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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
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Calculus differentialis
ratiobalis, in literis rationalibus integris
sit aequabio generalis ad differentialemad curvam
quaesitam data: X. + y. + X. y
X + y + X. y8.
aqu. dx assumatur alia
dy
etiam generalis differentialis, quaesita, ad eandem curvam, quae sit
X. + y + X. y
u
EX
aequ. a
XP. + y) + N: y
aequatio inter X et y. sine differentialibus, aequ. 3. inter duas scilicet.
Factiones unam aequationis 1. alteram aequationis 2, trarum duarum
factionum terminos multiplicanto per crucem, fiet.
NXbxp + yCxp + X. y Axp + ye Xbyq + yC yq + X. yRy4
+ Xb X. yY + yC X. yr + F. yhX. yY
aequ. XIXe + ym XC+ X. yn XC, +
+ X lxyg + ym X.yg + X. y MXy9
aequ.
Xlyf + ymy f + X. yn yf
Hujus aequationis quaeratur iterum differentialis, quae erit:
B X b ap dx + xp db dx + gc dp da f x p  d x p de dus 1 Xoy h dpdx + Xp t dr ts
.Xb dxi XP abaxa + yc ap dx + Xp dedy, t X. yh dpdx + Xp dh dx  u
h) dy
Xb dgdy + y qabdx, + yc dqs dy + yq de dy, + X. yhdgdy + yg dhdx r) y
.. (d4) dys
Xb drdx F Xyrdbax, + yc drdx + X yr dedy, + X: yh drax F xyr de dx
Caridy ti dy
.. dr) dy
.. dr) dy
de qual.
Xldedx + xedidx, + iym de dx tix edudus, +. V.: yn dedx +xe. andx
(dn) dy
Xldf dys + yf dldx, + ym dfdy + yf dmdys, + x. yn dfdy + yf dn dx
an dy
Xl dy dx + Xyg dl dx d ym dgdx + Xygdutys, + K yn dy dx + Xtg du dx
1. (d9) dy
daidus
unde fiet:
(a9) dy du) dy
Unde fil. Xb dp expab -Xlde -xec 3 + xbdr +xpdh = xldg -Xean
FoC ae rygab= gride- yt al Hyc ar +ygdh -ym dg - yf du
ge 
sectuecone
xyhdp +xgr ab =xynde- Xygd +Xghor +x yrdh - xg ndgs - xyg du (7) XD F GC + K. yti
aequ. 
abdqu rc AC ea +C) Expt Xtdg) Xeplu)
gedus tygde yndf.yfdm) + yedr) +yq(t)-ymdu ) Neryf xyu
txbagtxpdc - xldf -xedm +xbAr) ex (dh) = X ((c g) - xeldu)
+ Nyhaca y de xynds xsam YX y ( o) + Xg rAhi) X dg) -X. y g a)
Est autem aequatio 7. identica. Et quia fieri potest, ut fractio in aequ. b.
deprimi possit ideo non licet comparare numeratores numerator, t nominatorem
nominatori. sed multiplicandas st a termini per crucem, ut inde
fieret aequatiod.
aequ.
dx (6