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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 232v, page id 00068196:0460
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Conder, in quaetum ea aequabione explicari potest. Ideo quia punctum fixum, ex quo demMitten
dae perpendiculares. Talis 1 tali autem Et hoc modo habetur curaque in qua habetu relatio quae est non
inter ordhnallas et absiissas, sed quae est inter diffeneulia jordinatarum et abscissas, vel quae est inter
vifferentias ordinatarm et ubsustarum quaerenda ratio, in qua puncto non exipente fixo tamen
impositae in curvam vent figurum ex data pendentem
fiat
b. y 4 a
A 
(H
S. Ergo BSco
y m. fici ZY H nco
co 1I
est 
et Sip
2
si fignae evolutae et ovolutioni descript dimensio ex eodem principio
fgur abit, ex cujus dimensio ex utiaque pendebit
fguro.
hroc hocidis dimensio semper datm ex tura spatii curdae par quam in
hodio figur sitio finurae describentis. Error. imo non quia trochoerdes
perpendiculares non applicantur ad curvam, ibi ubi provolotitur
modu fi
Itaque necessario utendum est; si evolutione provolutione descrbere
vilemus figura,
perperducula
dimensio ex datae dimensio ne pendeat sis agemus ex
araxem productas aaut aliam curimm appliaemus modie
accicur spatium etiam detur
sed si ilam curvam in rectam expandamus, quae fit more meo
inervallis a puncto fixo puncto provolationis impositis. Ea curva
in rectum extensa, tum demum verum erit e haberi curmam habita
Spatii diniensio ne si modo inveniri queat quae sit curva illa expensa
in rectam. Investigabitur autem, quia investigari potent relatio inter
afferentias et ubscissas. Sd hic aecurendum est in calalogum ciurvatum Tangentium
btcaxtx
a relato curva illa ex earum numeo quae sunt analtiicae seu
169X. Bep haxr
CB 2aX+X, + a + 2aVF 
BC aMEF. et P
pI PF
d2ax
e e DD b srantae+
a 2 + -
raxt
Traxix
Vrax+ XV
Traxte
(247
P a
BCI
B arta x tx + a
PH2 Vrax+x + a
ja
a
ti
t
AZ
raxir
dx + f va
ife
et reducendo: b rax + bx + a + ac Yrart + ad X + fX t. . 1 va t. 
sive brax + bX + a3 + adX F) Prax + X et quadiunt  + 2 b X 2bX + 2b2a Y 
va - fx - ac
Eodem modo: si ad a sraea adu
2 + a1
241 +  Y)
et fi
1
cotraxix h+ lsaxuxax
b4a.. 2ad.
2629ad..
ad
va - 2vafX - 2vaac t fx es
arca
sive
trax
75V momentum curvae splices
 4aX +2X + a - 2la-
ex ver tice qubsito
quae tatur
n 2t
l’av
+2maX +y2
+ _ ve  Sgaxrixta-la saaurverae v VFX+
TraxtX, stantextae
yrAax +X +a  2aX + ∞
24 LX X
2ax + et
1d.
aXFEXTa
spiatur, sit ne in re
transcndentes.