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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 153v, page id 00068201:0306
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=306
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pro un
p
sublatio literarum
itec
  ralora
et
asmalsibus
conatibus
venieudo, quande
dantur duae literae et duae aquationes simplises
a
1IlAm  Lo pro una Litera tollenda
la  X0C
il + 2m + 3n =0. 1l + 12 m + 13n = 0
 Multiplicetur aequ. 1 per a, et og. 2 per b.
sit subtrahantur invicem aequationes, et
fiet aeq5. in qua ut loblatur e; prodibit
3a 13b0 101 a l +02 am +03 an 20
=a b l∞ 2b m 13 bn +)
in qua ut tollatur n. fiat 0za = 13b =0
seu b= 03a: 13  e c sed ut res procedat
in integris fiat a= 13 et fiet b= C3. Ergus
(97
et 4
1. 12-2. 7
03. 11 . = 02. 12
(8
312tBpro duabus literis Tollendis
-. 134)
DE137)
seu pro valore literae inveniendo, quando
un
dant dnae lelerae duarum lilerarum per
res aequationes simplices.
oc l +02 m + 3n + 4p 0
1+ 1 + 12m + 13n +14 p =
2 L + 2m +23 A + 24 p 20
Multiplicando aequa–
tione per a, b, C
et componendo, ita
ut a duabus prioribus
31 C2m auferatur tertia; et deunde
eseendo ut tottantur, H et p, fient aufera
auseratur tertia, fiat aquaho noda (4), in qua
ut sollaritur n et B fient aequattones tates
sublabiliae tales: 3a +13b + 23C =0 et
ata + 14b +, 34C = 0
in quibus
valor ipsarum B et E habetur per praecedentem
fit enim  pro 1, 2, 3, 11, 1Z, 15
sC
fit
seu
cribendo 3, 1, 23 4, 14 24)
+3. 24 a  13. 24. b =0
(13. 4 1. = 23. 14
9) ez. 14 54. 13
34 -4 23 et C=
a  -13. 24 + 14. 23
a -14. 234 13, 24
sit a = 13. 24 - 14. 23 hoc enim in potestate est,
2
(12
ut omnia fiant integnus fiet
a b =3. 24 +4. 23 et 6=03. 14 -4. 13
et set ex et ex aeq. 4 sublatis jam n et p
quia scilicet
fiet: +13. 24 ∞3. 11. 24 403. 14. 21 (13) M sublate u
o. 14. 23 44. 11. 23 34. 13. 21
∞2. 13. 24 43. 12. 24 e3. 1422
Ac. 14.24 =A. 12.23 FF 13, 22
n et ppio
quibus 2 et 4
L( et 1gro t, et 27
Ubi jam habebur progressus in infinitum
Nemse valo cjuque literae Scubi potest
per mnes combinationes. Nempe combinatnda
Cum quantitatum numeris desionatorum notae
priores sunt a,  ordine, (0. 1. 2. et posteriores
siml 1. 3. 4, ete supra in numeratore et
2. 3. A etc.in nominalgre ambae oibus modis
possibilibus Tcanspositae.
andum
irca signa id
et termini qui una tantum
berbi geatia 
traus
sitione
posseriorem notana
1. 3. 4 et A+.  i et 43) habeaut signam
ota diferunt
opposita Et similiter quae soli differunt lateras
minatorendiscriminantibus. Etigem differant
sa nujus termini signo assumto colliguntur sigua haeterora
num eratoru