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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23
# Folio 1r, page id 00068236:0001
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21 aequ. 4 2 +f 3048+ f0
21 aequ 4. 225 +. 1. 2. 3. 9. f 4 1. 3. 4. f F 1. 4. f + 1.2. f + 1 f . 1. 2.3. f- 4. 1. 3. f-H1. fnD
1. 2. 3. 4. + 1. 3. 4, + 1. 4 + 1. 2. + 1. B O
(168 aqu. 3. 21 +5 aequ. 2 3D + Q ax + aequ 3D + 8
seu tg aequ. 3. 4. 125 + 3. 12. 3. 4 f. 4 3. 1. 3. 4. fx 3. 1. 4. f 43. 125. (+ 3. 1 (3. h. 2. 3f. P3 b1 2 f( (1f.)
+ 225 = 1. 2. 3. f - 1. 3. f - 1. f
C
152aqu. H 2. 68 +4. seu 2. 8 + D aequ.
Ad.1)
+ 2. 3. 1. f
en 152 aequ 2. 3. 4. 225 +2. 3. 12. 3. 4 f 123. 1. 3. 4. f. 4,3. 1. 4. f + 2. 3. 12 f - 2. 3.7. 2. 3f-2. 3.Y. 1. 3. f - 2. 3. 4. 1,
122, 28171
a
+. 2. 225 = 2. 1. 2. 3.f - 2. 1. 3. f- 2. 1. f
+4. 225 + 1. 2. 34. f + 1. 3. 4. f 4+ 1. 4. f + 1. 2. f + 1. f Y-11. 2.3 f-21. 3 f. 81. f
1. 2. 3. 4 + 1. 3.4. + 1. 4 f 1. 2 4 1.
2
Ergo bego Ergo omisso  f erit b aequ map +m + p.
a Imnp + lnptprnt
Atque ita semper
tolli possunt omnia residua, ut restent dento ultimo quod in progression
Si jam ex his quotientibus
negligitur) ut restent soli quotientes.
quae sertes haberi possit series infinita numerorum cognitorum quod
prpecuti pipit
jen perpetuis substi
ribes+
fit methodo alibi explicata: tunc utique eadem opera habebit tollentur
cogn quotientes, ad est invenientur eorum valores. restabitue sola
litera a cum numeris, et datis aequationem ingredientibus Cum
ergo valor incognitae b, vel rationis b per quotientes, inventus sit
ope per quotientes  ex naturato calculi generalis, potent poterunt
jam tolli isti quotientes ex natura calculi particularis, seu ex aaequatione
data. Exempli causa sit bb+ vba -aa aequ. 0. (loco aequationis: bl +C aequ. a.)
hiiic aequationi jungatur ista: b aequ. me +d fiet: bb aequ. mc + 2med + d, quod substituendo in aqu.
aqu. a -c aequ mc +
priori fiet: me +med+ d+ vba-aa seu baequ. aa - mc -2mid - a.
seu laequ. vaa-vac
b + va p
seu ay, a- c a
aa -mmcc- 2mcd-dd
a va + b+ v+ 
a
V a + mc +d, a - mc -d
f2+ bf b + a b aequa. b + aequ  aequv+ 
V4 b
a
a
B. terabhit ess  d4  ergo quotiens primus est v.  residuum vero et Calb (tate enim
a-
qudemonaa sumendum loco b ut sit linea, quasi instienta esset divisio per a uti ec sane
brala revera per ipsum instituta intelligi debet nam dum dum ab uno latere per
signaa Ergo a, do ab alio dividi intelligendum per a ob aequationem.) hoc residuo
b debet dividi b. et fiet:  = aeqo Itaque erratum e
et sic potius procedendum; quia va +b aequa ergo divisione a simpra
parte instituta iidem prodibunt potieates qui a gextra. Ergo fier: v + b residiu
b, quo iterum sibide debet a. fiet
2
a aequ b + (∞a eu ) 7+ vaet a.
a b
5 + ba+b
aequ
aa
aequ.  aequ. + b (+ bb seu  - B sed it hor prodest, deo relmeamu aequ. X + b +bib. quod si
a aa
ac
sit b minor quam dimidia e a, erit quotiens alter v residumm vero ba + bb minus
quam aa, et pribemus: ba +bb aa quod iterum subtrahendum a divisore
isto aa. quiasut ante divisivaa ipsius va per a aequivalebat divisioni ipsius
a per, b. itta nunc divisio ipsius  ab + Bt vae per a aequivalet divisioni. si
a per P. et proinde ob eandem rationem iidem prodire debent quotientes
ergo continuanda semper novissima, idem enim semper prodibunt quotientes
pay. 5
=3.9. 1
C.3
bt a. Ergo dividendo
si r critbraepaa