, may be comprised 
within a short compass. If mental discipline and recreation are 
sought for, they may be found in* both methods ; neither is 
essentially inaccurate; and, although in simple inquiries the 
geometrical has greater evidence, in abstruse and intricate inves« 
tigation the analytical is most luminous : but, if the expeditious 
deduction of truth is the object, then I conceive the analytical 
calculus ought to be preferred. To arrive at a certain end, we 
should surely use the simplest means ; and there is, I think, 
little to praise or emulate, in the labours of those who resolutely 
seek truth through the most difficult paths, who love what is 
arduous because it is arduous, and in subjects naturally difficult 
toil with instruments the most incommodious. 
XXVIII. If in matters of abstract science deference is ever 
due to authority, it must be paid to that by which the study and 
use of the method of the ancients has been recommended. 
Newton has, however, brought forward no precise arguments 
in favour of synthesis ; and it is easy to conceive, that he would 
be naturally attached to a method long known and familiar to 
him,* and by means of which he was enabled to connect his 
own theory of curvilinear motions, with the researches of the 
ancients on conic sections, , and with Huygens’s discoveries 
relative to central forces and the evolutes of curves. 
The very ingenious and learned Matthew Stewart •f' encjea* 
* The circumstance of mathematicians having acquired a considerable dexterity in 
the management of .the geometrical method, seems to be the reason why they endea- 
voured to explain the doctrine of logarithms (a subject purely algebraical) by the 
introduction of the properties of curves. 
f Words are frequently stated in a delusive and imposing manner, not always 
