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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 14
# Folio 2r, page id 00068227:0003
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eamque dividens
sit ergo formula dividens aequatione data inferior quaecunque h+ K X + lXX + mX + n X + X
ejus altimus terminus x substituatur , ety fiet aliqua formula secundum y
cujus  insimus terminus (h erit h+. K et Leetme+ ne + e. cujus maximus termi
nus quicunque e, ut co hoc loco =5, fiat (h) - h - e : e = 310, adeoque erit
positr. C exponente in gradus formulae dividentiss
90= K+ let mee ne  similiter pro e ponendo f, et proch) ponendo (2h) fiat
(2h)h - f. : f = gi D = K + 1f + n Ss + ns3, ZF quarum duarum atquationum
ope tollendo K, et faciendo 910 - g1, :, e- f = 920, fiet 920 = l + m (ets) +n (eet ef. + ff)
pro  assumatur 9,  cui respondeat (3h), est ita eodem modo sde fiet
(34) -h - 9, :g = 912 = k +l9 + mgg + n 9
et 910 -912, :, -g = 921 prodibit
121 = l + m (er9) + n (eC + Eg +G9). Et ope aequation valorum 92a, et qut tollendo l
es faciendo 920 - 92+ conjungantur valores 920 et 92 a se invicem subtrahantur
930 = m  =+ m + n (e+ f+9). Sed quia adhuc una super est ita habetur et m
sed quia adhuc superest invenienda litera n, opus est ad huc una minatione. itaque pro
loco ipsius g, assumatur d, et fiat  931 = m + n (C+ S+D), et tollendo m
fiet 930 = 931 = n (9- 8). et sit 930 - 931, :, g. 8 = 9+o et firt n = 940
itaque m = 930 - 440 (et musqe ad 940 (et s+ 1) l = 920 - 930 (et () 4940 (et f, et 519)
seu l = 920 - 930 (e+ 5) +940 (est eg1 59) denique H = 912 - 920
denique K = 910 = quol. + 930e(et f.) = 940 C (ef + 19 + f9)
-930 ee 4+940 ee (et f+9)
940 (ee + eft A)
5G10 - 920 C +939 ef- 940 efg
generale ergo pheorema huc redit Quaeritur formula   aequatione data
940 e
xx + mX + nX + et c. Ponamus E esse divisorem
inventam methodo explorandi divijores ultimi termini, reliqui coeficientes X, l, m, n, et
interior exmas dividens, h + F L
feriore
inventum
sic invenientur; posito quantitates assumtas variandae aequationi datae, pro _ X ponendo
ultimi termini aequationis datae
meluti
Et fiet 920 -931 = in (f -9) 4 ne (f.9) + n (ff- 99) sit 920- 921, :, f- g = 930, prodibit
terminum prudmentes) ex hypothisi =
methooo
4+ C, vel v4 f vel Z+ 9, vel V + B, etc suisse e, 5, 9, D, et c. nempe pro
nempe pro X ponendo Yte vel V+ f vel W +9 vel 2+b, etc, et divisores
ultimi termini cujus variationi convenientes in quavis variatione fuisse
Nempe erit:
gto 92oe + 930 ef 040 efg  45 ef g posito non procedi ultra e, t, g, B, a
esque
N) vel (2h) vel (h) vel (4h) etc
920 = 930 e. +940 ef - 950 ete
+930 = 940 a 4950 ses
+ 940 qo e
+ 950
(= 910 = 92oC + 930 ef - 940 efg + 950 efg6
+920 2930 G 4940 es
sg
- 950 efg
9t
f90
+950 et
eq
95b e
910 = (h) = h - eE, il
920 = 910 - 911, :, e f
930 = 920-9213 21 fg
et significat omnia omnes ter
biniones, sed in secunda columna
sunt solum vra est, in tertia
sunt tres, nempe trium rerum
in quasta 6 nempe quatuor
rerum, et ita res etiam
in teliquis habet
posito non
procedi attra
variando
ultra e,f, 9, B, A
seu non esse diviforem
plus quam qui
Formulam dividentem
non esse plus quam
quinque dimensionum
Columnae ta et valores tot
ib actui
dent, quot gradus acesent
+ 950 audformutae, aut sot decedent quod
postremo gu, g2o, 930, etc sunt integri quorum valores erunt stiprodi
sic prodibunt.
rods dement adjicientur
adementur) quot gradus nut
(decedent) formulae
9u = feh )  h - 5 ., : f (912 = (oh) -h - 9 , :g (93 - (pli -h - D, 18
921 = 910-912, 32-9 922 = 910-913, : 9- 0
931 = 920 -9225:, f. B
continuando
Quedi una aequatis Et quot aequationes accedent unicolumnae horum novissimorum
talvram
940 = 930-931, 2, 9- D
lit eliam ceternis adiicientur
=
(d =
440
+94