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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 226r, page id 00068201:0451
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Quinquam hoc spes sefellerit mondum animum discondeo, resumta aquatione secanti scd cubria nova
secundo Termino carente, nempe: e X - L h 8 + 2h H. experiumur age novum aaequatione) cubicas
tractundi genus, quod nescio quid
-3lm.
pper P adjiriendoque itroboque rape apufict:
mapgis aequationis
quadraticam
singulare promiltit, nempe, mulliplicata aequatione
e prapb a pae pst e  ih e + a p.
atque ita tu habet radicem ex ipsa forma, quam praefert, efficiendum ergo
ut captam altere quoque latus habeat, necesse est autem ejus latus esse:
Da + ap. inde 2pA Y Da B Q a. adeoque + p Da   a
sive. 87+ ; ha +p2
+3lma..
ahm.
+ Ya at e + 2ti2e +ap
Lim +.t m 3.
olum.
Si ponatm 3liv + 3lm tim prap p a pollit Da. + sp divili p. +C + p.
dc + qa
qc + ap
aqe raipe
+3lm 
+ h..
um
B by + y B
conferendo aequationi erit aqpTa +2ap.
et  7ap+ 2ap + ap pa. quae aequatio
+aep. +ap videtur habere exitum
Sit erguaegutio cubia: yt  alu  y ali Vaal0. Sive V  rapV + a p B 2a V +aely + ap
Habemus aequationem inter duas quantitates quarum una est divisibilis per V + P. Efficiendum ergont altera quoque
sit divitibilis per Y + p. Multiplictur ay + ap per qV + ap. fiet: aq V + aqpγ + a p  quae formula
comparetur cum 2ap y +a ly +a p. Ultimi termini coincidunt. De caetero ex duobus primis fiet: aq 2ap +ah.
+ah.
 1
+ 4 P, Xh
ba tpitia
et PC 4 p p -h - a +. Th2 + 2ah + a - 16al, sed haec mugatoria sunt, uaq unum
lutus non dividitur per y + p. sed per y tax
10 oal
sit aequatio talis: y- ap Y at V + a l. y - p. Una aequationis pars divisibilis est per py-
quaerendum est an et ultera reddi possio sivisibilis: ay ap per qu 4ap fit aqV f aqpY -a pept
ZH v+ e.
= p.
n’a3ve + pe +e. v+ 2vC +et 2v , + Fre +1vC 1C
V7 agY F a l. erit ag B V et e +rag C 1 C tal 0
19) 7 +Su
ebve
sit: b + 4es ad. (3) p +b + 3b E sad. tum Cr. Y 362
CB et erit Ee + Y  4b7b
quae si vera essent vicissemus, Resumatur:
13bed + cd sod
 + E - Xb2 + b 5 ) 8a a
+(3) +9a +a- ad. cujus latus quod quaentur b += S- ad. (uligcubus. + b2+ 3bC - ad calculus ergo prior fulsus.
jamn duae aequationes. a b3 = 3bCd , 9at. et 3b cadc a4
unde H _ qat libxda s a dc
. et b, 439ac
27 a 9...
D3aod..
3bed +7 ....
npole, 9q at2
a- 1a de 4 6 
a + dc3
) ulividendum an 3d - 27 g- d+ possit esse quantitas aftirmatio
 er videtur. est d- H q + t3 unde +b3 -  9t - 3. dibet
esse quantitaes affirmuliva, quod non e semper in nostra potestate. Hinc si nullus enor in calculo idetur sequi quando h 57qV
tunc pose quapemulltum terminum hujus quantitutis sublate, termino secundo redoi affirmalivum. Nam si (- 5Zq est quantitas
attranativn, eris potent tota reddi majoi, quam d dum sculicet 5C. qua radices multi plicantur 
vel dividuntu, sit fractio maxinm denominatores. Operae pretium est hunc calculum repeter
b + C V- ad. cuius cubus b + 3b2C s ad = 2bC ad = C ad f- ad. unde aequatio nes. a b3 - 3 Ad bc e) 9a3. et abc - Ad C7 a
unde b p 9 a3 + 3d bc at  dc. ergo  39ac 
4d C (4 44 C
4a dua
at si facias CH (- 2add, c
a  d9. 3c Nb. et b, 34ac
, add...
a2 + dC adeoque multilicando
a8- 4 a + 4dE1 3C
yaqu
+a 04g.
per crucem, fier
Do. viditur posse remedum asseri, uia potes, intelligi d mulliplicala per s et d pr  
cum simper esfici potest, ut divisum per s sit minus quam dvisum qiper Ns aer
ob b + E Sad. erit: b x Cd patra sive b  - Cd + ah  dCta Ergo 38 43
12+ ~d + Ha b a +Cd B hX et 3bc - d c H a 5. fiet Va + Cade 3h bc - 3h d c3. quo posito
3. hili sipi culo cprua plm, vo nei cispenia
2a 7.27.
ena b8zuacc
= b. ab. - bac
n- 2lm -hm r, - b + ac
lacere +  H b. r umbatibnb- b3