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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 111r, page id DE-611-HS-958803:0223
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4
dc: esse aptater 7 = y, quando sclicet X fit = 1. hine fiet differentiando seriom
Xt
p2
12 1.23 125. 2 ec:-
+ + X
ds -1 = X 1
ac
XX
1.2 4
X
+22
Li
 ablato itaque primo termino t provenit series idlentucae
12.3  r2QC: de consepienter = i. de proinde cls =- ycx + dx
qua agilatio ostencit is seu potius s + 1. esse numerum ipsius Xx sul unitatis.
laterum reperio seriem lavr, + in + ins t in2 cs esse aqualem subie alteri,  +
16
i 12q  12S.qS_C. esto jam querenda summa hjus seriei = Y 24 Y 2.46
+
2.6ues Tiat.
2t 2 226 C yideogue X + 2 +
s
1
X 1 X
 transposito X d divisa cequatione per X, habeli Ad
c
+ XI
2. 4
1
L
2.4
+ F1s XC = yA di YXcX + XeZ quae aequatio (posito XX ~ = Z) reclcitur ad prae
ax
X
ad est
ceclentem. Auod etiam alia via invenitur faciendo XX = Et unde = + 5. Z L
225 Hc: = 2
1
vit L 202
L4
2. 9.6
de
1.2
is Nc: quae serces ulique similis
est preceente. auando ven clenominatores componuntur ex numeris imparibus
aqulatio procit omniro diversa ab illa praecedenti: ul si proponatur +
+1s  1.5 c: proindlege siat X +
(+ XX + X
1.3
dis
1.2   seux
+
ax
X
X
1.5. 5 +
+
d.l3
2
I2s.7 c poi set = yd
X
1. 5
+5
1 X
dec: =y habe-
1.3.5 135.
bitur haec aeguatio cly =xyclx +x qua, cum sit specialis casis aequationis à fra-
tre inaetis nuper proposita, d’ au se d ame solutae, potest per nostrus ale
methorlos ulterius recluci ad alium aljus indeterminatae separari possunt. Eiclea-
mus jam gulie proventurum sit e sue generali serie à
ats a bat 8 _c Ciontelligo per ad b nuneros quoscumple, ita ut a, a +b, a + 2b, at
va
36, 4e faciant progressimem Mrillemelium qlamuorgue) faciamts es co X
patib
Ya ∞atb-1
a. atbat 16 , unde 
divisa agulatione per t
ert
a
r. t2b- 1
a. a +6
cis
16
cx
et 36-1
rato
+2 a+b
a
auto. atio. d: transpesito  a-1
b
va
rato, Xa+2b
Si ie quod hare sugyerit aeguationem cles =y2-1
cx + Xa  dx
de