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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 32r, page id 00068241:0063
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impolupem (Z
sit l’am +n + p equ Y
C
Im + In +mn + lp +mp +p aequ C. lmn +ptmp pu d. mopous e
ex aequ 4 sit p aequ e. lum set trgo. Am aequ c. est omn imrequ d- eflibma
ergo estaeqo H dimn mmn fier. Imn aequ e: p. ex aequ 4
et ex aequ. 3 et 5 fiet: st aequ d. p = C.pp et ex aequ 2 et b fiet
fiet: Sim aeque - d: p Ex aequi sim aequ ec pst
Ex aequ 5 et 2. fit lma  ep aeque d cp + pp A (6
Ex aequ. 4 sit Imp aequ e: p Exaequd fit: Simaequ  d: p - e: pp
Ergo
ex aequ 2 et 6 fit. sl aequ cp depp + e. p
et aequatio
-c: p l + d: p l = e: p aequ. 0
Ad: pp. = e: pp0
- C: p3
si duae sint aequationes, et una litera extet in una aequatione, altera in utraque
tolleaque  itera que ecinntraque, tunc  habita nona
aequatie in facta deducta inde nova aequatione in qua sublata sit litera
ambabus aequationibus communis, litera residua assurget ad eum gradum dimensionum
litera
 residua
non extabat, veg si sit  ducto in gradum dimensionum aequatinis
qui fit ex eo
resi quem litera residua habebat in aequatione ubi extabat, verbi
2
gratia sit axx +bFyx +Cyy aequ.0 et x X +aXXt ex +f aequ. 0.
tollendo literam X, fiet aequatio nova in qua litera y assurget ad gradum sextum
 Ratio quia X nam ratio est quia per aequ. 2 habet X tres valores,
Quorum quolibet substituto in aequ. 1. habet y ibi duos balores; ergo ter duos
seu non per accidens, autem contingit, quod quidam valores evanescant, seu
fiant nihilo aequales aut locum habeat depressio
si eadem aequatio extet in duabus aequationibus, et sit tollenda
si ambae literae extent in utraque aequatione et una sit tollenda:
primum duae duneusiones altissimae aeqationis tollendae, ducendae sunt in se invicem,
diterae
et productum ducatur in maximam dimensionem literae retinendae
oujo lemxnxtqu
Ulile erit rem Eare generaliter: 
orgo  X a +bXC Cx + dX+ ex
Aqu. Y mult. per M. et aequ 2 per b subtrahantur a se invicem habilitur qu.3
O aequ. a X +bX +CX + dx tC X  et oaequ lX + m X n X + pX  9)
mullipe. aequ 1 per L et aequ 2 per a, s subtrahantur producta restabit aequ. (3.) gradus Z-1
Multipl. aequ. 1 per 9 et 2 per e subtrahantur producta, restabit aequatio (4) quae divisa per A
Mult aqu. 3 per 14+ be et aequ. 4 per bb+ am,
erit etiam gradus Z- 1
quibus subtractis a serivicem habetur aequi (5) gradus Z2. Mulliplicetur aequ. 3
B
per dq
E+la XZ, lb X + Lc XE +bd X +dC XE
= al X)-am - an - ap - aq
qa  +9b 4 gc + qd  qe
+ga + qb +qc +gd (Fqc aequ. 0
- et -em
+ (V(6)
= (a) (1M)
+ (9) (a)
= (C) (1)
= en - ep
+1(C) + (d) (C)
-(a) (12) -() (4)
+ (1) (b) + (4) (4)
Cesin) sesse)
e
aequ. 0
aequ. 
sta et
ubi nota esse
aibam
(a) aequam - 1b 6) aequ an - lc
(1 aequ el-ga. (M) aequ
quogodet