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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 65v, page id 00068195:0130
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vid. 4
et de reliquo
A duto puncto ducere Minimam ad Condeam
datam.
AB aequ. X. BC aeqe y.  DE aequ d AE aeque
3y aequ. 2aX + b Y yregu 2ab. f a xx
2a - x
yy
seu 2b - X
3y
aequ
Ergo  Axx aequbyu
seu 2abx - b XX aequayy
Ergo 2 bx  Xx aego 7y
rabx xx aequ byy
ABaequ X. BCaequ. y. DE aequid. AE aequ. C. yy aequ. 2ax + a XX
TB aequ. +. Uende per methodum tangentium,
y aequ eat paext.
Ergo fiet: da + d X - ay  + xy aequ. ey + Xy
m
quos valores ipsius Y et ipsius B 3) et ipsius X ex aequ. 8 et 10. substituendo in aequ. 1 er 7.
tunc ex aequ. 1. fiet: s eju 2aZ- eam v. f agque ful ehit vr + 2 ma vZ
L
2. u
- hn vn
da f da q f. dam v - ahv. = ajn Zv fetm vn liqu. 0
bl
= en). +
Hae duae aequationes multiplicentur illa er aequ. 1. per n. haec aequ. 12 per P
et prod post factam multiplicationem duae aequationes addantur in unam, quae
erit: pda tinazue- Enam v + 2nma yZ 4 na zy u namm vV
+xdazue L pdamp
- pati v
=peh v
= pah VZ
+ Ph vZ
Er
u
t
=atih vv
+pahmvo
bU
ubi faciendo +na aequ. + namm- utih + pahm. atque ope hujus
bU
bU
aequationis inveniendo valorem alterutrius, pvel n. (altera manente
arbitraria) erit aequae. 13, ad circulum, atque ita ope circuli
quemadmodum aequ. 11. est ad sectionem sonicam datam. Atque ita
ad invenienda (p). (3)h) ope circuli et sectionis Conicae datae solutiem erit problema
eritq solutio sin data Conica sectione) pplana; et constructio erit
eadem prosectione conica speciei cujuscunque. Ope autem reliquam
lgerarum, in et h effici potest ut angulus ordinatae tam in sonica quam circulo sit id
tutus ut brevis reddatur constructio
poratur CG aequ. Baequ dy Erit  o seu y aequ. Z v eit BG aequ B s U -tih seu m B
(10)
Ergo AG aequ. X + sit AGaequ. Z. firt Zaequ. X + m D et X aego Z - mv.
et Cx aequ. 7. fiet 8
D aequ
(14
b1
b
et per aequat et 2. fiet 1 et in aqu a pro yy ponendo valorem ex aequ. 1. et
Ergo +: y:: y: a + aX jam ob figmam TB: BC:: BC: BF
Ergo BF aequ. a + aX. porro Y DF: CC CB: BF
a fax
d. y etx y apax
seu ordinando da f da x = a2ys +  Ixy aequ. 0
ad Conicam datam
(131
b1
b Egu 1 bbex bXx aequayy e t) x 14EX
2b x X aequ
yy
2 ax a xx aequ. Yy
2aX
b
equ Prax 
debet h aequ ese S)
l
aequ. 8 sub finem
paginae retroversae
aequ.  comparanda
cum aequ. 1c. dictae
paginae retroversae
vibus ad circuli con
dauctionem indigemus