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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 87r, page id 00068196:0171
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sint aequatun data 50d = 5ocd + 60Z + 51 deo + 6i dq + 5b0 ( =3t70co + 30 Z+ 21duo + g1 dZ + 780 = () -0
sit co = Dy + dv et Z - n y + H V.
5050c0 = 50Dy + 50Av
1560
1780=
60Z = 60py + 60HV
S1 deo = 51ABy + SIdA V + 51Ddy + SiA dv + sbC
61 dZ - 61 deny +6i d n v + 61 p dy +617 dv
70W = 7oby + 70A∞
80Z = 60piy + G0 r V
7Idco = nidby + 71 ds v + 71Bdy, 715 dv 478
e1dZ - B. dpiy + B1 dr V + 81 n ly r S1 r dv
Et ex aeggus. datis, interpretando cd et Z fiet
(3) 70 Hae novae aequationes componitae intelligantur in unum
ne
it
identificentur jam aequationes 5 et 6
per y fiet
715B. 81fM
fa. difa
ib
multiplicatione prioris facta per e, et posserioris per f.
paeterea Et videatur an aequatio composita possit reddi
tractabilis, si possit coincedentiari identificari osi
 huic C + K d0 + n multiplicatae per 1. posito
3 = gy + h D, +dO = dgy + dh V = gdy + h dv. Et fit
igy + ih v
ikdgis + ikdliv + ik gdys + ik h do + ik n 
e et perire
51 eB +b1 e , et  (51C)B + Sie AB +((51 2) n + 61 e de
615
Pa715
7Sat
670
1 SeteD +B1 C)
t de + E lic use 8 sp
I usa BiSM et s (o) _se A F BC LA + d(B C)X+ B1 edX + dix  ed + 6  )
S1 fdu
it
hoed +boee +5, edB +6i ede (L sig  ik dg =) d su e) B+ 5ue
71 fd N
0d+bIB ScK d
C12)
20fD 80f 1fdB 81 fde
-
AS dat
ubi evan in qua aequatione apte eva nescunt dd et dM, et habetur B: n =
Eodem modo per v habebitur A: H: ubi tantum cavendum est, ne sit A: N = B: n, sed hoc fiet
Nensee scecse, fiot 60 si has literas conservamus  uod si velimius destmere _ et M, (undetram destruentur A et I
rota incidemus in difficilem nimis inont inquisitionem ipsarum e et f
Itaque istis quoleunque comparatio machinas non licet efficere, ut aequatio ex trans datis transfor
Si in aeqqe 3 et 4 liceret facere, ut coefficientes duorum quorandam terminorum unius
matis composita reddatur tractabilis
aequationis haberent inter se eandem rationem quam habent coefficientes duorum respon–
dentium terminctum alterius aequationis, possent posset componi aequatio in qua illi
Si F Itaque si simul vellemus tollere dy et do fieret
51D +61 n, :, 51A + bI7 = 7IA +BIM, :, 71N + 8II. Unde multiplicando peo crucem, fit
termini deessent simul
(51. 71 AB) + 11. 71 X n + 51. 81DH (+ 61.81 (n 1 = (51. 7IAD) + 61. 61XB + 51. 81 A n (+61. (B1 n ri
unde fit 61. 27 (51. 81 - 61. 71) (2C = nD) = 0 und sed non licet facere An = 18, seu K B:  = p: H, ut
jam dictum est.
si simu vellemus tollere, D et de
50R + 60H + 51 dA + 6, d H
fieret
7on +807 + 7id + 81 de comperi non licere facere rationem
7I A + 81N
itaque ciet: + 507XX + G0. _ RH (+ SP. Y. Add + 51. BIrd X
5I A 46IN
+ 60. 8IHII + 60. YI NH = 80. 71 AdX - 61. 71 nd X
= 51. 70NA = 51. 80NH
=61. 8OMM - 61. 8O N H
-51. 70
+ 61. 8I rdu
= 61. 80
+ 61. 71 A dH
- 61. 81 Hdu - 51. 817 dH
G+ 8
constantem ipsarum 51A+6I, et 71 A + 8I H,
ita enim explicato H evanescet A
AA AN AX XA SL d T
co
N = B RN = 88
N. 6271
sed ita deo evanescit
- 61.71
i- deo b bedtes
+61. -1
sit, A = b et ( = cs (d fit dA = dco b et dn = des b + pdco b. Itaque fiet
ex aeq. 1. fier 30 + 318 + 32deo +,d. 2x aeq. 2 fit 40 + 4 G + 42 deo + 43 de
438deo
Ex caq. 1. fit 30p + 31c F 32 d ip +33d9 +32deo = 0 Ex aeg. 2 fit 40Y + 415 + +2 d ep + 43 d 9 + 42 deo
Muttiplic etur illa aequatie per 43, haec per 33, et 30. et a se invicem subtrahantur, fiet
Goded
43Gdeo
multiplicetur illa per e, haec per f, et coaddantur
 =0 d( l. V + mg) ~ di y + dm 8 + ld V + mde
3. 43G. t 3143 +32. 43d V + 33. 43 des 1 32
+ 30 Crp + 31C4. = 32 C d p + 33C des
+32 deo Y F 33 edco.
-40f2Y 4158 - 42 5d4 - 43 fdes.
∞32le Y - 433 de es
vd3ge 1 Gd 33fC 5
+424 d f  +438d54
+dg2hf 1d43f9
ABec 3ge9
arfgip +43058
datur huic aequationi
Ht3rgdet + 33)de G
+ge fers 13des
-424 dfy -43259
diffip 13df 8
+ 32eg +33914
fit l = 32C - 42f M = 33e - 43f
(et erit 30c = 40f a 2e +32 de d4 f +  df = 0
4259 1 - 4395
pdc
- 61. 715F 1pdg   inf + 51. 81 9 4 deo . 51. 81 Ve duo
Aliter A = b ( = 8b ds = Idco b + dip bo et dn = c)dco b + d9 bco
33
(2)
30 d + 31 n + 32 d a +33d n =0 40N 41  + q2 dR + 42 dpr = 0
61. 70
A 4.X + 40 + 31 dx + 41 dn =0
+33 deo
 elo
fin  1. Vi 1 8g +. ps . S. 9 plo F. 19 0
11
3adio e gr cof
31C 7- 414
37deoe -43 dco f
dise +3y de-dgrs + df -
cofficientium ipsins g. astat equatio actabiliis quae est (g (3 e)  + (d e)G
sed video u vel deo, ad idem reduci, seu atterurum ( d sore Aeg
altenntium non prodesse itaque potest poni 9-0
435.
jam aedendee sunt injiceum aega. una en  sibi scrpposilis, altera ex  sibi suppositis
divisa prius illa per 42, hac per 43, habebitur aequalio sinc ef letiam etiam tollitur f  non possumus efficere
, bis. Ergo habebitur des ter log. C. Et hoc videtur
necedere; sit sc. f= βC. firt da= 41 β3 + 1; 13 = 43βd4 4b2 (2 deo = . 3) + 4B + aZ  Bd 42 + 32 de - q2de, :, 32 qu
sed im prori de simpliciter. Et proinde dues ipsius deo ralores aequando evanescit. Ha patet ipso deo noss
f in 
sed ita inubiliter
evanescit deo
ta divelli potest in tres, una coefficientium ipsius  sibi suppositorum, altera similite