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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 100r, page id 00068201:0199
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30 januar
1679.
rus ratiious
+d Fx +ad L.1. = bd
+CX
eberitea
X +ax +bsx
+X +CX X X -bd (D
+a
(F) (E) +ca
conser scrediasma ejadem diei, de
A Incognitis tollendis per aequationum exacta
tionem.) praectarum hic compendem
pro aebilianis autilibus vscindendis
X +raX + X + b
+a
un poshibilis
Deseriebus infinitis maniversum. de
9 potentus
proveniat formula () destmendi sunt termini
possililis +b2 aequ. a + 4aX +6ax + 4aX + X
possib. 8b aego a + gaK etC. Xx
ut
e, utque fil (2). (F) ideoque fieri
debet: + ad +bC qu. 0. et +d + b aequ. 0
Ergo d aequ- b per. 2. quem valorem inserendo
in aequ. l. fit: - ab + bc aequ. 0 sive
fit aae c aequ. a. itaque valoribus
+b
ipsarum C et d per aequ. 3 et 5. in
equ formula D. substitutis fiet
est impossibilis generalis
Hujus scribantur altiores:
trax ae aequ- b
(2) a
re
jucatur formula  in formulam (B
itaque aequatio X +raX + a aequ. 0.
secundi gradus.
imposs. b aequ a +2aX + x
adde
intel
redam
invenire F perx.
patet sequentes omnes fore possioites, et solam primam impossibilem
jam in prima  collatur, x ope ejusdem  in secunda non
nde fi
restabit in prima nisi X et X, in tertia tollatur tum X ope secundae
nova
prodibit alia in qua erunt X. X x Y  itaque in ea habebitur valor
ipsius X qui substitutus in locum ipsius X aequationis primae hansforma
ta, prdibit aequatio in qua aberunt X. X aderunt vero X. X. X. 
=b aeq. a + 2aX + X
+ cbt
ca t AcaX + BCaX+ZCX + C + 2
odb da  +6daX +.. dax+. da x+ dex L. dax +.. dx
+eb
ea + Beax +. eax +.. 1a X + .. ea X +. . eax +.. Ca X + eaX + ex
eti
X
e 2C
ubi natet loco arbitrasirum dari arbitrarias
dic. esse
tantumtres, una adhibita C tollendos tamen, desiderari teminos
tres X. X. X. ad obtinendam aequationem simpliceni, et adhibilis
duabus arbitr ariis c.d requii ut tollantur termini aideoque superesse
et dhibitis duabus arbitrarus c. d requiri
Terminos tollendas, 2. suliae
ut tollantur termini 5 et ita superesse tres tollendos. Et adhibitis
d tribus arbihraris c. d. C t tollantur requiri ut tollantur
termini septem scilicet +2. X2. pt. XS. X6. X x. ita supecesse
tres tollendos. Atque ita Supererunt tandem infiniti gollendi
quare ut res suredat nec proinde assequemur ccopum hac methodo
nisi demonstremque, effici posse ut licet progrediamur in infinitum
semper tamen finiti tantum tollendi supersint, adeoque negligi
queant.
Auic malo succurremue quoad ejus fieri potest, simulque
generalissimum exhibebimus modum, qui est talis.
eu
Series infinita proete
X +a rb
L +C +dB (B) E
diies ut
de modo extrahem
adi cen seve
infinitae per alioe
serrem infinita
= ++
9 l’eu