# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00069349:0144
# Permalink to this reading: https://leibnizlegible.com/page/00069349:0144?run=74
# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 72v, page id 00069349:0144
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 73r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00069349&page=144
# Source image: https://digitale-sammlungen.gwlb.de/content/00069349/jpgs/default/00000144.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 84 lines, status machine
# Lines: 84 recognised, mean confidence 0.75
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Sed antequam ut ipsas quo oeum sint literae indeterminatae
quinque nempe. β. C. V d. e.g. aequationes autem datae tantum
si
quatuor, restat ivenienda quinta, investigando latus rectum
et transversum sectionis conicae data, quae locus est aequationis
seta
hiujus
X, d X
+YPV teY +rc. 
  quod ut obtineamus, efficiendum est, ut non nisi anae incognitaum
simplex, simplici radicum 1v. g. V, resed,
lea dC, restet, planum
faciens cum aliqua cognita alterX, seu terminus dX, evanescat.
s
ponamus nempe X si v - d. eritque D ( dY +d
d
GtCC.
Jam efficiendum quaque est, ut tollatur terminus cognitus, exee
sive ++Y
V + eY +rc ( v2
d
am iut tollamus terminum _cognitum +re -F ponamus
y ( W + n., fietque aequatio + ZW + 2r We + n + e + e
+ rC - c
v
4 F
-
va
Aeris) quare ut  , + es, + YC - d Se mutuo
destruant, ponemus M + et 11) - rC + d, unde quis esse qualis ipsa
ips quae aequatio exhibet ipsius (n quantitatem, atque ita fiet.
+
EFe WV
+e
+ = 1 ~ 
v2.
quae est ad axem sectionis conicae reniversalis,itant labus
rectum sit 27n+ e n latus transversum  lateris recti
ad transversum ratio 2. Quae cum in data sectione Conica jam
tum habeantur sitque latus rectum 2a, ratio recti ad transversum a
A. ideo erit  Y , q ejus enim aequatio est
ue
2a W)n = a
ideo erit Ceg.da 
2
vo
Ateg. 8
(unde in Parabola
erit er2a:)
ioa X et 2a n 4e (, 2a.
F di nec q nod mnco
1
E
et pro e substituto ejus vasore ex aeq. 6 siet 24 (   - xC+ d sive
 si +2a  124 e = XC + d2
ja
4
12a
F)Dalo ergo vacore ipsius
en datur et valor ipsius ipsius e. Et explicatis rC, et d per
aequationes 2 et 4 feti. Aag. Ego em p qd et
et
q eq
2a
 Y1 4 vi + erqu quibus in ceq. 6 substitutis
s
fiet: Aaque ad
explicatis +I
a
442
 + equ Mage 2ae 4  sive C et d.
12k
8941
4a a+
ua
891
t
Hfet potest poni ria
ac qre a
laq
2x
eq
2a
nF