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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 388v, page id 00068196:0772
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X: a ang:a e= et differentiando secundum xetue, fit I ax Pn cedus 2o seu dy: dx  l: nee
differentiando secundum c et l, fit 2X. a l dt _ - 2n g: a ed e= edl+ lde. sit jam aequatio data
differentialis: X: a + 1 = y: a dy. dx B Ergo ex  4 per 2 fit Xra + 1 = . d yyll :n eeaa
Ex 1 est X: a = e: T +n gia ee: l. quo vulore substituto, ex aeq. 3 fit D edl +, n 7. a e dl: l - 2n G: a e de = (ea t Ide
et exaeg. 5 fit e:l + n y: d ee: ll + 1= yyiaa I: ee: n. Ex aeq. ) fit y. a  Ude - ledl,: 2n edl- 2n elde
et dividendo fit : y: a  - l: 2ne, nam si ed l- Ide foret 0, sequeretur e: l esse constantem, quod
puto evitandum. SRepertus jam valor ipsius y: a substituatur in aequ. 8. fiet
Et video istud, inconveniens semper
Resumamus aliter
tamen, e: l constans, quod non possum satis mirari.
X: a= n e n1: _ Ce. Hl + e: l, differentietur secundum e et 1, patet  cum una
t ad adsit tantum quantitas eit, evanescere d eil, adeoque omnem evanescere
onimi sC
diferentialem et proinde novam feri fieri aequ. inter X: a, y: a, eil, adeoque habertbur
relatio inter _ X et y, antequam veriretur ad datam Ergo non licet assumi aequadem 1
sic, ut X: a, yia, detur ex e: l. Sed oportet sumilx: esse
aego (1), ubi K, Ca C. a, l. a X. d  X. , Ed; 
aequ. (2)  ubi dx: dy 5 X: a; y: a.; eta; l: a
eg. (3) ubi dl:de; X: a; 9: a; e: a; l: a Acquatio data (4), ubi dx: dy; X:a; y: a
aequ. (1) ubi X:a; yia; eta; l: a
Sed ita non obtinemus quaesitum, nempe ut habeatur de: dlper solam eil,
Aliud ergo in mentem venit tentare  au possit effici, ut e et l maneant
impermistae sit xd etae = y a. Ut al  differentiando jam
secundum X et y, fiet dxtia) etac G2 gia disa Utal et differentiando secundum
e et l, fit X: a  2a+ade, yg: aa El ta dl. Ex datis est dy: dx~ X: a +1 1993
En 2 et 4 fit y: a= et ac: ltal yg: aa : 2X aYI seu y: a = 2 X: a +I. Utal: e tae
ist
sed video non posse facile oblineri ut de duci queat in solum spositam
ex et e et a et dl, in solam formatam ex l’ et a
Ide- es
ed ( - Ide