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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 85v, page id 00068196:0168
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In omni omni aequatione simplice  quotcunque indeter minatarum tolli potest terminus ultimus
nam in ea est una ex ipsis, non aliter quam sic 10W+ 1d + , nec refert quot aliae ad sint. F aciumus ergo
W = n + f habebimus dW =d + dp. Et fiet a 10M + ii den + 105 + 11de sit jam in aequatione absolutus 12.
et fiat 108 + 1 de + 12 =0 hatebim subt (quae aequatio est tractabilis) Et sublatus erit terminus absolutus quodsi
pluces adsunt pta literae plares totidemque aequationes literas illas continentes, poterimus unuue lotere
sint ergo jam vinae aequationes ad binaflim carentes absolutis 30X + 31 + 32 d +33d p = 0 et
40 A + 41 n + 42 d A + 43d n = 0. Faciamus 2 = Y. b et n = P. b erit d = d. 6 + deo l B. et
explicatione follerere
d n = d l + deo GF itaque omnibus existentibus divisilibus per t evanescit 1 et habebimus super numera
30V + 319 = 32 d 1f + 33d9 =0 et 40  + 414 + +2dy + 43d8 =
30l1 = - 30my. + 30 nv
32dco ) 3edco My 32dco nV.
31C51 - 31 py, + 319 V
33dc093 3odcs p y, 33dco qV.
33dG = 33 dp y. + 33 dqu, F 33 pdy + 339 dv
42do  + 43dc 8
+40lp, 240 myt +gonv.
+421B5 vilco Myi + 42dco nV.
o Et + A 7 141 py et 41 qV1
143dcoG r 3lco py 1 243 dce qu
112d=+ramus + qdnv + 42m dy + 42 ndo
43d8 - 3 lpy3 + 439 dv et 43 p dys + 43 9dvs
Hae binae aequationes 7 et 8 multiplicatae illa per e, haec per f addantur in unum
dabitur sin eeaq  ut compositum fiat aequatio tractabilis aodatur yductum in differentiam ectum
 ductum in differentiam eorum, quae afficiunt v
= d3 m y - d, en v, + d3, pN) + dusnv =  ad4 Smy-datuv + damys r da m
- 32d m y, - 32dn v. + 32cdm y + 32 an B
d33p y. - d339 v. + d3 n, td239 u
-33d9V 4 37dv y 4
quam-quanv. + 42Sd my + 43dnD
143y. 139V. + dispu 1dqetqV
+42y +42d9V
s aresy t
mats per f
Ex his  aeqq 7 et 8 multiplicatis auctisque fiet aequatio 9, hanc divellamus in tres
pite und
Ita joend aequationem intres, fiet quaram ana erit
huem dy + 3 en do
4im sy +grsndo quae aquatio est summibiles et fiet m7
33lp dy + 33C9 dv (10) 43 ds
demus +d38V = dartny
2uamys 12ednv
d33p Ry + d33qV
 ap Y +32dq V
Armdeus arnder
13p dfy 439 df V
32em y + 32 env = 42f my + 42fn v
33C p y + 33eqV
Reliquae binae aequationes in quas divellenda est aequatio
32Mde  + 3n de V
33pa C7 +38qdeV
pro destimendo v, fiet 30m + Sadcom +p + 3 3deo prum + 33 dp  
reliquis  et y et v
hae sunt, pro destinendis
(1) 4o fmt au deosm + q1 F  4ye diospr de sam ris pes +u n ot
usu ex eamdc
-de sm sp B s ( 42 falu 13se 13 pas
(+ 433C + 33 de - 31e) p 7 : (32C - 42f) m + β3C. = 43f.) p
(11  d32C + 32de -) M 4 - 443+
et da = -d42 f - 42 df
pro destruenda V fist
-d33 Cq∞ 2edn- 33edq 339de
n
aendsuqosinu 13 fdq 43 q
124,: (328 - 42f) n + (33C= 435)9
quo duo valores ipsius deo debent aequari. Ut vero aequatio fiat facilior, faciamus eorum nominatores esse
(4) (+re + 32de
d435- 43df + 4p)
in ratione aliqua V ad a, seu ut sit (32e- 44f) in + (33C- 435) ,: Bre - 425) n + (32 e - 435)q a: 
-da25 - 42df +40
et inde fiet n = (16) = ~ m +  (33C -435) p = (33C- 435)9. sedae quando numeratores
Sed aequando numeratores valorum etiam multiplicatos pereta fint similiter
30em 13(4 3e +yide 
et fiet n = (18) =  m
 v(a
d135 - 43df +415
a -d43f - 43 df + 1f
+d3rC +32de
dqs- 42d) + t0
-d4f Baf +4s,
- 1f  42d5 + s)
+d33C + 43de - 31e
Ergo ex 16 et 18 habemus duos valores ipsius n - a M, fiet vel N P = 1 vel - 435 - 47e5 + ail - 320- 425
-1425 = 42if +40f
se prius non licet aliops fol ( per 18) ct   m.a = p: q quod noulicet dais = qu.
quia ita V et C erit in ratione anad somet ut at B rideunt ad literam eandem, ilam praestat posterius.
2m =1 et (ct 1. q - m: n contra intentum
haestit aeg. 19. uibi faciendo
i inh 3ih valie
ponamus P = 1. fiet ex 16 vel 19 n = ~ m, seu
potumus enim vet q redici prodice y et V Y+B lit  in C
33C = 43f C 3.1 92e- 92 t h: a, seu
et ex 19 fiet: +d3 3ea + 23 de a  = i 32 PR + 32 de h - 30 et ubi p Psatu sX  exaeg. 2
2+ 42Fdh 32des d3 rek + 32e dh. 7tam ynjungendo cum aeg. 22
darsa -43d5 atusa- d42 fh - 42 df h, + 40fh
 rdirca tuiaeaqret  nea -rocti   E   2 sih A . 21) F38C at
22. 173fa =43d5 a + darsh +a2sh -41 fa
Cnet ACa Z-0
sit jum 2p 2) my+ nv et g= p9+ qu et a p = am y pdn VF mag+ ndv et 19  3 sq      qu. Fiet
32 du e + 33 lo 8
3idij = 32 dmy, + 3edn v, + 32 mdy +32ndv
1te
a a
agin aqu. u a Joh grat