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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 66v, page id 00068200:0134
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Curra sectionis conice ad quadraturas
tontata
rationales reduci potest (quemadmodum et superficies
com scaleni)) modo sequenti ne novissince ivento
Cum
ura cuj ordinatae elementis curvae Conicae proportionales, generalite
q
possunt
exprimi potest hac aequatione: Z aequ. b+ exx. Quaritur earum
Yd +AXX
summa; sive quod idem est quaeritur quadratuva  spatii cyrvilinei
planei, cujus ordinata sit Z (qualem dixi) et abscissa sit X. Et quia
constat haberi summam ordinatarum, b + CXX et Vd+X ex data
cuvae (onicae quadratura. Ideo sic ratiocinabitur. 
(2) et de ago d 
(3)
Vatur (d + xX dx aequ. C. Quaeritur Z ax aequ s S6 tex dx
S2+ FXX
tem
Assumatur aequatio ad curvam novam, cujus ordinata sit v, et aequalio sit
Ge aequ V b + CXX. Et ejus aequatio differentialis erit.
6
Gde aequ. dv b + CXX + V d Nb + CX. jam ex aequ. 4. est v aeqo de.
 d N6+ Cxx
V cxc
aequ  Cx AX. Ergo valores ex oqu. be7. substituendo
Nb+cx
in aequ  fiit. Ex aqu s fieri potest  Ergo aequ. 5 dividendo
per
d g
Yb + exx et valores ex aequ. 6. et 7. in aequ. 5 substituendo fiet
d+ FXY
ax aequ. Lv +
Nb+ CXY
seu vaequ
Ergo
g
(A2 +FXY
do
b + CXY
cx au
gc sCX
bhlcax Nb2 ex, b + 16c
X
+  gc (dx
brexz
es
CC
56p+ exx
e
sed ni hocaeqne
difficile magis
+CxXobZ
qua propositu
is quod facilia reducitur ad serie ratio nate
Uane dimensio (mvae Conica reducta est ad fationalem, supposita 
onicae quadratura tuto etiam hinc ostendi posse, qua an et quomodo
ex datis cois conicarum quadraturis, dimensio curvae prorsus habeatur
datur nempe exXe ex data ipsa e. ut constat per theorema,
quod differentiae in abscissas seu momentum summatricis Conicae, ex axe
poteramus loco  b +CxX et d2+ fxC adhibere
dxs x et bX + CXX et dx + fA.
ex + fxX
 aequ gex ex
bx+ax
unde his diabus quadraturis opus est
quae duae quadatiore haventur
enim dari summatuo hujus:
ge
dx
bx+
e +x
CX
et
et fiet
+x e
bFCX
C ex
ex artificio alibi a me usurpato. Ponatur
etx. Emnl ipsae
eex ejus differentiae. Ex ductae
in altitudines seu abscissas et conule co ex post summatae dabunf
spatium summatricis Erit ergo
Erga ece d∞ aequ. s etx 4.
sed
eti aequ. +e a
e
X (eaq
quae est ideulta aeo niholime
Mi