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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 115r, page id 00068198:0229
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e LG: GE: CL: CE. (L: BF.: 9: 1
pa 3 sex C+ = 4BF (pE, aeq3) sau  4bi
seu Ct = G. Z X LG: CL. TH: HC. ia
HCHC. q. FB. es, ZB (per let 5) = rrar X
tHC= yxfr GX sad THA BY AT
eAT  X -TB = 1+ Y - rYX = A4. Eg
TH = r-I. IAY- rYX. Ergo ex, G  et I
fit LG LG. C seu (perb) 92. C= C17
ETH: HC id est per u et GE: CE epit
e+ r rV: gY. Est autem GE= b- FG
e  rE st et FG = CC,:Y et
TF = Z - AT = Z - 1+r- pX = ZC. Ex
Ergo ex 18 per 19 et 20 fil G8= b- Z.Y + i Fr. VX: V
C=Ex CG agatur CM normalis in M adt
FE Erit AE = v - BC = v - r= IX= ME
et CEqu= MEqu + BFqu. Ergo fit
CEqu. = vv - 2r - 1 VX + r-1. r= (XX +
22= 2XZ + XX seu CEqu vou
V -2. =I VX + rr - 2YXX 1 ZZ. 1x
Ergo ex 17 per 21 et 24, fiet
I 1+r =rr: qqer= vr -Z+ tK NXXX,
Ero vv - ZV. VXF rY - 2VXX - 2XZ +23
Atque hc tantum quidem ex unico
puncto duci potest. Sed _ quoniam
 duobus punctis proximis C et (C) non
tantum maneat puncta adeoque B et B
non tantum manent puncta A et B
adeo rectae AFZ et FE, V. sed
etiam manet AC+ CE constans
seu aequalis A(C) + ( (C) E; ideo
BE vocetur AC + CE = C. seu fiet
Ov- ZY = IBX + rY - 2YXX = 2X Z+ 23
EC = 2gX + 99XX.. itaope
 quia autem duae ad sunt variabiles
nempe X er Y, (quae Y etiam latet in
hinc si differentiemus ae99. 25 et 27, habebim
epdx: ar bis  in differentiali ipsius 25
in differentiali ipsius 27, unde tollento ex
his duabus differentialibus prodit nova aequatu
ordinaria, quam conjungendo
t 26, tolli
loterit
1
ipsius 23
idem fiet
ope aegg. 23 et 4
ante differentiationem
tollas X, restabit equ fiet aequatio in qua
bla bariabilis erit _Y, unde differentia
evanescet dr, et fiet aequatio in qua
erunt X, F, Y, V, Z
erginee in qua t
cujus op
in qua sotae ordinario
quo juncta cum gg. 25 et 26, tol
itaque tolli potest c
videm abest X
be aequationis disperentiandae, et en
utroque ante
crfferentialis
modo procedas, supersunt veciabiles Y
v. Nob
indeterminatae X Y
, est autem C arca
er si malie 
urvae data demtus vel minutus
in i
data est curva E(E)
nem in rectam
hinc
tus extensu
soluta. Et aliter
habuiffumus Relationem inter
habuissemus et arcus longitudinem
curvae C(C)
ladeoquet
adinarie haberentur
cum tamen debeaut haberi e quad
granscendenter, itaque nec ista via tam
lansibiris, per cur
lineas datas CL
rectas vel curvas) quaesitae in dati anguli
dit dua
loco occurrentes;
edit saut
eoleum i
ne potuit