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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 63r, page id 00068201:0125
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(30)
St
pars I1da Schediasmatis de Transformationibus aequationum seplemt
unius incognitae inprimis (ubicarum e quadrato
quadraticarum
1679
paris
Canonem aequatione 8 expressum u aequatioais quadrato quadraticae
quantum licet explicatae, applicare ad cubicam openae pretium est, Nempe
esto Cubica:
+ fy2
2
Z
ponatur 7 X + Y. erit 73
et y2
327. fiet:
a
qu
1-
e
RH 2, X + 34 7X + 34r X +r
X + 24YX + . quibus valoribus aequatiom 30 insertis,
t4 f..
qu
+. + a3
+2a rf. +
+a ag..
ve
i
+agr
+a ah
(35) (4) Ponanus Yp , item r +2 rf _ ag B0 in qua pro Y
inserendo ejus valorem fier S= - 2 f2
vel fp. F3ag. ut supra aeq. 18. Quod ut obtineatur praeformando
2
fiet (9r +6rB) + f B (9r +brf) + 3ag Quod cum sit efficere
sics
idem per idem patet praeformundo cobtineri non posse.
(25) Recurendum ergo id hoc remeddum est, ut ponamus: 
8 Y + Yy + aCo
16) imo quod ultimum est ponamus L Z. DZ + B v
Unde Z
Ila
v
im
1 V +ay + VY + aco + v. sed tanc tollendarum
errationalim causa ascendetur ad aequationes ninis altos
si in aeg. 32. secundus Terminus nihilo aequetur, sive sit rp s, fier
Et X
a
tu
a ag
N+ a2 f3
15 2y10
X
aP 13 hoe
p 15
= aagf.
13
ut a x a3f3
a
3quo
2793
+ ag.. - aagf
quid sijam
393d
+a’at
aae Lositalis potest
sumi valor
quodsi jano Terminus Tertius est major nihilo; semper effici potest
ut quartus sit minor nihilo. Nimirum tantum requoritur ut
3ag sit majus quam fer facta quo dato semper fieri potest, ut
ae quatio subica extrahi possit. Sed hoc semplicibus prae forma
tionibus video effici non posse. tun fortisse debet esse
gr erf +2ag e 912 16Y +F, hgo faciamus
gr + 67f + sag. p 9r 1 6f +f Res ergo eo deducenda est
ut proposita aequatione quaeratur alia ex cujus solutione ipsa
peneat, ta qua  hactem oltineri possit
10
BaALB
beLA
decum