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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 81v, page id 00068196:0160
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Sed quia ope aequalionim biliteralium differentcalcum simplicium
solularum, solvi pd aequatio in qua βB, Bdβ, B, ds3, et B. Hinc in altiortus
non nocebit reductio ad hanc aequationem
sint bres aequationes pro literis Y, D C explicetur, V per β y +Z
a
et co per V4 Z ly + 2, habetur aequs in quibus 31Z 2
ope aeq. 1 et 2 tollatur du, et ope aequ. 3 et 2 tollatur du; habentur, buae aequationes
sed ta non hicebit ex hris formare binas quae sunt etiam sine y. Itaque praestat
sic facere, ut ex 1 et 2 multiplicatis per arbitiariast compositis tollantur
simul y et dy. idemque fiat per aequ.  et 2 et d Possuuit eliam
omnes bres conjungi multiplicatae per nver arbitrarias diverso modo.
sed videtur sufficere prior modus.
pro quatuor aequationibus dalis, et quatuor Eteris, posset quaevis
litera explicari per y artiharius multiplicatam cum addita. inde
multi plitants aequationes per arbitranias componeatur, ita ut fiaut tres aequationes
novae in quarum qualibet absint tam  y quam dy.
Quod oplumae fiet si componantur 1.2, et 2.3, et 3.4 aqq.
sic pro quinque aequatio nibus componentur 1.2, 23, 3. 4, 45. Et,
cearex pat essatione
oecatione
sit A 10y + 1x dy + 42o v + ndu + 120Z + 121 dz + 130V + 131 dv. + 100 dx =0
Videndum an non opus
210y + 211 dy CbC + 220Z+ 22 dz + 2∞ V + 27 dv + 200 lx 3
310y + 311 dy  + 320Z 7311 dZ+ 370V + 331 dv L 300 dx = - 
Fiaul bres combinationes pta, ut in terniones itam ut in prima aeq. 1. solum multiplaetur
per a, caeterae duae per f et g; in secunda ternione at2 mulsiplicatur per a.
ina 84. 3, multiplicetur per a caeterae
s quadzentemus remin una ubi si succedit
 succedet in ouibus 10a0+ et in qualibet ternionum sollantur simul votar
pet 2, per singulae per l, et m,
Tenlemus rem in una aquubifternione, ubi si succedit succedet in omnibus
110a y + 11 a dy + 120 aX F 12 ad Z F (30aV + 131 adv + 100 adx _
20fy +21fdy + 220 fZ + 22( fdz + 230fV + 231 f 1 + 200f dx =0
31og y +3119dy +32092+ 3219 d2 + 3309v + 331 gav 4 300gdx
fac o Ad tollendam B, fit 1304 + 280f + 330g = 0 et f - 4 B 130a + 330g, : 230
Ad tollendam de fit 131 a + 231f +331 g =0 et s - f = (31 a + 3319, : 231
quos duos ipsius = f valores aequando fit 130. 231 a + 330. 231 g = 131. 230 a + 331. 2309 unde fit
italib
a =  a, 130. 731 = 131. 230se, +230371 23t 330 et pari jure spermutalis Qet 3 i ) f = a, 130. 331 - 131. 330
Eodem mondo invenientur _ h et K, pemntando linitiale cuni 2 initiali
e
e
.
K = a,
et m
230. 331 - 231,339
H id est fit h = a, 230. 131 - 231. 130
130. 331 = 131. 330
= a, 330. ∞1 - 331. 230
230. 131 = 231. 130
et prodibunt tres aequationes bi literae
110 a y + Ma dy + 120 a7 + 121 a d7 = 100 adx 9
210 fy +2115 dy + 220 f7 +221 f de + 200fdx
310 9y +3119 dy + 32092 +321 942+ 300ga
M =
230. 331 - 231. 330
330. 131 =331. 130
10 a y + n1 A dy + 120h2+ 121 h dzue + 100h dx 2
210 a y + 211 a dy F220a Z + 221 a dz + 200 a dx ( = 0
310 R7 + 311 Ky + 320 K2+ 321 K dZ + 300 K dxd
10 ly + 1B Ldy + 120 lZ + 12) l dz + 100 l dx
20my + 211 m dy + 2e0 MZ+ 221 m dz + 200n dx C = c
o ag +31 a Byfgoa ZF 3ut a l 4100 a ap
a, 330. 131 - 331. 130
131. 271 - 131. 230
(t2. 3: E
lec3. 1 34
4
234
vel potius2
in relqquis attioribus
1a pali 12
330. 231 331. 3