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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 110v, page id 00068200:0222
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tem sic
Assumta nova litera sit ad eam aequatio
differentialis tractabilis per quadraturas. continens si placet
X. y. Z. ax. dy. dz. sublata jam dx per datam potest fieri
it simul destruatur dx. quo facto vel fiat vel saCtom habeatur
az
nova litera trnct aequatro tractabilis per quadraturas.
(∞) init de
D)eritaque
AP sit Z. AI, V. et BAaqu a. a7 equ vV.
et adZ aequ. 2P aequ 2 VaZ Ergo  dvego d2 a
a
Ca
28a2
r: (Co, seu dv:: AB en Z: Ao) seu V ergo C raego dvZ
seu cor aequ. dZ  aequ dz. Ergo Tor dimidia )
2 iaz iaz
2
Posito jam rectas P∞ et (p) (d) concurrere in puncto Q.
erit  PQ dupla ipsius 0O uti P(∞) dupla ipsius coV.
seu erunt 1G et po aequales. Ergo et AE apta aequalis
ipsi AP et Eq dupla ipsius A seu v. posito
ergo AD aequ. Z. erit EQ aequ 2 Vaz. et
punctum q erit ad parabolam. sit E9 aequ e ert
et aequ 4a7. et vertex parabolae rit A, latus rectum
erit quadrupla ipsius AB.
evolutione parabolae descripta.
curva C (() erit quaecunque
si fuisset aa Z aequ  V. feret: dq aegu 3VV aequ. 3 Z aequ 
la
et do aequ. dz aa
du
aa
V aazue
arxiam cor aequ. a0Z. Ergo _rag dE
eritque g ad parabolam Tubicam. se
a
potest si relatio inter AP et Aco sit ad aliquam curvam
simplicem erit et Gtad eandem curvam simplicem ejusdem
speciei Generaliter enim sit sit 
sit ym aego. v fiet: mdZ aequn do
aequa
c0
W
Quaego V
D jam Ergo duaequ. mv
jam ToY aequ. qu deZ. Ergo r aequ m dy.
Hinc si sit
13
n Z
ag7 aequ v2, vel avr aego 73. velo eaqe aeqo v
algebraicet
et vel a74 aequ v curva, CC haberi potest analystice
quia curvae ad quas tunc erit g. algebraice extendi possunt
in rectas, quemadmodum olim Heuratius observavit
Curvae Tangentibus positione datis invenire curvam
problema est semper algebraicum. Eravae terpendicularibus
positione datis invemre curvam, pendetex prioris currae