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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 311r, page id 00068196:0617
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Hic a ve
Q bihi per X; a y in differentioli non post
potest simul tolli X, et a, nilis sit Z= mX + na +   51Z squi
Mxa na = valori per B y, Z
videamus an possit inveniri   slere er Exemplum, ubi Z- valori
ubi Z= vatori per H, X, a et quaerendo differentialem, ac
Ope ejus tollendo X simul connescat a. Nempe
Z= valori per y14 a Ergo X: a = valori per Hoc rgitur
fieri potest, si ponatur X: a = y: Q ita erom ex = a 
ex idque  dxia =  d ytque
aaaxxtyy- dy
X7  Ydx
sit a G dgrus x dy: yax = _ valori per y, X, a
Sumatur  GB  om aequatio inter X, B, y, X, a, Z, tatis
ut tram x et a servans leges homogeneorum, in qua etiam y et a
solae inter se servent legem homogeneorum. Siet y: a= valori per z: X
ergo dy: a = valori per de: dx , Z. X. Ergo dy: y = valori p 1 x es Z.
sit aqu. apty A y
agao
ae qu propo ita
y si ergo sat gaxedys=
ili Ga X: 4 sutratur ydx: du = 8
et absit 8 y: a= 
le
A
K
 Sumatru pursus y: a = valorip. e
dlela
pinprementalem
val. per P. X = valori per v: X jam per differentialem
aequationis 3, fit dy: a = valori per dv: dx, v:x Ergo
(5) alter
er ae 1. 3 et 5 sit dy: y = valori per dx: dx, v: X
per
6 et
jam per aq. 1. et  dy: y = dx:  ergo fi   x div. per vabr  do.
Aor (St
fit = dx divis per alteram valorem ex de, dv: dx, 8: X; jam ope
0g. 4 et 8 collatur , et fiter valor et fiet scu ho- AX. 2
valorper v: X ((g. 3) nl pl. in X = dx diuis. per alterum val. ex d v: dx, v: X
id est fit ex du: _X = val. per vex sine interventu ipsius a, seu constantis
ergo solubilis aequatio per quadraturis. Gentemus in exempeo, sit
3:a + d. x seu yx +Pa = ax seu  jamas- A 45
a jam 1y9 =LXy seu   a y: dy Ergues 2 13 fit yxty + adxY extus
seumus seu dy: ex Fya: aX Xy, quae aequalo reduretur ad quodraturas
essuratur a B:x siet v: x1- D. jam perdif. 44. 6. fit dy: a= vdX XB, ZX
rio ayin ieu uX  dx: . Ger aq. Eseu _ Rs:   p.X) - v xin XX, sebit
 a0 qu vex aercndiatis e
ingens compendium pro
nera liibus
aequationibusad Mechodum anque
tiam javerscem. Mhullucianu
sit dy: ex = v ( sit jam aolat no
 aequatul) inter v. y. X
Moto hacter
me excogitato sumitur aequatio generalis inter X et y
Et hujus differentialis dat Y X. V: X. 9 quum substitua
 ita habetur v ratis abiter vul cui valo
substitutus in aeq. 2. reddere debet aeque, 3
quid si sic Aequationis rpperatu
5 Ieu dationis  e smplicur
differentialis erit eg. (4). Sumatur alia
differentialis AB
D = X. .y: X.. y arbitaria; ujus ope dab
B) ~ 1
e
iteram de puremplicter, duas to aequando
similles
nos valores do aequando et dabitur aeg. 19
ia
X Y. V dy: ex ubi follendo ly. Ex
per V sit eq. (10dm qua solum p y. v. quae
et ita e illud
dbet coincidere cum eg. 5.
est egnerium quod arbitariae assumta
ad omblas polentias littoleunta
_ V = G a +by+ Cy etc. posito a ex b, c, daneo
fit dv= ada + b ly + y db + 2c y ly+ y de erc seu
do=  da + ydb Ly Ac + eu G 1 1bv + 2C70+ 3Cy v
essumatur v l+ mu +n s etc py eu fiet
v2 1l= yamy du et alvtmBL cu Et
equando aos oatore do ex eg. 2et 5 fiet
e
tua
a + db + 5dc etc. c it a 24) e + 3y p C_  V abus quam
e
e 08 aqy eu
ibet
s at  al  Pa si 11 2. 
aa
n 
a 
ul oer