The Principles of Fluxions Designed for the Use of Students in the University

Samuel Vince

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Waring's Med. Alg. Last edit, in the Addenda, K + L -f &c. =0 ; Ka-fLZ>-|-&c. =0 ; &c. Through all those terms, when m is less than n ; in this case therefore F=Ka m x h. 1. X — a -f L. B m X h. 1. X — b + &c. If m be equal to or greater than n, the coefficients of the first n — 1 terms will become=0.
136. If m be less than n, the quantity - — i)x n - l +tx. C. ' ' ' may be resolved into -i J f-&c. For in x — a x — b x — c this case K x x — bx x — cx&c. -f-L x x — a x x — i c x 166 Fluents of Q...uantities.
&c. -f-&c. = x m ; hence, if x=a, K= = a — b X a — cx&c.
' b m if x=b, L= : — ===== ; &c. The reason why b — a x b — c X &c.
;;z must be less than n is this : The quantity K X x — b x x — c x &c. -f L X x — a X x — c X &c. -f-6cc. — . V"'=0 ; and that this may be always true, the coeffi- cientsof the like powersof x must be assumed =0 (Art. 110. ), and by such an assumption you would deduce the same values of K, L, &c. As above. Now the pro- duct of each of the quantities into which K, L, &c.

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