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# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 77r, page id 00069349:0153
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tres
si duae sint aequationes duos habentes terminos imognitorum communes
a illarum
illi duo Cermini semper aequationum duarum collatione, tolli
possunt ret estu RY +LyX + a + y 
et
d
S
Xy
+ Z Y X + b f X d. tolli possunt xy, et
2
 X earum collatione, quod ita ostendo. X Xy, in utraque aequatione
reddatur Aerminus pujus.
Vimtandem reperisse visus sum, aequationes quibus continetur Xy faal
perducendi, adfericulum  Esto radie BA centro B. radio BA circulus descriptus
et punctum in cucumferentia ejus, Xa quo ordinata
D ad radium BA, angulum faciens datum. YAX Y XB
producatur YX, si opus est donec ex B centro
in ordinatam Y X productam si opus est, dem
ducatur perpendicularis BC. Quonam Angulus XAA
YBEVXB
datus est, datus erit etiam angulus BXC, ei aequodis, ergo sic notus. Ga
et  et ratio rectarum BC. CX. BX. ponatur BX N.
cut et t ert BC p = X. posito DX BC E. Unde
ex t a
CY, Radius circuli ponatur b, erit CXF
et XC 
V
2
NB- = X
AX - =X, sive X (a -C eitue
TN i seu Y 1 So C X (+) X saC quod 4)
significa = si angulus YXB est obtusus ut in figiora, atsi
idem significaret +, si angulus esset acutus. Ponaum autem hoc
locuresi ergo 2
sve fiet 72
vor quo
=) x 12yx sa ( +Kas- KEbZ
Sac
Jam aequatio d ea est
e
2
a
(a2
VX +X - (6) 10.
literae autem c. b. mulentur  alias
Jam aequatio oata est  ne aequivocationem parcant, et ponatur:
D
v (F) sa per
 VX + X
V
= (A2) 50
At aequatio data fuit b Xy + ad X + Y + ad 0 dividantur
2
D)
onia per Fa et si poteda semplicis substituatur ejus valor y + X et multipheentur aunia
fiet 
ax +add dyr + aX pdeus + add
fiet.
ga
Xy +ad vita
292
a
et divedendo omnia per 4d, fiet: + 29b XV
ad
2a
per du L.
addantur a
Porro lc in circulo assunto in figura loco rectae
27a F
a
a)
aa
Vq
B~, quam appellavimus X
deo appelletur DX. appelletur X, tum BX erit Y , C X
F) a sa e
ad
L
N + dCY  F29a 70
 adhibeatur recta XD, quae ad ipsam BX in ratione sit data u et it
et apratio ad cirutum eut.
VX + n
q2
en k
12
7.Y
TIX. vD d.
AAS