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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 5v, page id 00068197:0010
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(sB. si volmissemus accommodare notres radices aequaces non debnissenus equare axidus jarum curvarum. ita enim sapponimu
curvas se tangere in duobus punctis. Sed debuissemus tollore
cetus duplice dy + ydy . Z dx  x dx aequ.0
quia in aequ. 3 sunt
2) at. v. CZ. ) sunt simplices. Seu mutendo aequationem in atulogiam
siet dx: dy:: v+y: Z-X. Ergo per l et 4 erit a: y+ b.: V+ Y: Z-X
d
seu az - ax aequ. vy + vy+ by + vb.X Et ita
(5
quae aequatio debet adhuc habere duas radices aequales. Tollamus
Jam revocemus ad literam aequationem
unius tantum literae
duplicis, ope aequationis 31 Tempe aequ. 5 quadrando
fiet aa ZZ - 2aaZX + aaXX aequ. quad y+b. y+v. Ergo
b 
ex ((5) et 3. fiet: quad. y + b. y+ v aequaass- quad yt vaa cujus
6
aequationis quaerendo differentialem. fiet. Cevanescente dy)
y +b. y+v. 29n +b+v aequ.
per y+v fiet
- y +vaa
seu dividendo utrobi
y+b 29+ b+v aequ= aa seu 29y+by +bb, 49.0
vy +0b
Tibus raa
jungendo aequationes 6. et 7. hasublata y haberemus recationem
inter V et s seu inter Rssive AQ, et et inter RC hoc est arum
Hinc illud saltem discimus, si
ensum nevis quarrabilius figurae
quadratrici, ejus haberi possent curva
arcum seu filum AWVA in rectam ext
arcub aroportionalis) tmiq. qule vis quadratura
in rectam, seu per evolutiones curvarum
alu
an 5qu.2. tunc
ii veniri posset per extrntiones
xinis) Relationem autem inter solas
titamen
utn
in aequ. 6. praetersregulariter fuiset et Z.
1
Z et V invenire, qua
habita haberetur curva Ra positione, nondum exhris in promtu
ingressas
Dideamus an prosit aliquid, si poro
quaeramue differentiales, ubi omnes diffecentiales sunt
est
tangentem curvae RR
et esse ps
Rursus PS: SR:: PB: BC sye
Ergo
(7)
2
(Y
dz: dv:: do dx: dy:: dv: dz
ds aequ. d1+7 dy + do
2
habendae  indeterminatae jam habendae erunt pro duplicibus
Scimus autem RC esse
PS: SR:: dzue: dv.
B = BC.: dy: dx
Quia differentiae 
seu elementa ipsarum s. sunt elementa seu differentiae arcuum AR vel toR
Ergo Imo amplius
nram habesu curra KR. haberetur curv  quae sita pererohotion
habers possit inrua elementis proportionalis; (id est
invenienor seur