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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 6r, page id 00068051:0011
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quide
didendum an conjungere liceat translormationem et foctionem. e
sit dy: dx Gra, X: a assunctit BC, _ V, Z, C, fiat y-.
sit dy: ax = (rt.1) s gta. X: a assumantur v, Z, e. et sit e cotrithmetice coescens, fint
y2 ErtL. 1) v: a. Z.a X2 ErLL. 2) v: a. 2. a = frtL. 3) v: a. Z: a
harum quaerantur differentaales ex 2,3, 4. fiet dy = . . . .  dx . de =..
per 2,3,5, 6, obtinetur dv:due  B_ Ert. 2) v: a. Z. a.
si tollendo x 9a effici pF ut simil sollatur  s ut supersunt , dax dus dtus de
problema est solutum rechictum ad quadraturas
potest ratu exhiberi a nobis oper affectionum unius literae ibg. (ax:X. est
atio seu numeus et quide e logarithms ide est De Sdax: dx Eoganthimo ipsius dx.
ay: dx = X: a 1 γ. a.
syide
a B: a =   scdx.  Ax Z: a = Segy
liet dex: dx: day. dy Sdax. dx. Fady. g
sirt Cx  AX X: dy. dx Sgay. 
xeds nu  x ay. Ex
quam differentiandus, abebitur aeq. in qua ddx ddx adue dx dui dadu et faciendo
aodu =0 habetur relatio absoluta inter ddx daus ex, du, sine a, i dat Ei seu
generalissime resamam
d dy: dx = X. a. 9. a sit y y. a = Sodz. dZ et Y: a = dv: dz
Ex 1 fiot X   atoh   dviaque: 1aq L = 1aq. dq. dv. d2
+
len (AaZ: d. =
du: dz. ddx: ddque . Ergu daque. dque = d
Ergo _ dd ax: aaZ = div. deZ. e dv: dz, d ddo  sdder du dl p. HB sx
ingerum  aeq. inter sed hoc scunde est ac su va etur c qui sine a
utto X, y, ex dy, dax, ddy. ubi ratones.
X: y _, dx: dy Xdax rax Xddys: dx day: adx. ubi fuciendo ddis =0
necessario evanescit, et ddx. nam evanescit ddus: dax jam etsi affiusset
xdax: x tamen reduci potest. ad xddus: dx si illud multipliatur. per
ddus et per ipsum dividatur. sit enim X ddx: x in adx: adus. Et licet quantitas
a
ha
pe
ddidet un s
 hy: dx men aa: ay  Xxt ax, : ay. ft seu ayay = _ x axt axdx
videla habem solutio
seu a 2 XX dxG: ydy - ex ax et sinc 0= ydyap  
O = xx dax + 2X +X, : ydy -x dx = XX dx pidiy + aus - Xditu  a x  B ydys - xdx
XX yly olx + 2X  Exy dy ax x datex  (3X dx = Xy aa doy + X du Ax - X ax 1d9 = X dx
axic pestur considerinda determinatio curvae ope solidi
clatio ejus ad duo plana.
AB, x ; BC y. Bd, v.
Nempe quia curva  langens in sublimi positae (sive
ipsa in plano sit sive non tangens habetur, per ejus projectioneq
parallet) ratiis puctum ad plana plopendiculares, in duo plana,
set et langeptes projectionum erunt projectiones Tangentis curvae.
quae est duobus papis projectinum unde project plana projectoria tangentur
ipsau protes tonum, secant se in longente curvae. Hic habebrimus.
plures literas  d nempe uas treset duas pro iis aequaones. Sed et quod
notanor duae exliteris posunt assumi ut Aiithmetrcae. Et notandu
es, quod non solidae tantum sed e planae curvae ad aliud planum ralatae
promovendus ergo Calculus differentialis
ad superficies. Nam et superficicum interfectiones dant curvas esi duo
hanc linctavem recipiunt
et duo plana superficies in communi puncto tangentia dabunt habebunt
xngenltu cva protam  eam cots sectio est tongens anve.
et