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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 118r, page id DE-611-HS-958803:0237
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 119v); this page is its right half.
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Datur  - 2 + 3 = 4 + 5- et C Logarithmo Binari.
(2d0)
sed him
videtur prima specre sic concludi posse: + +  +  + = et sit = A, et
 + 4 + l + = etc = B (3tio) B. per 1, 2, 3 fit (4t0) A - B = C. jam
(660)
porroseto  B = A + B, : 2, ut videtur. nam A+ B =  + L +  + = + = +  etc
Et A+B, :2 = (7 mo) Z +  +  +  etc.  Ergo per 7 et 3. fiet aequ. 5.
Sed ex aeq. 5ab videtur oriri absurdum. Nam ex inde
fiet B: 2 = A: 2. Ergo B= A seu (8) B = A unde fiert per aeq. 4+ fieret (9no) 0-0
quod est absurdum vele faltevi Respondetur  hanc conclusionem esse absurdam
vel etiam veram si recte intelligatur. Nempe O esse aequale nihilo, si comparetur
ipsi A vel B, quae sunt infinita At tamen non esse nihilo aequale, si numeris
ordinariis comparetur. Unde vener etiam est  aequatio articuli 8, etiam
secundum leges infinitorum, regligendo scilicet discrimen finitum, totisinomparabiliter
Eadem alia Methado ostendere licet, si
t inaequiparabile
per finita procedamus reperietur enim in f ipsis finitis non esse B et A
(imo  puitilo
aequalia nec locum esse aequationi 7.
Sed ppogrediamur jam ad  - - + = - 1 + - - - = C. quod sit
2
36
25
5 16
paa terdet enim haec summa ex quadratura figurae logarithmicae. jam eodem
modo sit  +  + = etc =   (2d0) A et  +  +  etc = (2d0) B. Ergo
per 1 fiet A- B = a(2tio) O sed e   sed B A+ R,: 4C 
Sed B = (4to) A+ B,: 4. Ergo 3B: 4 = 6to) A: 4  Ergo A= 5B A (5to) = 3B
Ergo  peer ex 3 per  fit B = (6t0) = O: 2 et per 5 fit A = (7 mo) 3O: 2
et A + B = (800) 2C = (9no) = + L +  + 6 + L- + L etc
6
Eodem modo sit = = + - -  + = -  etC =  (1mo) O
64 125 216
= 1B
per 1. utique B A-B = ((4t0) O sed  A+ B:, 8 = (5to) B. Ergo
 R: 8 = (6697B: 8 seu A = A (6to) = 7B et A=B seu C = (3 mo) 6B
seu B=  (9V0) O: 6 et A = (9no) r7O:6 et A+B = 8C: 6 = 40: 3
Sed praestat calculum generaliter instituere hoc modo:
1 -  + L - = + 1   etc =  (1mo) C et 2d0) je + = +  etc = A
2
4.
5
6.
3.
et (3to) c +  + etc = B. Ergo ex  aequ. 1. fiet A B (4t) A= B = C.
(6to)
porto A+ B = L + = + = + = +  + L etc t) et (A+ B,: 2. = B per
2.
3
4.
5
5t
6.
evidentiam calculi. Ergo pmo) A = E. B = B. Ergo (400) A+B = 2? B
Ergo (800) (A - B _ seu) C - 12. B - 2B. Ergo sistanamus dari C habebitur et B
et fiet (9no) B = C: 2. =2 Et (90) A= O (.,  - 2) - B
2.C -C; 2 - 2 sec  seu Amo) A = O 2. - 1: 2. -2
fieri 0= 0 vel B = d:0. sive C esse mcom
In aequaparabile ipsi B, t B vel A, et B vel A incomparabile ipsi O
Hinc patet cum C est
 itaque ipsa in speciem absurditas aliquid veri probat.
seu 2 0:, 2= - 1
. 2. 5. e de etc
2
Se 4.