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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23
# Folio 8r, page id 00068236:0015
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de quolientibus replicatis. Scheda 1V.
proratione a ad b
Tit series quotientium replicatorum e 1. v. Wv v. v. v. er
quaeritur  Erit aequatio exprimens relationem inter a et b.
a - 1 b. aequ C. b - C vv aequd.  c - vd aequ. e. etc.
a = vbaqu. 1. (a) - v (b) aequ (C). Et generaliter:
(a)- v2 (2(b) aequ (2(C)
sive (Z(a) - (2+ 1 (4) Eequ (Z ( a)
quod si aequatio
(A (21 (a) - (B ((7, (6) aequ (211 (C)
(2 v ,  (6)
vel (Z (a) 2. v (Z() aequ. (Z + 1 (c)
vel denique: CE (2 (a) = v ( (a) aequ.
Eodem moda
(211 (a) - (2+2(a) aequ (2+3 (a). Et pro (Z +2 (a) substicuend.
volarem ex aequ. 2. fier:
23+1
(7+1 () (2+1(a) = v (a) + v (2+1 (a) aequ. (((212(a)
Ergo daegu;
seu c aequ a - v b. Erga d aequ b- vc aequ b - v a + p b
seu
+ B1 2b = v a
p
+vo1.
fiet: e aequ. +1 a - v 7b
10is
= verdt
fiet: f aequ - v a +.
- 1 7
pis
+voH
+ v
+ vor. 3 B)
f. aqu d - ve.
vel genepaliter assumendo quotientes
l. m. n. p. g. 8. et faciendo: Reis quantitates. a. b. c. d. e. f. g.
a - lb aequ. c.
b - mc aequ. d  C - nd inqo e. d -perequ. f. C- 9f aequ. g.
erit c aequ +1 a. - l b. daqu. b - mia + l. m. b
d aequ. - 1.m. a +1 b  equ +1. a - l. b. + 1. M. n. a - 1. n. b - l. m. n. b
e aequ. + 1.
+1. M. n..
faequ = l. m
+
+ l. m.
a ct1
+ l. m.
a +1.
= 1. m. n. SP
. +l.
Pa ego qu 1 a
+ vel Y
+ l
+
um
+
ut 
b aequ +E a + y
C aequ. +V a + 5
-nl
e Et il porro
faequ. - 1m a + 1+ l. mb - 1+ 1.m. n p a + l+ 1r Lm A B b
gaequ. B - gf. est autem C aequ B a + A b.
et f aequ. B a + Z b. Ergo 9 aequ. +B a + A b
ergo coefficiens residui sequens fit ex
qu. =95.
sequentis (exempligratia D- qu. coefficiens cum a. pro
residur  ipso residuo g.) it conflonitur ex D
resic coefficieate refitii verultium respontente cum
a scilicet) residui penultimi e, et eo efficiente
respondente in residui ultimi f ducto in novum
quotientem q. et subtracto. Habemus erg. regulam
proprediendi.