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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 369v, page id 00068196:0734
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Exemplo uutamur sit
ac XIX+ odus ad fd = ady. sit e
siet du = Xdx tyAX,: a sit ddx = 0 fiet ddus = dxt F du lx,: a seu ddus = ad x + x dx +yx: aa seu
ddy = dx. atxry: aa et dddy = dx. dx tdu: aa = cx, a + X ry 3: a. et de d4y = dx axtya
jam (y) = y + dy fiet (y) = ay +   Xty dx, : a et (y) = y + 2dy rddy, et fiet
(Y)) = y, + 2dx Xty: a, + dx. atxty: a = dy + 2 dx. xiga + ax utxtys,: a
Alia esse potest calculi ratio, ut A y, quaeramus per  x ax,  et una
 diffeaentian ab y. quam longussime remotam fiet
V = adu - g xax,: dx  aa ddus = atxde,: dx = aldus - atx dx,: d. etc.
Et hoc calculo utcunque continuato, cujm novissima dado dy, sit aequalis nihilo, seu possit
negligi fiet  s ax et dy= dx et fiet ty Hoc posito videamus an sit
dy = Xdx + gdx,: a. seu ady = xax + ydx. nempe pro du, et y substituendo rolores,
fiet: = a dx = xdx  =adx = x dx Et ita res sucedit
Ldy B 9 - x x r tadus 1 27   35  + ade + Bady :
Generalius: ulamur 100 a dx +200a dy + 100 Xdx + 210 X dy + 101 ydx + 201 ydy  0
toncns dd x o  difecrtiando fies A  4200 a ddy + 110 dx + 210 xldytuo se di urd + 201 yadys + 201 dus =o
intor, ordinanium; cum res redire debeat
simpliciter; patel sec erus
fet. Ita sic ingenitur verum, sed plecumque non invenietu 101
pleruuus ad seriem inficulam, ut quando y datur non nisi
salorem hic haberi rationaliter, ergo velat per seriet appropinquandu non exact
=adus aedes aipldus = x ex tad a sit ddx =0 fint adius x NX + rydy dX, a et pro _ y  substutmer de valorem
fiet: deys = 2xdV a +7. y x +2d, dx a a y= a y - 2Y a dx,:, p te r 2lx
cursus cddus = 2 dx ae + 4yxde + EK dya + 2a dy dx3: a3. seu = rdx a + ~G d + 2K dx Y e daytra t traiay, ea
Ergo 9 = a tddus b dx 2a 14a  +2aex: aux trar t aaHXta
aectus- X dx 3: adx sit LdX = 0. fiet dy = a ddy = 2Xdx,: adx quo valore substituto in aeq. 1.
fiet :  = a day - 2a  x - Ax x,: a d seu ddy = a ydr + 2a xdx + a X dx : a
 inagnastat Naa
Erpo addy = a dxdy +2a x + 2aXdx: a et tollendo dus fit: dldus -  adxaydx ra da x dx + 1a a 2a xost; a
Ergo y - adu - x (X- 24 dx - 2aXdx,: adx. underursus dy = a d: y - 2X dx- 2a dx: adx - ydxo pdx: a
et sit y = ad. G LaXAxt- XK AX: adx et dy = a d’y - 2a dx = 2X dx: 4t X = ay x +X Ax, : a0.
et fit y = aL. y - 2a  - 2aX du - x x3: adxs et  2 a dy- 2a dx - 2X tx: a d = aydx + X dx, ia a
et sit y = adey - 2a dx - 2aX dx X dx3: a dx Cumque sic prodedatur in infinituu ergo ft
tenis y= 3a  2aX + XX, : a unde dy= 2adX + 2Xax; a. quos valores substituendo in aeq. B1. fit
alo i a  a7a rahidx Exel + X ex: aa qua
adio ves pucrectit