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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 9
# Folio 4v, page id 00068104:0008
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sit dy ydx +Xdx fict Y- fy dx
caeterum nombire est alium adhuc calculum potuisse institui
locoquan
in ag. 4 non substatusen sem substituissemus valorem ipsius y ex aegl.
ad valorem ipsius u ex ipsa aeq. 4, ut in ag. 3. subptis semsubstiferimus
1)
exsagu
valorem ex ipsa aeq. 3.
Nempe faet lobaequaro
y x x+ LXX+  X+ X+
113
et rurjus in aeq. 18 emisubstituendo aeq. 18. fiet
1.28 S.
k. dx
2IX + LXX + F+ 1 X + X + X eu. et ita hocmdo
1.23 b2.38 1. 2. 3, 45 1. 2.3.4.5.
12.
prodit eadem prorsus aequatio quae per viam priorem
umamus aliam aequationem
dus = ydx + XdX. seu v= =X + Sydx. Et semisubstituendo in aeque 2 exaya
fit y = LXX + L X + Sydx dx. Et rursus semisubestiluendo in aeq. 3 ex g. 2. fit
4)
ZXx + L9X+ X +Sydx dxde et ita porio.
1
Ergo habemus problema solutum. Nam quia posita BY X= sdZ
e
quae est aeq. 2
est fera raculi scedentis
ita
(
est per rq. 2 et 9 calculi praecedentis et q hujus vagx C-E+y.
fiet utique y = 7 - x, posulo Eberi bore R ad , ut num
posito 1+Z habere se ad X, ut numerus ad suum logurithmum ob aeg. 5.
Hinc si sit du = Ydx + dx + xax + X dx erc. semper  solvitur problema
dy:dx = y4 N. semper solvitur
per loganthuos. Sed si sit generaliter talis aequalio per Hyperboles quatraterom posito
du a+bxicuFaxCf ec = dx L= mx tnyEppEgru e (esse rtiona
cribere poterimus sic du fnium se dy- D+x. 
per x
sBn
si sic dy = dX + (X dx + X dx erc + yax + m y ex + ny ax ere satasse similitur
serviel methodus Y = ax + bX + L Cx etc + L ax+ bx + L ex + en sed 1es pauto implicatia
sed sorte aliud onmodm  remedium, quaerantur deq et adius, ec. Done ponento
d
ddx =0 perdd sit aeq. dy = ydx + my dx sirt ddus = dus ax +2 mydydx
Ergo log dus = X + 2 in sy ex ab fyax = y - sy ax. Ergo log. su = X + 2mys = s ax
sed hoc parum potius inaegor. An sic det de- adus: N. dus+ Emyay
la
differentio. Differentialis =0
Hnc arte semper effici pt ut ea litera, cujus 
habeatur sola ab una parte sit
ere
iter express