EXCERPTUM i.

EX EPISTOLA NEWTONI AD OLDENBURGUM PRIMA.

[Vide Commere. Epiftolic. N. 48.]

formulis algebraicis in series infinitas

RESOLVENDIS.

F Radiones in Infinitas Series reducuntur per divifionem; 8c Theoremaquantitates radicales per extradionem radicum, perinde i n _ BlN0M1ALEj^ituendo operationes iftas in fpeciebus, ac inftitui folent in deci-bilibus numeris. Haec funt fundamenta harum redudionum;^£_extradiones radicum, multum abbreviantur per hoc Theorema.

t> 2 m m — n m — in m — %n

+ P <*J = P"+ 7 AQ.+ — BQ + — CQ + — DQ+, &C.

2. Ubi p + PQ,fignificat quantitatem cujus Radix, vel etiam di-benfio quaevis, vel radix dimenfionis, inveftiganda efi ; p, pri-bum terminum quantitatis ejus; q_, reliquos terminos divifos

P er primum. Et 7 , numeralem indicem dimenfionis ipfius p+ pqj

** Ve dimenfio illa integra fit; five (ut ita loquar) frada; fiveaffirmativa, five negativa. Nam, ficut Analyftae, pro aa, aaa>

^0. feribere folent a z , a\ &c. fic ego, pro \/a, \/s/ c.0 5 ,

^0. feribo a*, & pro feribo a~\ « -z , a~ l ( a ).

Rt

fic

pro

== feribo aaxa 3 +b z x |"1; 8e pro

*/z-.a z -\-frx " ' " a /c-.g i +b 1 xxa i +b'x

f cribo a'bxlp+Fx 'H: In quo ultimo cafu, fi concipi-ar efie p + pq^)” in Regula; erit p=« 3 , Qj=-^r> m—~i, ?i~ 3*

inique, pro terminis inter operandum inventis in quoto, ufurpo

(“) Vide Arithmet,. Univerf. C. L

A» B,