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# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 75v, page id 00069349:0150
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e
Esto  sed ut aequationem a sectionem fonicam datam clarius intelligam,
aequatio haec consideranda est: AX + XdX + Hfr + + X) tCY.
Hanc aequationem ajo esse ad sectionem (gnicam quamlibet, quia ad Parabolam, si
ponatur infinite magna, ad Hyperbolam et Ellepsin si ordinaria, et si + signi
ficat + erit ad Hyperbotam, si = ad Ellipsim quodsi re F. erit ad circulum.
Jan ejus latus rectum traneoersumque investigemus. Nimirum, dividantur omnia per +.
et facilioris calculi causa, muttere tfr. alioquin enim possemus adhuc augere nun
cum quantitatum super numerariarum, sed earum satis habemus. fet ergo
X
 + dX + a
qo
F= y + ey + a(fnde X+d5 +2tey+ desr
et ponende W , X +8, fiet: W 5 +2y + ey + d fY)
rursus:
v
ua
W(+fr d ete
FZ
12TI
in
~
+tCy) +e
Unde sW B- 4 Ergo
e
Unde fiet
Hy t +
sam si sumatur aequatio haec 2d + a 1  W. Inde fiet:
=29)+ y +g rtua + q
Ergo eut te
et 19. et
+
23
siet q Py e Anurqu
a. Ergo tp ar. Ergo QVe B q. Ergoe
a
1
2sc
Ergo e N 24. Ergo e. arbitiaria non est. fat vero s F sed si aequatio
fuisset +tq + FX5 S+ W4 + qu, et posita jam fuisset X ,S +Y.
tinc aut Z aut C fuisset determinanda,  alterutra vero mansisset arbitraria
comparando porro. Rostant comparanda: +1f + +a
ar
13ea
4r3
qua aequatione necesse rursus est aliquam ex incognitis determinari
ut f. resat ergo incognitarum non nisi una. et addi possunt du, adhuc
ut d et h. ex explicatione ipsarum W et y. tes ergo, incognitae
seu inde terminatae pre arvitrio assimi possiunt. fiat nimorum:
a
+ dx 
anto
x l
sed plus aubitrii; minus
tr
1 17 +Cy. catalus erit quiante
sV
e
Y eut et 2 20
determinationis habebimus, si 
in irsa aequatione determinat + et nempe 4t T F y F7+ =W
L +q
po y. et W alias nempe X + A, et W pro WV _ quoque a alio
 assumsisemus sed id videtur in W potum, utile sd ipis opus non habemus nisi
dia velimus problima solvere cope datarum duarum sectionum. ut huc tronsferamus aquatio
de nem ad sectionem concam indefnctam pagnae primae hujus schedae, loco fr, ponamus 4= sV
e la (_, ponamus 4re = 2Y R pro (d) fiat dtr per consequens:
4h14
 ergo np 4-28
v
e + 4arhare teh Ata vel +Xba- p C +he
seque E +h- ra
si
=
nec
era, vel q. vap ra gura
+
  A. 3F  id Ep +
tis
e
at 10
+
+-ra +id
Zabra