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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 112v, page id 00068201:0224
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sit (0) dub ras ac. Quaritur ejus rodix. Sonatur esse: aP + Y sae + q. vel 
vel asae + rde sae +4e. unde cubando: ta ae tae 1hep ae qea ap sac qe a  que ea
Equante omnia:
+aep a 13apqae ac
+raxis
naprer
+ upr
ponendo ap +re e na fer: n + 3gen ebr0.
et et n + 4’e - ea 0 eritque er ng et e, nq
Cuumque valorem ipsius e inserendo aequationi praecedenti fiet:  +39ng - nt g+
et fiet nri a 2a, 44 + Dj a B
abq aba a9 196
Repetendus est calculus
a-2a9 4
nn ab rabest
gelibus 8
1) an sac + age.  a  a hge sac +randeage  an ae die + aqe  ab + a tae
et divellendo atque ordinando:
n + 2gC n -  Yo. itemque 3n ag + q et  ab
ex posteriore eio er) yriaq ct X 9a
et fier n
ab -43
. quos valores inserendo aequationi priori feb:
a+ b - 24b93 +q6
à b (2ab4 49
+9b4 
ponendo scilicet cea vel c sae esse cognitam,
TX + 9aq n -9aq n
1 a b 17469-390
9aq
ab-43
a +b- 2ab9 19
arbitraria. ideo, ut En fieri possit, sic
procedendum:
ab + detac et an sae ilge enaesaer inde qronasaeriqe raie
et divellendo ace   n’a + naq
tir. n ab  ent ae 34a aeqte
An ita ansue tagee  anaetae e na e  thnavaeaique a
Ta n ailae B
 ) s sit aequalio y + ah Y  a lro erit y B + E l + S: 12 =, 3 a 50 : 1 - +: p,  h
ergo y B i l  (d - Y) f 2 ( - 35, : l + S + 3 s0  1 - 34, + l - s
et fiet: v - =l p 3 s0 : 12- 0  s: 153 r s0 : l- 5 Eautem  (2. DB (= 1 - : 12 )  
Ergo fla V- 3 +e
Tronsponanus: y - 1B : t + D  s) Et - D cubando 3 - 2y : (+ D + 3y Se (: P. : 1)  1. . + LD
 - = l=D  a t 1 (D) siuis - 2γ Ergo 29t s0: 120 r2yS): 3 + 1D h
si sit g A ∞ +n. ponendo g. et n. esse radices cubicas, faciendo: GG. et Np 12. et Xp y 2. et vocundo N-GB H h. iet.
G⊓H +G2
fiet Y2 + 3HY - H Y + H. conferatuo cum aequatione enbica V + dV  d9B + 431 B. cujus rudices divispe per d. et quae angendo
jeas pro v. piucudo _ Y + e. fiet. 1ed +3C Y2 + 3C Y + e3 250.
erit He PC et HB  C+ dC  + 3C 4, 1
quem ipsius H vatorem comparando cumi e + de = 39C + 3l. tet : c + d  ge + d. vel
yae + ad s 279e +27d1. erisque e
it enim sunt termini penultimi; scilicet fiet:
3 Fir G2
C ea
1d + 17 , 324
42.
 144 4 543
13352 ad
5+872
FH 271 = a sive er d. Restat ullima aequatio, conferendi
ga = 279
+ + H G + 17 8 )
 ubi patet d esse imutilem. Nemus
eo redire ut constet an Radix extrahi
possit, et vereor ne res redeat ad deter-
minationem scipionis Ferrei speciem tamen habet diversi
Plane evensus: vel. Ros in numeris tentanda sit aequatio Albessi
t inZ + 1o ponc ZH v + 3 a friX a2da
seu y . y 
Ponendo ergo compendii cansa in praeserati
adet; +ned rnd
exemplo O20. et 91 - 13. quo plus quam opus est
FA) contra not grcedimus, fer. B00 + 180 =13- 10
 27, 272100 4 17 27 210+ 1702
y12c  ero d  4 uC 9724 e
d + 38 1 65
 es ponendo = H+. fiei D p 1317
Sed repetendus est calculus, cum videatur habere nescio quid
Si get 1126 foret 102
ves as e 
d 351
Singulare; illud certe, quod ea ratione videtur venitur ad radicem  aequationis cubicae 
20 + = - 3
secundo termino non sublato-
Nemmur