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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 364r, page id 00068196:0723
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ga- do: dz X: a =sZ Z dy: ax 2bri Z S ddv dutratue: q datz
y: a = d2. 10 _ x. a t (12Z sit los cotans fat dy: dx-  2 dq. tu bo
Aanc aequaven dy: x= x: a + jgiaa ex periundi causa vertamus differentiando
in aliam, ubisite du, dx ddus, dax, duo. six i fit deddu e- dytn, : du = dx: a + 2ydu: aa
sit ydu yyddus = adco et sit ydu adeo et ergo ex 5g. 2 fit
dx ddy - dy ddx, : dp= dx: a +  2 adeo: ad Rursus ex 3 fit g = adoidu quam
differentrando fit: dy = - ddu a deo: dij. seu a - dy: Hydeo ddus. Ergo ex F et 6.
collendo a fit  du ddx-dxddys, dus  dx + idio x deo ddus
suod verum sed non profutum
C. y: a. = dx dee  cv: deo X: a = dv. deo (ddv: daque du
dy: dx = a y: a = de + dz: deo x: a = (ddv + adque: dv
dy: dx ~) du: deo Sit jam dy: dx 2 x: a + ygiaa. fiet:
du: de = (ddv +daque: de + av. B dvodi: do, seu fiet
d
(51
ddo : deo = dav idr + daz: d Ld: deo a ritcqu dive  2dvrd dav + 3∞: di
sit deo. d dZ. da = dlv: ddque n sa ld Z: dq dut to
lit deo = du dZ Sed ita sit non solum poterit tolli deo,, sed et dabitur
Ax. a = actx: n ax duo
Vlatio inter ax: du et ddv: ddz. bis, quod absum
X: a = 4
(12
y: a = f8 a ddz: deo
Yia = seaalaque Bduao,: decto xia = du F dz: dv
dy: dx = a do daque -  az ddv: ded du: d vddz- dzddv: du = do: deo
y: a homogencmm atzide u si esset y:a = dZ: deo et X. a. Halaz: d = a
et X. a - fdio daz. d2 - 46i
et dy. dx = et X: a = 5a dax: dx deo
Xia=a. x de: duidx d deo
dique. adx
X. a = _sdZ: duo a
dy: 1x = dtque H a: qv
(3
x dy: dx = X: a + gyi aa tollendo e per differentiationem, fit:
dxtlys = dys dex: dx 2 Ax: a + 2y dgs. aa fingamus dx:a + rydy: aa = ddx: dus
imo non puto licere
(adx ddus ∞ = dydix: dx = dy + ydlyrar = dec: a et fict ddx: a + vydllu. aa +rag. ac = a
Sed ita non licebit simul tollere a y deo
si villemus uti ag. 3. fieret xexu de dy ditus - dus dix = dx ddx
dc. dy. y. x sit Z cblys:  dys : dx =Z dly:  = Z fit dux: dx = aZ  2
log ex = log. E logZ ubi intrat  (opinor) deo, nobis a non licet
nos autem ex assumta aeq.3. nescio an possimus habere deo
Ea est proporitionalis ipsi aa a deo: a = ddv, posito alo est
Nante
sit dy: dx L) X: 9 + xytgy, gaa
dxAdus- dydex  Xdy- ydx  Xdys +y dx + 2ydy. fiat xdyaydx trydys = dae constanti
a
a
et fiet: X ddy + dx dy + y ddx+ dxdy + 2y ddy + 2 dyt = 0
Omnis calculus, ubi sublatis quoad y et du fractionibus 
fantum  et irrationalitat et sablatis etiam rationalitatibus habetur
tantum X et dx non xdx vel simile aliud, item XX et xdx, nhil aliud
 facile tractari d per series.
si possent tolli illa conposita resemper
 idem est, si detur X, dx, ddx.
educta ad simplicia pulcherrimm. set ae. g. aady aa  = axdx = gy ax. HiC
duo sunt termini sed non respondent aa sit dy constans, fiet ddy =0
aa ddu   a x adx + adx +2ydydx + 9y ddx =o gady: X = aadyolx; p et fiet
=aadyodx: x = a ddx + isG: X ddx + dx X2 ydy: X = dx gydx: y
seu aadus ax = a X dax + X yydax + 2 Xy d Xdy - yy dx2
non dy: aA daz: Aco
seu agdeo honisit