 | George Baron - Mathematics - 1804 - 318 pages
...or decreasing state, the fluxions will be increasing or decreasing* t 8. It has been said, that when the increments are actually vanished, it is absurd...let the increments of two- quantities be denoted by ax* -\-rnx and bx*+ nx; then the limit of their ratio, when x=0, is m : n; for ax*-\-mx : bx*-\-nx... | |
 | George Baron - Mathematics - 1804 - 274 pages
...said, that when the increments are actually vanished, it is absurd to talk of any ratio be-- fween them. It is true; but we speak not here of any ratio then existing between the quantities, but oF <hat ratio to which they have approached as their ffmit; and that ratio still remains. Thus, let the... | |
 | English literature - 1812 - 712 pages
...to talk of any ratio between them. It is true ; but we fpeak not here of any retío then cxiltiiig between the quantities, but of that ratio to which...they have approached as their limit ; and that ratio (till «emains. Thus, let the increments of two quantities be denoted by ax*-4-mx and f/x -(-nx ; then... | |
 | Florian Cajori - Mathematics - 1919 - 320 pages
...generated quantities fluents, I fell by degrees upon the method of fluxions.'— Introd. to Quad. Curves." actually vanished, it is absurd to talk of any ratio...let the increments of two quantities be denoted by «*2 + mx and bx* + nx ; then the limit of their ratio, when x = o, is m:n\ for in every state of these... | |
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... 8. It has been said, that when the increments are actually vanished, it is absurd to talk of any ratio between them. It is true; but we speak not here of any ratio then existing between the quantities, but of that ratio to which they have approached... 