374 Opuscula. 
pnciorem fumcre licet . Nam fint Jl\ B' ; f /" 
quantitates determinatise , & fupponatur f ^ -\- / ' y f z, 
xqudle f X plus tundioni arbitrariac lineari x -{- J y B 
X + A y-\- B z: ; erii f x -\- f y -\- f z. ~/ x p {x-\-^ Ay 
-h-^ 2:) -f- ^ (^ + ^'jH--B' : eigo f — f -hp-hq; f =z 
^A-^qA^; f-:=.pB + qB': unde q ^^JfzAC^ p 
= -—- — -— r ; unde / determinatur . Ergo forma e'^ 
,V X -\- Ay-hB z> ^ X -\- y -\- B' z eadem pollet generalita- 
te j qua torma primo fumpta , modo non fit B A' — B 'A 
= 0, vel = , quo cafu F evadit funClio x-\~Ay 
-{-BzyX-^-P.Ay-^-Bz^y & ideo duas tantum variabiles 
involvit. Deinde cum pro x -\~ A y -\- B z , 81 x-{-A' y -^- B' z> 
ufurpari polTint x ~{- A' y , x jB"z,, modo multiplicando 
x -h Ay-\-B'z per q ^ q , & detrahendo ex fundione 
X -\- A y -\- Bz fatisfieri polTit xquationibus qA — A = o, 
q B' — B — o , nec q jcquetur q\ nec fit q — i , vel / — i — o ; 
in primo autem cafu fi quaeratur A' & erit A' = S"— o ; 
in fecundo erit A' vel 5" xquale infinito : his pofitis 
Sit u — M .e^ ¥ x-{-A y^x-{-B z : cum poft fubftitutionem 
quiiibet terminus evanefcat , erit b-{-fc — 0, c-\-gA 
=z o , c h B = o : unde , modo non fit c ~ o , nec ^ — o , 
vq\ h ~ o , u — e ^ Fx y , X J ^ ' 
Si f — o, aequatio variabilem x; fi o- = o , variabi- 
lem _y ; fi ^ — o, variaoilem z, non involvet: ergo in his 
cafibus duarum tintum variabilium u ent faniiio . 
hrgo generaiiter forma ufurpata vaiorem quantitatis h 
repraefentabit . 
Si quxratur expreflio quantitatis « per fundionem unius 
tantum quantitatis , ut e ^"""^^^ ^ x -\- A y -\- B z , vel 
potius e f'''^^ y Vx-\-Ay-\-B%, quoties B non eft zero, 
erit b-\-cf-\-gf~o, c -\- g ^ -i- h B — o ; unde va- 
lor // erit fumma funftionun^ N . e s H- feries in- 
linita rerminorum e/us foimx ){^ ^-h^J ' "^* 
