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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 313v, page id 00068196:0622
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Hic  ir
Q toriG per X; a y in diffecentioli non post
potest simul tolli X, et a, nilis sit Z= mX + na +   51Z squi
mxa na = valori per  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 cX: a = y: Z ita erom ex = a 
ex idque  dxia =  d ytque
aaaxxtyy- dy
A yax
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
ayloy
ae qupropo ita
y si ergo sat gaxedys=
i Gxa X: 4 sutatur ydx: dis = 8
Et absit 8 y: a= 
le
A
K
ex simsre tivn via d vatrip ee L.
dlela
pinprementalem
val. per P. X = valori per v: X jam per differentialem
aquationis 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 4q.1. et C dy. y = dx: P ergo fil   x div. fper vab, e do: C
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=1 seu yx +Pa = ax seu jamas au A
 jam sy =EIxy seu c ay: dys. Erguer 213 fit yxty ) adxi exdu
seundaus seu dy: 2x ya: aX Xy, quae aequalo redmetur 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
neraliibus
ae quationibuad Mechobum ianque
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. Y: X. y avum sabstatua
G
. ita habetur v ratreabiter qui vul cujus valor
substitutus in aeq. 2. reddere debet aeque, 3
quid si sic Aequationis rpperatu
16 rebi dationisd  smplicum
differentialis erit ey (4). Sumatur alia
differentialis AB
D = X. y: X.. y arbitaria; cujus ope dabur
8) ~ 
e
iteram de purempliter, duas to aequando
similles
nos valores do aequando et dabitur aeg. 19
ia
X Y. V dy: ex ubi follendo ly. Ex
per 1 sit eq. (10 dm qua solum p y. v. quae
et ita es llud
dbet coincidere cum eg. 5.
est egnerium quod arbitariae assumta
ad oullas polentias littollunta
 V = G a + by+ cy erc. posito a ex b, c, danco
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. ch it a 24) e + 3y p C_  V abus quam
e
e 08 aqy eu
 ab  ab  de
ibetq
a 
n 
a 
ul oer