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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 13v, page id DE-611-HS-958803:0026
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 14r); this page is its left half.
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# Lines: 65 recognised, mean confidence 0.83
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12
Adeoque fiet ly = 3+ L Z
1 73+L
2.3 l
34 1
15
37. = 45 C et quemadmodum
et sine hoc calculo primo obtata haberi poterat sed malui formam generatum
inquirendi servare. Atque haec est ordinata artificialis (ut Angli solent loqui,
magna smplicitate expressa. Unde ex Tabulis Logarilhimorum habeh facile ordinata
naturalis. toque sufficit in prapi, cam de arca figurae similibusque non quaeritur
sed si quaratur ipsa y per seriem, licebit uti serie a me adhibita, pro
invencendo numero ex dato logarithmo sit log. lerit numerus  el
+  + = l2 + 123 (3 + 1. 23. 
T2
1+ LX (X +  X 2 (X +  X etc Dum hac scribo ad tuam seriem respi
ciens video plane hanc ipsissimam esse, nam ante quod impeditior
calculus videreh, fugiente tantum oculo lustraveram. Ubi illud prae,
carissime a te animadversum video, quod termini ut XLX: possint
summari, quod per se egregium est, etsi ad inveniendum (yax non serviret
sanc tades quadraturas et misidudum fuisse cognitas, dicere ausim
te non invito; sed tu et hoc ausim addere, facile obvias non esse. Originem
quadraturarum huiusmodi ascribam. saltem ut videat an tuae ispire. Nempo
(23
C)
eon
si r-1 fict h sah= x dx= Xh (X x Xh Ergo si h- 1 = m. patet utique
Summari posse omnes, X lx de seu dan (Xm Ix dx. Sed hinc rursus ope
aeg. 1. inveniri pt etiam (Xm
2
dXh (x  C3) h.Xh. 1 lX de +2. Xh.  l dx Unde h soch. 1 lx dx
(4)
= Xh CX2 -2 (X=1 (xdx sed dah sxh-1 x dx per aqu. 2 Ergo datur
et (Xh -1 (-:
sam (XE dx. Hinc vero jam iderum oste
aq. 1. inveniri pt eliam sm (X. dx. Nam si in ag. 1. ponas r- 3, fiet rum
d. Xh l= 3 -(6) h xh - 1 (X dx + 3Xh -,
C7
-3 sxh.1 12 dx Unde cum detur. (Xh- 1 1  dx per condusionem
dabitur et (Xh-1 (X dx, per 7 adeoque dabitur C0s
porro pergendo dabitur generaliter
 m
(m (X dx et quidem per soriem
finitam si e sit numerus integer. In nostro autem casu m et e sunt
aequales et quidem integri.
Sic etiam cum varia olim circa variorum graduum differentias
Tuae
tentarem i seriem alterius ex illis ductae,  similem incidere memini
gito
hinc fuere ha cogitationes intor meas primas parienses, cum sum,
mas summarum Edetlonvillai vel pascalti meditarer. sit series ds
decrescens a b c d etc
Ejus differae primae e f g h etc
secundae
tertiae
quartae
quintae
d
m n0 etc
q
r
5 ete
 W 3 etc
u
0 etc.