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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 435r, page id 00068196:0865
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fingamus aequationem inter A et B generalem, quae
 sit e s. ∞ ex n + _, A+ a5B + 4 A
Oa nA + 2+ B + 012 A1 22B, 8n2t AB + H
 2 A + 3B + 4 AB + SA + 6B = 0 multiplicanda per 7A + 8B+ gC
et 2B + 3C2 + 4 BC +sB +6C = D maltiplicanda per 10 A + nB + 12
nam non licet solum assumere A et B servantes homsgeneitatem
 quasi caetera essent numeri quia alioqui daretur ratio
inter A et B. porro componantur  duae aequationes
productae intersc invicem, et fet nova comparanda
sparand
3 Nempe termini in
est ers com
 habemus autem arbitrarias 2. 3. 4. 5. 6. 7. 8. 9. 10. H1. 12. solimodoqe
unde spes solutionis. Ren reapse tentemus vitetur decollare
3
5
 2. 7. A + 3. 8 B 4 2. 8 A B + 37AB +
2, 1 3 0 10
1 4 10
Tres literae A + 4D habent
pro qu  tas literae A, B, C thabent in primo gudi for in gradum
nullo formulam 1. in secundo 3; in tertio 6 in quarto 10 etc
 inde videtur calculo praeviteri posse, quid praestari queat per
comparares. Duarum iiterarum equatio sit gradus cujus cunque pro
Summa omnium terminorum copletorum pro duabus literis, si uujus gradus
est + se duo si assurgit ad 1. gradum e inde a nullo est 3, si ad
Hinc si potentia sit  e
Edum, est 6, si ad 3tiuu 10, ex.
fiet numerus terminorum pe p+ 1. p+2: 2. Haec multi.
plicunda per aliam formulam trium literarum ubi prodeunt
it ergo
pyramidales ut a+1.. _+2. 4+3: 1.2. 3
numeus arr arbitrariarum +1. +2CE + bis quququ
(1. 213
productum autem pro numerat arbitrariam. prodit autem
formula assurgens ad p+g. trium literarum, cujus proinde
P+9+I. p 4+ 2. p+9+3
numerus terminorum erit pyramidalis
padum
1.2.
data jum aequatio assurgit ad leium 3. (nempe ACC + BCC - 2B3)
haec multulicanda per formula lium literum gradus
cujus arbitrariae sunt numero
 + q- 3
P+92. p+4-1 pIq sunt ergo
in universum crbitrariae i p F1. pA2 + bis 4+1. 412. 4+Z + P + q. 2. p Aqu. prus
+
1.2. 3
1- 2. 3
quae summa simul major esse debet quam p F4+1. p +4+2. pF 413 + 1 436
et videntur primum lantres procedat Pa sumendo 2 etul. 2. 3