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# Title: [De la Methode de l'Universalite] De la Méthode de l'Universalité (shelfmark LH IV, V, 10)
# Folio [77]r, page id 00066634:0153
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ra
ue
i
pes
si duae sint aequationes
illi duo termini semper
possunt let esto
et
D F xy
a
a
duos habentes terminos imognilorum communes
illarum
aequationum duarum collatione tolli
exy +_CyX
a
+ g Y X + b3+ X d.
a + y
sC
tollipossunt xy, et
Y x earum collatione, quod ita ostendo. X Ny in utraque aequatione
reddatur terminus pujus.
Vamtandem reperisse visus sum, aequationes quibus continetur Xy fal
C
perducendi, adfericulum. Esto radie BA centro B. radio BA circulus descriptus
et punctum in cucumferentia ejus.  a quo ordinata
ad radium BA angulum faciens datum. YX Y XB
producatur YX, si opus est denec ex B centro
in ordinatam Y X productam si opus est, dem
ducatur perpendicularis BC. Quoniam Angulus VA Y BEYXB
datus est, datus erit etiam angulus BXC, ei aequatis, ergo
etgu et ratio rectarum BC. CX.
BX. ponatur BX X.
 erit BC = X. posito DX BC
c 
CY,F Radius circuli ponatur b. erit
et XC 1
2
e. Unde
extt a
Cx 1b-
X
AL X - EX, sive X sa- eitque
I~ i seu y
significat si angulus
F
Sbc
irX
X Sa cE
a
Va
quod
LAB est obtusus ut in figiora, at si
idem significatet +, si angulus esset vcutus. Nonamus autem hoc
losi ergo 9V.
sve fiet y2
E)
Jarc
Jam aequatiodt est 
Jam iaequatio data est
v
yx C2yx sa ( + qvo
2
cV
a = X
VX + X - (6),70
2
bs2
literae autem c. b. mulentur i alias
ne aequivocationem parcant, et ponatur:
F) saper
VX + AV
(A1) 510.
At aequatio data fuit h XV + ad X + c + ad 10 divitantur
onia per a et si puseda smplicis substituatur ejus valor yr
fiet d
xy +ad
 et
X)
9a
4
X
292
+dcy +ad
a
,fiet: +29b Xy
+
ad
a
a
a
2
TX et multiplicentur nunia
X
Vq
B~ quam apperlavimus X
X appelletur X, tum BX erit Y
et aequatio ad circulum erit:
D
per da .
addantur uta
2ga X
a
, adhibeatur recta XD, quae ad ipsam BX in rationo sit data uet et
deo appelletur
=) a sa ei
a
2
4y + a X +dCY)  +2qa 5j0
Porro lco in circulo assunto in figura loco rectae
C
VX
+ M2
nx Ca X
v
sic potius. Gja 
IX.
XG,
g