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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 161v, page id 00068194:0322
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p
et ago
23. C +2d
e
b a)baequ scad. Eugob aequ 3etd eequ. 3+3. (et a aqu. ) i  aru. 2+
3Cx d
et Eaequ4re
CI caqu adre Ergo F aequ. 2e aqu. 4 +  ( q E aequ.
d) d aequ.dets: Ergo  aqu set 3 aqu 5t F  
3C + d
Let E aequ 25. C +45
115)d
3+ 4
5d  s aequ 2 +E aequa+ e
. d F+ 3 aequ. 3+  aqu. 3
e
4
1. e aequ. 2 + 
83. 4. d + 3. C
+ 1
s
5
e
24 d + 23. C
2. d
3. 1. 5C + 3. 4 f
f
aequ. 3. +
et 2 aequ. 2. 3. 4. 5. C + 2.3. 4. f
4. 5. C
2. 5. C
l. 3.
3. 4. 5. C F 3. 4. f
 4. 5. C 4. f.
Data sptratioa sit aaequ
incerta
Clarius et brevius
(2)
vel q aequ.
Eodemundo examinetur  est enim B major quam c. alioqui F non erit fractio inlegro minor, seu 2 non firet quotiens, et c non foret residuus.
pro b. B ib misois ap X 3 cX d (ponento 3 pro nnem inert. serit. B aqu. det d aqpu. 3 4 2. jan  . denquod . erpo i aqu.   quen elaem alt
C
(7)
(6
foret quotiens
quem valorem ipsius (inventum in aequatione 9.) substituendo in aequatione 3. habebitur a dqu. 2 +  vel valorem ipsius b exaequatione 5
pntu ac
Eodem modo continuando  infinitur
2bf1c
Ponendo B aqu. 2b+ c. fiet: 4 aqu.
3+ 1 parum
4+8
(.9) 2. 3. C 2Dd et posita d aequ. 0. fiet 1397
ponendo et b aqu. 3C +d fiet. a uqu. 2. 3. C + 2d. et a ag C
porendo c aqu. 4dte fiet b d
(17)
c
2
3C + 1d
(14)
3+8
+ 2. 3
 3 aequ. +  justo minor
19)
e aequ
e 6
(18)  4d   e
ponendo d aqu serf bet C aequ. 4. 5. 8 + 4f et b aequ 3. 4. 5. e + 3 4. f et a aequ. 23. 4.5 C + 2. 3. 4. f
e
(31)
e
f
45e + 845
(2. 5. C.
2. 3. C
2.1.98 1 2. 1. e
348 + 3e es posita het
34)
Et.
qu. + 4
65 19 et b aqu 3. 4. 5.6. 5 +3. 4. 5. 9 et a aequ. 2.3. 4. 5. 6, f + 2. 3. 4. 5. 9
ponendo C aequ. 6 f1g. fet: D equ. 5. 6 f + 59 et C aequ. 4 3.6. 5 4 4. 5.9
1 e
4 e
(35)
S.b. f.
3.6f 39
3.4. f
4. 5. 6.
2. 5. 6. f
Ut habeatur modus continuandi in infinitum; ut in valore ipsius a, ex ivefficientibus ipsius f fecile fiunt coeffi
etentes ipsius g.  tantum pro 6f Scribendo 9.
2. 3. 6 f
23a7
4. 5. 9
si facias faquo. fiet a squ 21  just. mjor E aequaque
justomajor.
ret autem cvefticentes aipsius se habeantur fingatur primum 2 2 et 3 aequm . fiet 2. 5. 6+ Abi patet multiplicati  per 4 n1
f plus prodndum ex 113 14F set
et f per 4. tam pro 4. 5. substituendar. 3. pro 55, substiturmus poductum ex 6f in g. ex 
Togitandum primum si ponatur 2 aequ. 0. fore valorem ipsius a. in aequ. 34 eundem qui est in aequ. 29. fantum pro 2. 34. 5.  f. ponno et si mantur 2013. esse o. fore veclorem iesis 
fore vulorem ipsius a qui est in aequ. 34. eundem cum valore ipsius a qui est in equ. 23. tantum pro 2. 3. 4. d. e. paondo quae qued atque itaporio etsex  3 par intol sro orittur valor
faciendo: 4. 5. 6. f
ponendo 3. 4. 5. 6.f
Ut inquam coefficentes aipsius f habeantur, fient, illi ex coefficeentibus praecedentis valor ipsius a
qui ties ex valore 19 pro 2. 3. c. d. ponendo
hoc modo litero pracedentis dutoris erunt e et f. primum ergo coefficientes iisius   mstiplicentur per 6, posto et pro e ponatur f, cvefficiente, autem ipsius f ex praecedenti
ponendo 5. 6. f. 9.
v. g. ipsius s.an Cd, et cocficientem alterus litere, v. q.bocemus 7. et ten qualis 6 in aqu. 34. nocemus R n. fiet  si autem luijus aterae
C2C
penaur
repetantur ois volemus
aequationis 34 loefficiens est C erit praecedentis (0) et antepraecedentis (0) et ita porro Utude aequationes dude: C aqu. C ) + (D. ). et 9 aqu. (6)
po f
Biu. g. in eadem equ 34)
Ergo (1) aequ (O) 4 per 35 et 37 fier C aequ (O)n + 1C) et (6) aequ. _(CX n), + (DD aequ ( An) AC Dn Ergo O aequ C) Ba + ( Bn rusus CC aqu ACD + DB equ ( + (D)
Ergo C aequ  vel inveiendo satius erit semper ex praecedentibus componere, et scribemus: (0) aqu. Aon + D. et (D) aqu C et (6) a qu. (8, 1(3) _ D aqu )
On +D
C1aqu (() () e) + (∞) _ (3)) aequ 10) aqu Cnei t D6) + 8. (nC) aqu. _ Men 
(9) nind (n) F N ahA + C. AnD + C n + D
.... 9e
+ACy Omtis . n) 0
G Nen (nB + NNANDE) HOLNLPH) F C attm + 9 nspu O n (1) + Der
fie
1, 2. 3. 6 + 2d
pram substituendo in aqu. 2
3
5
Et sic in infinitum al
si facias d aqu. o. fiet a aqu. 2 +  justo major ex aequ. 10
S. facias e aequi d. fiet  aqua + L justo mino 2. Ex leq. 2
7 Nota bene
Unde ethiamnotanda hecremata de majore et minore
2.5.9
234 5. 6
at
3. 4. 
d