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# Title: Commercium Epistolicum D. Johannis Collins, Et Aliorum De Analysi Promota (shelfmark Ms IV 379a)
# Folio 114, page id 1882181034:0122
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quam Calculum suum Oldenburso communicarie Deibnitius; & nonemde
eim annos anrequam Vir Ilustris eandem in ACtis Lipsiensibus edidic: ex
certe ante vitas hatce duas Nemtoni Episcolas, Leibnitium Calculum Tuum
Differentialem habuisse nulla apparene veltieia. Iis omnibus rire per-
pensis certissime cuiris conttabir, D. Nentonum pro vero Inventore Rrich.
meticae Fluxionum habendum cRo.
Restat jam ue inquiramus quaenam Fuere Indicia Leibnicio a Nemtono
derivata, unde ei facile Torer Calculum Difterentialem elicere. Et pri-
mo, ut dixi, nullibi oltendit Leibnitius libi norum fuisse Calculum Differen-
tialem, ante vitas has duas Nemtoni Fpictolas; imo ante illud tempus
lonsiore utus et circuitu, cum res Facilius multo ex succinctius ex Cal-
culo Auerent Differentiali. Hujus rei rectis sit Epistola ad Oldenbursum dara
8 Novembris 2676, quae in Operum Wallissanorum Fomo tertio etia ex.
tat, in qua modum cradit exprimendi rarionem Pubtangentis ad Ordina-
eam, in terminis quos non ingreditur Ordinata; ubi A locor ec du ipsarum
valores vinculo inclusos votuilter, Ccarim Pcopum actisiset.
In prima Epistola quae per Oidenburcum ad Leibnitium transmicta clt,
docuie Nemtonus methodum qua quantitares in Series Infinitas reducenda
AnC, i. c. qua quantiracum Ruencium incrementa exhiberi portunt. In
ipto enim initio Seriem oltendit, cujus Termini hXC InCTEMeNTA RePre-
sentant. Sed illa D. Leibnitium prortus lacebar, ance vitam Nemtoni
Epistolam qua exponitur.
Sic o incrementum momentancum quancitaris Auentis x, er index
dignitatis ejusdem, e si prox Scribatur x + 0, x = 20, N . F 30, X F 40,
_C. et Ouantitates x F op, v. f 203 v F 30, x -F 40 EEc. in Series In.
finitas expandantur, habebimus totidem Series, quarum prima haec eA quae
m = n
m - 2n
2n 00x n + md-3m n + 2mn
6n3
sequitur, x + = Ox n + m-mn
m - 3n
=aOOX  _C.
In omnibus Seriebus primus terminus erit ipsa quantitas Auens x; ex sI
prior quaelibet Series a polteriore auferatur, habebimus harum Serierum
differentias primas, in quibus omnibus primus terminus est scriei prima
m -n
terminus primus quem insreditur quantitas o, scil. =ox ; e cvane
cente ofr ille terminus differentiis hisce primis aequalis; vel quod idem
m n
eAt, eric quantitas =ox  Eluentis incrementum primum.
Praeterea B differencia quaelibet prior a Dolteriori anferatur, devenie.
mus ad differentias secundas; quarum omnium rerminus vrimus per 2 di-
visuS.
apparent
ist
Herotonum habuisse
num Cal
u dilm a teobunto