 | 1802 - 708 σελίδες
...a ratio of equality. We mud therefore be careful to diftinguilh between the ratio of two evanefcent quantities, and the limit of their ' ratio ; the former...ratio never arriving at the latter, as the quantities vanith at the inftant fuch a circumftance is about to take place." This reafoning of the author is... | |
 | Samuel Vince - 1812 - 274 σελίδες
...; for in every state of these quantities, ax3+mx : bxz+nx :: ax-\-m : bx-\-n :: (when x=0i) m : n. As the quantities therefore approach to nothing, the...vanish at the instant that such a circumstance is aboBt to take place. PROP. III. If the fluxion ofx be denoted by x, the fluxion of ax •will be ax.... | |
 | 1812 - 712 σελίδες
...ratio of equality. We muft therefore be careful to diftinguiih between the ratio of two evanefcent quantities, and the limit of their ratio; the former...ratio never arriving at the latter, as the quantities vanifh at the inftant fach a circumltance is about to take place." This reafoning of the author is... | |
 | Samuel Vince - 1818 - 414 σελίδες
...that of m : n as it's limit. Hence, if m = n, the limit of this ratio is a ratio of equality. We feust therefore be careful to distinguish between the ratio...quantities, and the limit of their ratio ; the former ratio of a fraction, and by the motion of ff and P to A and F respectively, APAP AP, FG, vanish together,... | |
 | Florian Cajori - 1919 - 294 σελίδες
...the quantities therefore approach to nothing, the ratio approaches to that of m : n as it's limit. We must therefore be careful to distinguish between...that such a circumstance is about to take place." By aid of the binomial theorem, Vince finds the fluxion of x", when the fluxion of x is given ; he... | |
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We must therefore be careful to distinguish between the ratio of two evanescent quantities, and the limit of their ratio ; the former ratio never arriving at the latter, as the quantities vanish at the instant that such a circumstance is aboBt to take... 