4jB Opuscula. 
Eadem methodo res coiificirur iii feiie tertii gradus. Sit 
icquatio pc^ — t — s x -A- s o , quce habet pro radice uni- 
t X 
tatem . Samptis primis terminis ad libitum by c formetur 
feries multiplicando tres terminos aiitecedentes , incipiendo ab 
ultimo , per ? i , s — f, ■ — s. Sit autem aybiCd^eyf^g 
&c. Patet d—tc-¥-sb — sa^ e ~ t d s c — sb &c. Su- 
■4-c — tb d — tc 
mantnr differentix , & nafcetur feries a — b^ b — c, c — d^ 
d — e i e — /~, f — g &c. hi tertio terraino pro d fubftitue 
ejus valorem , & invenies tb — • t c A~ s a — sb^ qui refultat, 
fi fecundus terminus ducatur inf, primus in s. Eodem modo 
polito in quarto termino valore (? , invenies / c - f i -f- j ^ - c , 
qaae quantitas nalcitur multiplicato tertio tenTsino per fe- 
cundo per s ; arque ita deinceps . Quare feries differentiarum 
eil recurrens fecundi gradus . 
Si feries fit gradus quarti afiumatur sequatio ^ 
x"* — t x'' — s x'^ —- r X -i- r — quae componitur ex duabus 
— x'' t x^ ~k~ S X 
x"^ — t x^ — s X — rmo, X — i=<3. Acceptis quatuor pri- 
mis te^"minis by c^ d conficiatur feries muJtiplicando qua- 
tuor terrainos antecedentes , incipiendo ab ultimo , pcr f -f- i , 
s — f, r — s y — r . Series hxc ita exponatur a , b , c , d ^ e , 
fi^ih &c. Confcat fore e~td-hsc-\-rb — r a y f 
d — tc~—sb 
te~^sd-\-rc— rby atque ita deinceps . Series difFerentia- 
•4- i? — t d — s c 
rum exurget a -—^ b ■> b — c , c — • d , d — e , e — f'>f—-g &c. 
In quarto termino pro e pone eius v^dorem , & habebis 
t c s b "h r a ^ quse quantitas item refultat, fi tertius ter- 
— • t d — s c — r b 
minus duotur in t, fecandus in j, primus \n r . Eodem. mo- 
do in quinto termino fi valorem fublHtuas, invenies quan- 
titatem , qux nafcitur raultiplicato quarto termino per t, fe- 
eondo per s, primo per atque ita deinceps . Itaque con- 
ftat , differentiarum feriem elTe recurrentem quarti gradus. Ex 
hoc progrefTu iure optimo colligimus, feriem recurrentem , fi 
onitas fit radix aequntionis refolvendae , ut detegatur terminus 
generaJis, exJiibere differentias , qu^ conitituunt feriem recur- 
leutem gradus inierioris . Quociica feries recurrentes cum ap- 
peii- 
