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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 403v, page id 00068196:0802
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Hane semiex plicationem experiar in calculo commani
(2)
BL = 10 fiet a = e - Y X +  XX +  2E
t
valor ipsius a vocetur (a) et ex aeqe _ 1 fiat a () + ax + (a) X
22
haec divellatur in duas: a (a) + ax =0 et (a) X = 7. et ex aeq  sit v
et ex ag. 4 fit (a) + X (D0 habemus erga aequationes duas
unam _ ex og. 6 fieiet 1X x 4 = 0 quod est et ex Ag. 15
ps (1)
sit XX  seu a = - X ergo ex  5 fiet - x + = ZZ quod carcidit
Cum aeq. 7. sed ita non obtinemus duas  (
quid si ficup ex aeq. 1 fiat  a (a) (a)x + 3 aX = 27
((12)C
 quam dicellamus in duas a (a) + 3 ax = 0 seu  ( +3x = 0 let
(a) X = Z2
cum 15
leq. 13 fit
s
E
(6)
2
(3)
exi
L= (3XK
XX = pL XX+ZZ = ZZ seu XX - X Inprn  q xit Z- 0 et X s
vel si fiit Z. sed si Z- X s non potest ita barsus coincidunt duae
suppositiones vita rarsus duae aequationes e divussione natae
taut idem. Et sanc video id revera debere Aeri itque
Ita per hanc semiexplicaoem et divusionem non prodire mova
nisi unicam aequationem ipsa a carentem - et
revera id debere fieri vel hinc patet, quod X: Z repentur
subata a, quol e quod cum sit numerus non pt haberi nisi semet.
An ergr adicollendum a et a opus Y
duabus,
citerX componere ex pluribus literis(nam y non attiugermus
quia ipsa y adest, cum de X solum adsit dx et ddx) inde
jam poterimus jam praeter y, du, ddy, habebimus du, ddv, sq dtu
ubi tres ita faciende aequationes, ad lalter duas ad tollendum a, et a
habemus tacs aequationes porro trra sunt in arbitrio, relatio inter Z et v
et aliquaet determinatio progressionis itaque duas licet
D
assumere aequades per qua seudatam divellere in tres, atque
ita tollere a, et a sed ita novis in commodis pera mremimur
heque enim possiuus tollere affectionem ipsius Z, et praeterea y,
ut quide desideratur
Et generalis est illa difficultas, si sint duae aequationes
una inter X, y 7, dx, dus de altera inter easdem; non
apparet modus tollendi Z, nisi per differentio- differentiates ipsorum
X et y, nam ope duarm aequationum tollatur du habebtur
Squatio inter X, y dx, du et Z, quam differentiando ibitur ad
X, dx adx, y, dy, day, et ad dZ. sed rersus et haberi poterat az.
sit  ylte a XdZ + ZdZ + actqu 9 dus = rursus Xdiy J 2yl2 + Z ed
2 affert
itu tolletur plane
fit d2 = -Y ay C:, Z1Z = xdy ydZ 3: du-Xdy -7, . y
Ergo yran  = ZX dy +7Z x ZCdy + Z2dx+ XXdy + XZdx
 mZ + nd, + p = 0 et 97 + ndus + 5 = 6 fit imz + p = 42+ s
C
et dygdus
Sup,: m-q et du = m - 9 d5 - p - 5. p dm- dy ; M - 9
et sit 2 et ex auolitib  p n. Si e
merur