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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 216r, page id DE-611-HS-3653099:0431
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decretant in ch, 5f_. Cum itaque sucmlis TR pro unita
Le affirmativa et Tr prounitale negativa, EtC, SF expro
maat logaritharos nucrerorum affirmativorum; expriment
eaedem vel ipsit aequales eh. sf logaritlimos numerorum Te
15 qui respatu alderorum E, 15 sunt regativi; verum
igitur eat unum euudemq, logarithaum respondere duobus
numeris aequalibus uni offcioatioo alteri negativo; hoc est
Cor. 79 +n aequalem ese lop. F8 - n. 2. E.D.
Commaicavi Zecum jamr olim, si recle memini, quadam qua
ia Nevlonianis animadverte: aaimus mini eit, Meuscenio ila ro
gaate, aliquid ad Arta Lipt. mittere, de motu projectilina, ubi
quordam errores Newtoini notabo, quos octendatu originem traxisse
ex prava sereu applicatione, ia quibus sumam rei illum po
scuste rectisciare dicis: sed et hoc ipsum graviscimum erroreur se
perit, qui lale serpit et omnes fere ejus solutiones circa hanc
materiam in opplicatione inficit. Erion autem ia hoc consittit
quod sar. 263. catuit ad habendatus fluxiones altenvium qra
duna alicuscr quantitatis fluvilis, sutor num ipsius loquladi
more) conjiciendam esse quantitatem fluentem in seriem per
extractionem radicis, tunc eaa fore puaum ejus seiner terain
num ipsam quaatitatea fluentem, seuudum vero esus fluxionem
primam, tertium fluxionem fluxiomic qaum vel fluxionem
secundam, quartum flusionea terbiam Y. hoc eit, secmaduu
nostiuem exprimendi morem si differentianda sit ex. gr. xa
scribeadum esse + dx, hocqus per extrartionem vel potius
per evolutionem in seirem conjetum nempe hoc modo
-
2 -1
X + dx = X + n X dx + a. n- 1 1. 2, 2
X
n
1. 2
ex +
R. R - 1. _ -2 n- 3q
1. 2.3
X ex + a.
exhibere differentias omnium graduum  in infiaitum conti
unatas ipsius x, quod autem exceptis primo et secundo terminii
de reliquis omaibus faltuu est, docet eai comnais differentiandi
regula differentias continuatas hanc exhibere Cerieur X de+
2
nX dx + n. n -1X dx + n. a - 1. a - 2 X 2.3 
a
ax +B. quae cum surore
n.2
duos praecedenter terainos tantum comunes habet, relquos omnes
diversos; cinde suspicari fere licet, vervionum sum temporis
fluxionum contianandarum ideam nullam adhue claram tabuisse:
quid enm opus habuiscet confugere ad radicum extractionem, 
si differentiationum naturam satis perspectaem habuisset: at adeo
e10