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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 271r, page id 00068201:0541
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lonatur scilicet aequatio cubica assumi
3
2
y3
conferenda haic
 +pZ2 - 3aq Z + aY
1 +b93
2
-3a9
∞ ac
+a. qua collatus temnis perultims fieri  mups aq. et npu ag
+p m2
 = 2mN
=a M
+ ac N
L3In
3mp
quem valorem ipsius n, inserendo in terminis altimis, fier.
M +p M = ac M +ar M tacaque M +p a 1)) 
Abq
+3ab9 .
u
Acquatio sexti gradus in qua sunt arbitrariae numero quinque
et quae ad Tubicamo (uno si terminus m3 desit ad planam) re ducipotest
ubi si ipsum 9. non eyplicemus sed reserveruus, (modo alicorum artitrariarum sit satis.)ut
quantum licet magnam assrmere liceat, erit Cybica assumta 23, etc. utique tractabilis
hebet autem 9. esse affrimativa ergo bcuia etiam affirmativa, seu a A b.
si scilice 4. liti hoc modo volumue.
sit jam culua aliqua data intracrabilis atis t
multiplicetur ter tractabilem, et excitetur ope trium novarum arbitraviam s
+ Ba
bua
ide conferendo, eri q ex term. ult
ex perlt dn. qh  patqut aile -a cqt 3 abq
he . + a B m
b. a d b=a d
X  atd. +ald m
la abb- a
Ahb-a
aV acqtaqe habitas   pla + p aeqlaat
q dR  
aot aacnb BIBLADEAEBI
+aem-ahe. + a le
AICEL+
EIANBOVBHAEEA
Rectius sic aequationis prioris  term. penult. ad secundo ut aq ad 1. idem ergo et in
t
posteriore, ergo de Pa ae qui
+ac + 3bg
b a
b a
a b9t vat ( qh + 1
la2
cut
il
+ah  ad  ap - aehd  sustulimus erg e,) et c
1a
b-a
dei ahqebua - aelp p aqeh bua + pa t
buan) a 9 - ae h
a B-a,
Ergo a q- ah   Ergo Xq- Xh + a l que aeque dificius ac data
cursus cupo clapsa est natura
qu
Resumamus ergo aequationem ex quadiato quadratica stusiana, et quadratica impostibili exertotam
nunc tamen autem videanus un quaedu quadra trquadralic redncibilis sim erter
excitari possit, sit aequalio plam: Y. Z  cZ + da ponamus E, Z m= n
explicando fiet: E H
conferetm cum. Z p mid
= 2m1.
an
bini
-imn
sit cubicu dH. uq y + aY
+
yA + - aqy +ary
by2
a- b7 f
pro ma scribamus ea  per: m tac m + da m eac M - fe 2
Quae aequalio semper plana,
97. X -agg. tarm
plana
conferatur h oyorutica cum sensinua:
et si d,o etium latioculis reddi
e potest
fea
af
si =en  +. un + posibile: ut si Z e 4Z. quadratus
quod facile, quando e aib hari erit etram rationais 2
onflundo gB = Ca  e  = ac e - arf. quas duas aequationes
a9f
A explicare possum omnia habermus, ex primo et ultimo valore ipsius g
erit cag - aCe B f idem ex imo et 20, fp, = caY
aer et destinitur CAitq: C3 - 9 + Ya quae redit ad datum
X+ + en X3 - 3a X -nan X  anBo crit  si  -ac)) et. erx er a.  du ac c. 3a - ac
ano an
imio vilo gparationem institui non posse quia uttrimus
dratica plana est:
in
+pXrq p
aum cae etrans oae nucn totue  a pe. 1 e u i ft 1  1
t 3mnz +m
quadrato- Tubicu hmic similis:
M X. Lah M + a
+ad m + ae
+pa N
b-a
X - ah M + ael B.
X
ad
potito
et ZB M = n.
explicemus LZ3. + pZ -acZ fer
+a 9