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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 90r, page id 00068198:0179
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1
dy: x- fes y ah,: 3y +i, fiet quadranto
byrbi = ggyys tcaghus taatit et diferentiando fiet abaqe ydb tabdi 4 1db. +ggydu
a
=dydys: ex ex = b: a
Fragydus  Eagh dus + 20yAh Frayhdu Fraahak seu firt dy: dx =. bd i + id b 4. ydb-raqdesti)
d. Ax= bdi + idb ib cag g  raahah Liggydus L gdb = ray d(gr),: 9gy. + ragt - ud b
b: a fiet 299by A2glb = abb =- regyyag F ytalba rallyh, a ralhah = b  + Idb
aequetu huic -2g.  -299yylg 4a ghydgs
+29by
dydys: x dx = b: a dy: dx L sy t ad B aytak et fsyyt ratgtaagus = abpys + 2abhy + abhh
et diferentiando 2fF ydus +2afgaus +2f yydt + 2a7 d(+9) + rangdus seu erit
= ab y dy =rab_ du - 1a99. lb - 2a9 dibh) - 2 a d b2L
dy:dx = +2 falf yy + 2ay d5g) e + 2aagdu 3: 2ab - 2fsyt rabh = _ b: a
2aa h) des )+ ab Jadb iniog
Ex aequadis yu habetur SS Ex  as  sit  in y ponendo f 9 - bh = a
-2ay dbh)
ra
ra y
 fieto 24 al  = 2 a dl = 2 bb + 2b: a) B. Ergo habetur f4- bt seu al
e abi, ag9- bhih vocetur nam, et siel am atam + ab al
5yt ag. aytali.
tandem sit, esse patorem in chlculo
dudus ddx b: a dy: dx = 
Ergo. aejus + rabhys + abhih = ffgg +2afgy + aagus
d
a
seu abu e(fs. ab Jyu + 2 a( - bh) Q + a AGG- btrh) = 0
seu yu + 2ly + qam = 0 disserentietur fiet
2Kydus F raldus + yydK = 2a d y +aagm =, 0 seu cus
 = f ydx + agl:,
fyt qh
fiet no dK 4E. Eruntque utres in indeterminatae, sed duae tantum
seu dy = 4y tradly + aadm,: 1 ry 
coincidentiationes Nec tur  Aissumatur nova pro cubitrio arbitrio aequatio
pro tribus incognitis en differentiatur bisdiversis modis habentur tesli duae
aquationes in quibus eaedem differentrales. Ergo per quatuor aequationes
in quibus extant differentiales tres, tollentur ipsae et habebitur aequatio in
qua aberunt differentrates, quam adhuc serull differe utrando habebitur
nevus modus tollendi differentiales vel omnes vel quasdum. ita putem
perveniri posse fud jolitionem. verendum neminium praestetur, et
bis prorsus tollantur differentiales
Vereor etiam ne tandem incidamus
iu quadrasuras rationalium quadratvices
quae nondum omnes sunt in pte
lxdx: (x+b) = y
utt ut ista
funsta
lx dx =  (X + b) dus si dx constans
fiat dxdx = x  XXtbX ddy + Xdxdy
 sed niil
lx si oet dus conssans fieret Ix dax 4 dxdx = Ax dy
Xtbdu et sit ddxdus 
dupure
hinc
Haec prosequenda, quia altem differentiales ad potentias
elevatae sic reducuntur ad simplices sed affectas. Quod
ulisiter fieri puto, ex melhodo hic detect a. Cums se per
ncupe aquationes oes rationales diferentiales licet, aD
affectae, videntur posse reduci ad quadraturas rationale
seu hanum quadraturas quadraturarum sed id tantum
superesset, ut videreme an quadratulae illae quadra
turatum ad fexporentiales possent reduci, ut sax logx
ut
=(dx sdx sex slogx adatur
quad montuam prlsum altigst
Et
 hi dit