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# Title: [De la Methode de l'Universalite] De la Méthode de l'Universalité (shelfmark LH IV, V, 10)
# Folio [72]v, page id 00066634:0144
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eq
Sed antequam ut ipsas qu veum sint literae indeterminatae
quinque nempe. (3. C. V d. e. g. aoquationes autem datae tantum
u
quatuor, restat invenienda quinta, investigando latus rectum
et transversum sectionis conicae datae, quae locus est aequationis
hujus
X d X
J.
=∞Y +e) +rc. 
quod ut obtineamus, efficiendum est, ut non nisi una incognitaum
implx, smplii radicum, v. g. y, reset, altera X, restat, planum
faciens cum aliqua cognita alter, X, seu terminus dX, evarescat.
ponamus nempe X p v - d eritque N (dV+
Jam efficiendum quaque est, ut tollatur terminus cognitus
sive 44
12
+ C) + rC F) v2
c
2
ex
Frycertrc
 E
Jam iut tollamus terminum _cognitum +rc - ponamus
v2
( (Aepis) quare ut  , + est, + rc - d se mutuo
+ rC - c
2
y ( W + n. fietque aequatio =  W + Zr W. +n + et + es
 + eM 1) =rC + d, unde quis esse qualisipsa
 quae aequatio exhibet ipsius n quantitatem, atque ita fiet:
+
r
n W
+e 
+ = 1 V. p
v2.
quae est ad axem sectionis Conicae reniversalis, ita ut labus
rectum sit 2n+ e n latus transversum  lateris recti
ad transversum ratio X. Quae cum in data sectione Conica jam
tum habeantur sitque latus rectum 2a, ratio recti ad transuersuma
ideo erit Z  ejus enim aequatio est
ideo erit
2a VI = a WV2
Ceg. da
es
v
Her. 8
uq
(cunde in parabola
erit er2a:
a X et 24 n  e ( 2a
 F in q mondmne
et proe substituto ejus vatorem ex aq. 6 siet 2    - rC + d sive
s 12  11a  re +
2
4
172a
10 Dalo ergo vacore ipsius
e datur et valor ipsius ipsius e. Et explicatis rc et d per
aequationes 2 edt 4 fiet: 4ag2. Ergo eM p gd e
et
 FI 44- e + e
fiet: daque a
explicatis F
2
C
v
q eq
ea
d quibus in Aeq. 6 substitutis
4a2
qu Mage -2ae 4 a sive C et d.
12
3p
49412
ratu
ra
g-Y(
gt
asisc
et potest pon
e
s
Ca
ea