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# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 9v, page id 00069349:0018
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00069349&page=18
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 123 lines, status machine
# Lines: 123 recognised, mean confidence 0.69
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

quam a
e maji quam a, eut 2a major quam X si 2a mina quam X eut qmajia quam a. si X nesjos quamq debet este 2aX = ax + aliqu id
quod ur sepatet
In Ellipsi si q aX e
 miner qaux
cooperae pretum est iem problema solvere methodo sectionibus Conicis omnibus
dis nunc
communi. Est autem sectionibus Conicis omnibus compnnis aequatio haec:
2aX + a X = y. posita 2a. latere recto, 24. Iatere transverso.
Unde fit. fal + a Xl = Ay, Unde habenus l= Y. Nanc ut
a(GX
etiam X. investigemus; ponamus 2aX F  X + a9 = y + aq. sive ponamus:
sert3 L)  () X +aq F Y = + aq + a x + 2aX. Unde radice utrobique extracta
iu x- ( Nag +∞9 (+ )a
novo opus esset signoa
fiet: Sag+s = +A  + X s , vel  Xya + a. sed
patet pdentem expressionem Joriorem religi debere, ciam vel = significat ut
in parabolat et Hypersola, af tunc nihil refert, utram eligas, vel significat
ut in Ellipsi, oc et tunc modo quadrantem non excedas, quod minime necesse
est, fit ultique  est major quam uutique 2a est major quam X. et utrum XV
an a major fit en quaq la
Sciri potest. Quare commotiaris calculi causa poranus _  aqty = a +X q
1q
secto Conica data sit criculiet. Hunc autem extractionem
radicis rectan esse, patet multiplicatione ejus in seipsam, ita enim fit:
quod etioverum
7
a4) aq + X f (: ax s 9) - 2aX, ut supia. = aq + y
Yq a
+3
dam quoniam et dixi   X s = Vaq +, ideo erit  X s= = aqF -
sine  X = sa4 +7
erit ergo
pin et e
414
+142 164
vel = +
ag+on
A4
agx at q sag gra ( + (44) a) - a
 q
L, veltr aqtra + a
V.d
21
na
4spguYa
e n lni
vel d ed y+ra =-14 q2
Aet -  + qu
X- f vel d - y = V, X. f et quoniam  + at Yq
saa t r4
d- y - +74 = 4. - )
 et
A
vel a duy = Y
ita
a+ Lx
a1
+9= f2a 2 Unde fit.
3Aec
uere
odingmar moduad nu
a
(B - a =
+b
a + = b = a - b.
vit. 
=+
F+ =
H + - + = =
i ∞  +q f  q sapt pq, nequadnatisque xmuibus, habetaa: +.
25
+q.
vel i
d-2dy f.dya, +y iy
ta1 ta
tag +v
 H
a
Eq 
ra
+49490
(+
D ex PC
+9 + fe L 2f4.-   v
qdua, fidyaeq idya, fedyga 2d74, txagera, 174a F W A
Fida
= q + y45 2y 925.
Quae Aequatios in ordinem digeratu fieb: +. H q
..
protaq+ya
eper crucem
12 fidaque
2
Redsa
tirqu
+daq -0
qu 1- (4+)    (14
satra
Atqu ista num ad aequationem generatem pplicertur: yda y = Xl= fb applicentur
fiet: yd - y
d -y-
ve
a + ax
hanc dubilatirtam
exprimendam.
a pis aller
a 
L 420
Erua=x  EC
Ergua - X
X= = sa
das
1a =
pq eut pt
N1q = b, eit
a - b = X f
e di
seq 
n aax
si aupo
a = X
Eux