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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 211r, page id DE-611-HS-3653099:0421
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 212v); this page is its right half.
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# Lines: 76 recognised, mean confidence 0.90
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series e
cum est senies um
Locarithmo sunumeri progressionis
arithmebicae respondentes N
seriei numerorum progressionis Geo-
Ngadeo quorum unus atenntas assumi potest unitas,
metricae, Datisque, duobus numenis
dats aliquis
positivus
vebe gratier
est numerus
o
ubi cunitati potest assumi pro loganth vero ipsius 2, namerus quicum
eleet
Manis estam in talem seriem numerorum
progessionus Geometricae non posse cadere
Fingaurus hos numeros progressionis
Cum haec series mediis proportionalibus
Georgehrice
assumtis ita interpolari possit fingamus
quantumvis
interpolationem eousque continuatam, ut
mere inter unitatem eknumerum 2, ut
tandem minimus interpolatorum sit
non nisi in assignabiliter differat
ab unitate; patet omn it is numerus
vocetur n, patet contia in continuulam
sed ponamus esse Unitaten L
progressionem 1. n cadere omnes numeros possibiles
mneros in hunc seriem cadentes aut certe eos
qui ab ipsis minus differant quantitate assi
hac
Huc posito manifestum est assumlis quotcunque
d data vi
tertius proportionalibus, nunquam perveniri
ad numerum negativum. Qua sed
videbur ad eum perveniri posse inter
eom
assumtis quotcunque
et assumtis quotcunue
c Tac
sin noptraserre datur l. 2.a
am
assumtis mediis proportionalibus, nam mediam quod
videm
ni
vide
esse tam +_2, quam= 2
quaeritur ergo au, quia dam 2, quam - 2 in se ductum
ea quae sumi potest inter 1 et 4
sed incommodum hic oritur, quod - 2+
tam 12 quam = L,
non  potest esse in progressione Geometrica
dat
in qua est +2., qualis nempe est nostra (ex hypolhesi) est nostra
derum
e
ubi pro Loganithio unitatis assignari potesto, pro logaricue
et alter est numems alte
vert. gratia 2
eu non
s
e
L
log 1 esse0
qud tamen de quovis numero potitivo dici potest 
exponentem queurcunque
alio
+4.
pepo sethum ipsus esse 0
a
proinde
Clogarich um habente recipiente
in hanc seriem 1. 2. 4, etc quantum continuatam
ultro citroue
esse regarithurum ipsus 2