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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 105r, page id 00068196:0207
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s
ex aequatione data differentiali tollatur constans a tollento
s
differentiando habebitur quantunas differentio. differentialis aequatios
ellen , vetentm et in qua regulariter extabunt X y ex dy
dax, ady.
is B aequalis( 3)
idcatur an haec digelli possit in duas tractabiles.
A, homogenea,
mulliplicat per ordinariam quamcunque
7
Itaque assumatur formula homogenea ipsi dx. Cna dfferentiatur, productum multi
pa diferentietur
plicetrur utlunque
1d
de titu et  diffenentia ponatur aegralis 
quae est differemio differentialis tractabilis cordinaries
habebitur. aeq. (4)
taec mult sclicetur vtcunque, fiet aeq. (5) jam sumatur
extraoidinaris 6s
 aequatu differentio differentialis tractabilis  quam scilicet ingrediantar
quod duplici modo fieri potest vel ut in ea tantum extent dx, dus ddx dayue.
vel ut in ea  absis alterutra dofferentio differentialium, ut dus et ejus
loco adsit constans differentialis dB. cujus valor jam affuit aeg. 4
simplicior moduse . sed cortasse plus prodesse modus 8.
ana multiplicetur utcunqee cabit e4 (9) porry oportet
a
videtur
utcunque igitur eliatur 6
of eportet les (ag. 4 et b dare nostram differentio. differentialem 2
Sive ita ut ex divulsa 2 oriantur 5 et 9.
Crimus desideratum
Et ita assecuti
sed etsi ex divulsa 2 non oriantur ete duae
tai Ractabiles vel tractabilium maltiplae, suffecerit posse ex duabus
cinctabilibus effici ipsam nostram differentio. differentialem; vel
quod ad huc est universalis, sufficit e ope aequationum 2, 4, et 6.
collendo ddu et ddx redire equationem ipsam 1.
pacuis, huc redit:
Itaque
diferentio diferentialis
Data aequatio (1) differentietur prodibit
equatio C(2). assumantur jam duae aequationes tractabiles differen
tio. differentiales (4) et (8) et ope aequationem 2, 4, 6, tollatur
tollantur ipsae dax ddue. prodibit aequatio (0) qu debet cujus ope
+
odentica. seu aequ. 10
et 1. debienc expresse vec implierti, esse coincidentes, siscil. habe aut divisorem commanem
solendo dy: dx ex aeg. 1. proirre debet aequatios
eterum rebus omnibus accuratius expensis in eam devenu
dubito an non idem multo facilius asse qui liceat per uan solummod
sed sub certi
 ays
aequationem Troctabilem differenlio.
tamen limitationibus.
es Vimorem Melutca assumatur differentia nifse
ractaturlis rentialisetractabilis, in qua ope du reperiri possit dis
quod si absit constans d (
efficcet per doc, et per logaiith. efficietur
() iaveniendo dy: dx per logarichmum ipsius ax seu per Sdux: dx hoc posito auferatu
et losq
sed jam video id quidem esse gerum, sed non cilo nos ocrventuraes ad _ id quoid desi
verabamus, nam ope aeq. a, poterimus quidem ollerc dy. dx ex q. 1. sed ejus.