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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 9r, page id 00068196:0017
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et xarallet
1C(C) = EVLV
(1C
2C est motus
proprius C2C
compositus
itaque motus
souncti describentis
seu mobilis
incurva erit
compositus ex
a6t. pm
parabela et.
aequali illi qui est.
motus puncto fivi
curvae, et ex
nota stropero cicluria
Quemodo
avaeritur ergu tutrm aequatio diferentialis
formetur ex concursus curvarum positione datarum
sit cuva C(1) formanda concursi curvam 1(E) 1E,
2E) 2E, sit
A B
d
axis AF, et ex 1E) ad exea
gator normalis (F) datur relatio sit AF, Z et
E v a et reta vari semiconstans m, quae
manet constans in eadem curva 1E1(E) sed variat d curva
in curvam seu alia est incrtva 2E 2E), et fiat
isi
s
lurvae fiet
LV
in
1. rursus ob proprietatem tangentum
ns
s
3.1. av.d
Ergo fet
X5V (2) 9; v: d r.dzue) quae determinat punctum
mai
concursus duarum curvarum et fit
= X et Y=
et dv:du = dx: dy, hoc sciliget casu. Adeoque
X;y = X V; Cly: dx) aequatio
cflentialis ad curvam, quae concursu daarum
es
Curvarum rrdnalim positione dalarum s imatur
sed ejusdem curvae equatio  exacta haber
pete
poc
ile differertiando aeq.1 sceandum M, non differential
in et e, unde orietur aequatio nova cuique ope sollendo
m ex aequI orietur aqualio 4) i n quae si
matas V et Z in  et y et X prodit a aequatio
absoluta curvae concursu formatae su generaliter
Ex his casus unus
surva formaturo esset
TM
s sai singularis, si curva mou suo aliam vestigiorum
mebisa Mouobus formet sane quaevis data curva
mou suo quamvis formare polest sed antes foret etivere
unaudm
artis et foret incenire formatricem, quando curta salum
lanegrraliter datur quo imo quaelibet quois puncto suo potest 4
fermare quamlibiet curia. sed potest etiam mulare
puncta contactus sui. Nempe dunosurva movetur,; potest punctum
noverin curva quo motu descirbetur curva nova lo autem
al motus anus punct cumcuova etermentariter repente, alter punctintom