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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23
# Folio 10r, page id 00068236:0019
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quolientibus replicalis scheda
disdem ergo positis sit seu aequatione.
sit caego a a - lb et fiet: haa, sa et
seu ph aa CC
tis ab..
+nt bb..
-It bb..
h1b + s L et
lsbC aequ Ih b
amh aa ae
fier: +ms ab
+ n + bb..
= 1C. bb..
had + sa + t
in seu
_ +lm t - 13 + + ls - lh aequ. 0.
seu posito haequ imt- 1+ +) fieri
hbb + s + t
aequ cc
haacet sabcet tlbC aequ
hb + sbc + t bbcc
Et ponendo pro C substituendo: a - lb
aequationem productam fieri cubicam destnitur enim
itaque si jam vel contingat, vel ob arbitrarias effici  assumtas
efficiatur, ut ut s duo primi quolientes sint l. et m. iidemque
eadem opera explicentur habebitur se series quotientium. 
Compendii causa ponatur F aequ. 0. t; et tunc si volumus
tillere b fit Saequ. h. adeoque evanescit tam squam h.
et fieret:
maa ec a maacc - lbc aequ lb2
sive meaat a = miaal 2t ab + maa Hbb = LV a (+ lb 1b aequlIb
seudoniue
lntae + mab-2m abb +  aequ + lN b3 F Ebna
-Ellm... +m... 
ergo a aequ. vel
-em  - (3m
lma = 2lm a bb aego _ + l b3 - m a b
+ l3m. . .
possumus et sae problemqe formare;
 F u b
d ab c: + Ubb = 15b a + Isb equ It b. 4
et omnibus ordinatis: + mh a + ms aeb + nt aabb
ubi nota: posito 
- 2 l inh
- (2m ... + eum ...
invenire quantitatem b. quae a quantitate a sublata quoties
fieri potest relinquat quantitalem C, sitque a + sab ad t b
ut a4s b + sbe ad cc. Unde videamus an sequatur b et a
eandem habere inter se relationem quam b et c. seu eodem modo unum ex altero
formart sit a aequ 1b +c seu caequ a - lb. et H aequ ac alabrbb
substitur atur Vulor ipsius cc in ejus locum in analogia. aa + sab: bb. : bb + seo: CC pallpabene in
a et: a - 2l ab + Uaa bb + sU a b + argo 64
 - s1b
+ 5a3 b - Elsaa bb sY
si vero in analogia aa +sab: bb:: bb +s bc: cc. substituamus lone in locum
fiet aa aqu 1bb +2l9bc + cc ergo puilliplicando fieF: est veu
sed inde
Ubb CC +21bC3 + C4 + slbbcc + sbc3 aequ _ b2+ (b3C
video hanc aequatione priori inter ata inter b et .
priori inter a et b. conferri non posse, et sane alioqui quoticus conegetion.
potiber. foret ader hri re te 
=2lnt ab
npi
tis iiti
a quod estrectum contiper
et a. t Retatio siailisilli quae intor bit. N
Hus cum sit apb. erit bp. c. ergo in aequ
a. aequ. 1b Ac erit a diidendus b. divisor
quotiens C. resictuus Ut ergo
divi soo, ale divident
quotieas. nam
pMC. et et a 1pb p a 1be
sem ol.. qua
ut (nam apibre et bpb
pia a    sinaib. 
itu ita cpk-M C
Ha consa, entia sit
 probatae; ponatur hader
relatio aequalio ra lation
inter b et a. et
1. b. 1. hujus ope inveniatur
tum valor ipsius  tum valor
ipsius a - 1b. et notetur differento
iite hos valores. similiter ee relationis
inter b. c. m. inteniatur vulor ipsiu C
m resu et ipsius b - lc. qui dec
valores utiue eodem modo formati
erunt ex  b. c. m. uti priores
ex a. b. 1. Ergo et si prioresdio
se vatur ipsius un et respondebit
valor. b ratori C. et valor
a - lb balori b - me. ergo
ilor b. major valore a - 1C
etiam valor c erit major
valore a  b - me
 nam eodem modo
um sint exprassae
Eaedif
t au pa seu
b + b0 a b a + D a. b. Er
 B hinc
 braba nopa
cofficuiua, eritne
 affirmatva
ad eoque en B a Hlo bua 3
eme css
iode
ula