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# Title: [De la Methode de l'Universalite] De la Méthode de l'Universalité (shelfmark LH IV, V, 10)
# Folio [9]v, page id 00066634:0018
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In Ellrali si minor In Ellipsi si a.
e maji quam a, eut 2a major quam X si 2a mina quam X erit q uija quam a. Si X ni quamqu debet esto 2aX = ax + aliquid
quod pr sepate
dis nunc
en
u x. (1 + Vaq. +∞3(L)
novo opus esset signoad
hanc dubitatialam
expiim
dam.
in pis alle
Xt9. -0
Egua= =G(1)
Ergua - X
X =  = sa
da
si au pis alle
a X)sa =
23
a erit se
4- 4s - b. cid
a- b = x f
cu -
4
eu q +
a mi quax
ed operae pretum est iem problema solvere methodo sectionibus Conicis omnibus
communi. Est autem sectionibus Conicis omnibus commmnis aegratio haec:
2aX =  X = y. posita 2a latere recto, 29. latere transverso.
Unde fit. fal +a Xl = fy, Unde habemus l= 7. Nunc ut
fiet: Sagt = + a = X Y , vel a X Na + a. sed
Va
rae
in Parabola, et Hyperbola, at tunc nihil refert, utram religas vel significat
ut in Ellipsi et tunc modo quadrantem non excedas, quod minime necesse
est, fit utique A est major quam intique 2a est major quam X. et utrum Xv
Sciri potest. Quare commodinis calculi ausa ponamque Xaqt = 
a
a
ra+X
radicis rec esse, patet multiplicatione ejus in seipsam, ita enim fit:
- 44.) aq + aX + (: a X s 4) 2aX, ut suma. = a9 + y
a
a
Jam quoniam et dixi  + X s = Saque F, ideo erit +X  = faqF - 
sive
et
 X = saq+Y a
Bnih ergo 
+s4
F42464
ag+
Aq
2
, vettr aa+y4
+G
I 1X-
F(39) 5)aiq sartra
a
Aa
a+ 3X
49saguty4
  in
=q
t
Le
 i m Fq A 4
+4 + f
yrya
 2fa
9e
X-f vel d - y = V
 a4 = 74
u
ita
Vy
Rasa
+Esaae +Y
n
se
+
P
4a
d
B
agut
(-5 
(4) e
2y925.1
uae Aequatios in ordinem digeratur, fiet:
at x
qloda
agt F54q
ta
X. fer quomantts  
in
+g- f 2a 2 Unde ofit.
43agt
rugitiiqu, noquadratisque
+Yq
)
2
C.
Hida
2
aurd
udu ad nk= = +
(B = a = =
+b
a + + b = a - b.
t
4
+- +
F)
habebanus:
+g Aq
2n na--
a
(4+) (  (
Atque ista nunc ad aequationem generalem applicentur: yda y = Xl- fl applicentur
1.
d - y - +74 =4. - f
vel died 
vel i duy
-1dy 
vel -
x a+ 2 apqva (x
fiet: yd - y=
y
ugn
6- 9
vel n
a
patetprdete expresionem Toriorem eligi debere, nam vel = significat  ut
qud etreerm
a
a
uaeqaia, fudyaqu dra, dga d4, tyageya,
=
Gs
a+GX
etiam X. investigemus; ponamus 2ax +  X + aq = y + aq. sive ponamus:
segF ) a  () X +a4 Fy = + aq + qx
a
X
e
+
F7 =
-+= =
F7- +
profa9+y a
omnibu
ea
ra
+
egt
1 fac
multiplicatione
per 
daque
as
da
n 
2.
--