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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 221r, page id 00068201:0441
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quae per regulam Cartesii, a me quoque singulari ratione demon-
stratam, reducetur ad cubicam hanc
ve + 2V 14B
P a- 2 abV + aet v- a d 70.
cujus ut tollatur terminus secundo ponatur P, c + 2ab
P 10 (F3, 2bCo) (+2, 44ba) 
143 C0)  c ( 40b)
Videndum jum est, an haec aequatio (ubica possit reddi tractabilis.
quod quidem effectum esset sine controversia si esset +ac   sive
si esset 12 ac pab.. est autem ab f 16 m 4 16h et erit:
ab7, 36m + 192h  + 256h+
Sed ac ( - 36m + 192tm + 768 a lm
ut orgo naec sit p b. erst 768 al m p 72 m 156ti
vel onidento per 8 erit 9b alm p 9m +)Ctt
quod si possibile est licebit etium ponere mt 9b alm  32ht po.
porre generaliter siendum est, omnem aequationem guaehatieam nedaceesse
dHact quadrato quadraticam sicundo simul et tertio termino
carentem reduci posse ad Cubicum tractabilem, quae statim meducetur
ad Tubicam hanc. P Quod satis video, sic quidem
simpliciter in multis casibus
possibilae non esse, exempli causa si tam h, quam l, aequentur 12
Sed videtur alio artificio subreniri posse mato  ponendo L 
et loco Quodsi jam:. aeb- nac non potest fieri 70.
videndum an non saltem  ab +4aC posset peripjo.
nempe: 33M + 176tm  +256ht + 7 b8 a lm po.
sed hoc quoque parem aut majorem habere difficultatem patet.
scribamus: X A - h X X + a
am... mtex X maet 1
totento sprmrae    
2 + 4tZ +6tZ + 4tZ. +
Exaeq. 2. Regula Hindemu per spbica:
tiW Am W (n
sive pro in ponendo Hyfier.
M sut iliM-ta H0
sue M  uti quidem s pta
3(2H
4 a + mat hat
M + M + la po quae aequatio 
semper tractabilisQuoniam vero
omnis radix quadratica, est ut ita dicam
ambigua nata hinc videndum in progress
W +h W + 14, ht aat M
rectius ita, pro m, ponerat
p. fet: Moti a +
+t V +2. ergo signa duo
unum ipsiu, quod in ejus
valore labit et pos arbitrio assami potest,
vel oppos salterum  vel opposita sunt
vel si slinidunt, utrumque significat +.
alterum, necessario coincidunt, ergo
lae + n le apposita sunt nec
proiie aequatio reddcta tructabilis
aequatio. M pro im ponendo fM
fiet aequatio + M la
et M r1 + ∞
et Me l a M h ergo signa
5+ la = et l. coin-
Ergo aequatio erit reiditus tractabilis.
si Hl. multi plicetur C et
fiet: Geee
6- 3, + et 4 - 3. sive 3+ 1.
V. HY + indc. ypy ay
  athatitesesultantis
mutile
 170 m + 9 
 vt ie alint 
l p aB3
patet ipsam lredhi debere affirantionem regativam  id
quod in nostra est potestate. et fieri
an possis explicari per +. Nimirum 
residua aequatio erit:
+a2 rI 4a ( a
at
ponumus eltimum terminum
AB. Singularis culculi com–
omnuandem compensantur
ut destruatur arbitraria,
potest - BS + aC 54.
ualioquin ope huujus mod
Oplicationis statim eundus
terminus posset reddi nihilo
aequalis. idem est in ultimo
proposita, ita sossit explicati
vlletur fieri posse, quander
tunc aeprimi poterit aequatio
poterit habere termi num nuuu
pure bitrarium datario
Si aequatio Cubicaeterari
possit ad conqucum, secundo
et tertio ermino simul
carentem, semper reddi posset
tractabilis. Nam omnis ejusma;
Tabisum actabiletuu ad