Full text: Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli (1. Abtheilung, Band 3)

33 
eritque i + l- + i+i + i + i i + i-+|+i-+ 1 3 5 _ A 
= hinc pro singulis sequentium decem terminorum ab — 
i i 10 i 
usque ad — ponatur adeoque pro 'omnibus — = -y> ita 
11 10 1 
etiam pro 10 seqq. ab at ' yy ponantur = yy» etproseqq. 
ab 5T ad ik substituantur — etc. et ita consequenter us- 
31 40 3u o 
que ad adeo ut summa terminorum ab i- ad —fiat y + 
11,1,1.1, 1,1 A 1 . , . v 
2+T+4+F+6+8+9 = A ~ 10’ J USl ° maJ ° r ’ Ea ‘ 
, 1 , 1 
dem ratione ponantur pro singulis terminorum ab ad ^qq to 
tidem et pro singulis ab ^ ad totidem atque 
, 1 , 1 
ita porro usque ad ^; quo pacto summa terminorum ab 
ad 
1000 
fiet ut antea = Á 
— justo quoque major; ideoque 
summa omnium mille terminorum ab unitate fiet A -{- A 
+ A 10 
3 A 
10 
1 q 493 . , . Tf 
— = justo major. Iterum pro 
..,1,1 1 
terminis ab — ad -- ponantur totidem 
20 
1 
20’ 
et pro terminis ab 
1,1., 1 ...1,1 
oT & o on totidem — etc. ut et pro terminis ab — ad toti- 
¿¿LuU OU IUI allU 
, i , 1 , l ., l 
dem — ; et ab jrr— ad —r- totidem etc. qua ratione summa 
¿¿UU flUl DuU 5UU 
i .i „ l.i.l.i.i.l.i.i 
8 + 9 
111111 
terminorum ab — ad — fiet 2 + 3 + 4+5+6+7 
, 1 . , 1 
-f- fQ — A — i, quanta quoque erit summa terminorum ab yy 
ad sed utraque justo minor; unde et summa omnium mille 
661 
terminorum obtinetur A -J- A 
III. 
1 _J__ a — 1 = 3 A — 2 
3 
840
	        
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