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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 10
# Folio 8r, page id 00068105:0015
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A
AF. TE: dx. dus
dx: dy:: y: P.
Bp p. GC, c.
Ergo de P aequ dusus
Spax aequ  yy. si p. datur
ex data X. Quod si P datur ex y.
fiet X aequ. sdyy
TE aqu:: dx :dg. EC: AB:: de: dx
fiet ECaego de X et TC aequ. TE + EC.
dx
fiit: seu TC aequ d AT du + dc X
2
cx
dx
jam AT + TC aeqo XXaGy. sis ATaeqo D. es+
s
fiet (61 +72 aequ xx +vy sunde differentialiler7
tiet:
 Odb + Z lZ aequ, xdx + y dy
e
AFA AT: AE:: dx: A de seu A qu t=X AE dx
MA: _E MB. seu + -X : X :: AE: BC, y.
at
Ergo AEaequ. +y -xy. Ergo AIago ty -xy dx
X de
est autem + aequ. y du. Ergo AT seu Daequ. 3y x- y dx
dy
Xayde de
jam data curvo quadratura datur (dc. et eadem data
datur
yy
ydx Ergo data curvae quadratura datur
Ax
dy
quam recationem in curva
praesenti habesent AT. TC. AC. eam in
aCB. Bp. PC
trochoide ejus habent
A T ductae in GC, seu e in dc sunt in trochoide
ipsae y ductae in ax + dp. genemtricem
Data curva invenire, ejus dividem, ef
nochoide
educitur ad hoc problema, data curra invenore
elemento caroqdi
dala Tirchorde curva dantur enus AP. ergo et
differentiae ipsarum. sunt autem ipsae eadem
rochoidis
cum ipsis Gc forchuidis, seu cum schrvae gerratiiais
genratio
escil vala sed non contra
Elementis. Eut contin
ircubit exdata generati methodo inveniendi genera
e
dato
hicem, non habetur
mothodus videndum an habeatu
1. +
+Ea