[ 5*9 ] 
Sect. 8. 
Reflections on this Contr overfly. 
Upon the whole, I cannot but think the Contro- 
vertifts on both Sides have had a very hard Task > 
the one to prove, by mathematical Reafoning and. 
'Experiment, what ought to be taken for granted, 
the other by the fame means to prove what might be 
granted, making fome Allowance for Impropriety 
of Expreffion, but can never be proved. 
If fome Mathematician fhould take it in his Head 
to affirm, that the Velocity of a Body is not as the 
Space it paifes over in a given Time, but as the 
Square of that Space ; you might bring mathemati- 
cal Arguments and Experiments to confute him j 
but you would never by thefe force him to yield, 
if he was ingenuous in his Way; becaufe you have 
no common Principles left you to argue from, and 
you differ from one another, not in a mathematical 
Proportion, but in a mathematical Definition. 
Suppofe a Philofopher has confider’d only that 
Mealure of centripetal Force which is proportional 
to the Velocity generated by it in a given Time, 
and from this Mealure deduces feveral Propofitions. 
Another Philofopher in a diflant Country, who has 
the fame genera Notion of centripetal Force, takes 
the Velocity generated by it, and the Quantity of 
Matter together, as the Meafure of it.. From this 
he deduces feveral Conclufions, that feem diredtly 
contrary to thofe of the other. Thereupon a ferious 
Controverfy is begun, whether centripetal Force be 
as the Velocity, or as the Velocity and Quantity of 
Matter taken together. Much mathematical and 
4* experimental 
