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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 365v, page id 00068196:0726
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An sic. sint res aequationes, binae ad tres literas X, y
binae quadratoriae tertia Z= a, quo est ad planam
2
ope duae priores sint quadratoraae tales, ut differentiastoae nota
summae tollatur. Inde tosentur ope productarum vinarum tollatur
dy ubi collendo prodibit aequalio pro dys. dx, X, y, Z. ponendo
jam Z=a, habebimus differentiatem nostram ordinariam
quae hoc modo poterit construi. videndum an hoc possit
accommodari ad datam
30
Ex gn (X. I = fy dy 52
1Z =0
62
Sx dx + s dy 56 = 0. qu au sx
Tollendo utrobique dz siet X dx + 5 alus iZ = X  yty : Z
2t
Hinc nil dueitur, sed instituenda mistura vius prima aequatione manente
secunda fes = (Er 2) (dx rd3) + Scyt  (eg rdz) +et y ea (y 
di = (( dx + 9 dus,) Z) + at Z ex + y+ Z dy + Z + 9 F X (dZ + dus1
Z  =
30
 ti
soud
=X ex + ydy, Xt + XtE + xty
3u
quos ipsuis dz valores inter se aequando, et in aq. in de prodeunt
AZ = X dx +y dy 7: Z
ponendo Z a seu onstanti, prodibit aequatia differentialis permi
gradus more communi in tractabilis
illad etiam foret maximae utiliatis, si ties etiam hausferri potest
ad eo ut differontialis primi gradus habdantur, ubi xdy: ex ascendat ad
quadratum, si nempe radio quadratica una sit in altemtio valore
videndum an non etiam hac methodo posset quadratura intractabilis
possetreduci ad tractabilem seu rationatem, qui foret cymulus methodi.
sitx SZ+ d+ +) + + 1X +)fex dy) 7e
patet ex priore ub X IX ducitur in XFZ veluti si Maxeaa) dacetetu
in _ta vel tale quiddam quid si ibi y plane omittas. Di