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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 276v, page id 00068201:0552
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Videndum an possit novi quiddam ciria qcubicas aequationes fieri facta
positione ejus modi.
ap
qX 1 dqu F (0bc  5, +bc + la + 04(bc + d (Obc + m qu
erit PX 2f 196C + F 19bC + la + 2dg s0bc + Z Bbe tm 4
+2dupt . . . . + 2 n q (Obc + q 1Dbc + m + n p
a s.
df (3)bc + f19bc + la SF 12) BC + F 15) bc + la
a3
+B3) 4 13 bc + 2 (3)bc + in
d f136C + f 13bc + la 15 bC f13b0 + la
+ 3d q 1 bc + 8 (0bc + m
(BBC Q 13) bc + m
Sb 10bc +28 bc + 2gm (8bc
a 510BC + 5 s0betia
+q2
+
ag 5 10bc + f 1.bc + la
+34 n. 5 s8bc +f50bC rta +6dn  3 (bc + 2 19b2+ m
+3n d (5 1Bbc + f (3b0 + la + 3n
AN H
+n
+gn,
+   bC +29m 1bC
ut q
Ponendo jam 3n p - p. et efficiendo: np + a +YF0 sive A P - P +Y 10 sive 2P +Y10
tunc ante omnia simul e fractiones et criationales quadraticae tollentur ex aequatione: Videndum
autem an hoc sit in potestate:
X y+ ∞ ah y + a l. 10 VY X + Co. X + 3C0X + 3co d + co
et debet esse.  1 = r. sive C)  Co ( 1) ratico - at
Unde nr -co 27
et fiet co  ab co a at A0 Quae aequatio potest I na ctabilis esse etiam num data non
est tractabilis et fiet : 2, 27C3 - 3c0 + ahco  - c + an Cd = a l. Unde esse deberet 170
Quid si sit S +y + ab y + a 70 fiet et y, X + co. fier
X3 + 3CO X + 3c0 X + c. et fiet: E(∞, 27 C (3, 9Co  3, 313 3 n 2P
+: 2dc0. +E C I
tah _ rahico
a
C
M
Cec-co (34)- 
C2o)
dud
+at
MH
( ( c0) 4 atica ract
e qn
et tentandum aufieri possit esse : 2c0 3  - 9ah + 17 ast pjo sed haec conditio priori
cincidit. Quid si faciamus: in aeq. y x - ah y + al: H. VH 
3
PH   + ScX YS  inde aeqpuio  X 3
Unum adhuc tentandum superest, si
3 
ah Ex at c .. - a β3C0 X
o
aequationem cubicam per qubotraria mulliplicater X3 +Y3c. 2r3c. +Yco
ex. V7
X
ex quadentica rursus ad cubicam reduramus. sit. A yZ -ah y + a 10. in Y  12. dabic.
rnV X = mati. + mas frso Unde per resulam Huddcuii, cubica:
A y X - ah y + ady
fiets
fi et culica haec: X3 + ph X A Smfr X = mA
+27 X +D et +D 27lmA
et fisi aequatio: m +  +2 h  + hm - 2ti tapst +A
et sublato termino secundo
M X + h M -oto
Noti penultunum coati
M affinnation redoere velle
= 4h
 2742
redit ad determinationem Cardarii
Terminus illimus est quardratus a 1 4h - 27A
Termipenult. est: h2, w7N- at3 23a sa
27 A2
(2FY 13
(16 H
8, 17 N s C
+27, 173
27, 27 43
14
7 h3 2b3
cpnregut
 m A
nA
pa Fsbc a flObe ala
+29 bc + 2yn 36
+C (3) bc regn. (b2
+ m
at f16C + 10bc rla
n
bs01
=ah. =ahico
rebi mirabili
calculi exitu
destrnitur cd
adeoque nihil hinc
po est duu
Nisi nos putemus
duci ad calulli praepa–
rationem
N r
4h3- e  vocando
+4+ 22F2
8172 3.
= ha2kr
2h
ea tinro
 sed sed hic rursus co eoamesct
et β Credo dacet
adem quod ante
(xtimA
rah
 neto
-h-ni
+hi =( 2e m3 = 5  5
+3mA h
+m 62
sive detet esse  + hd - 25 de p 4h
qod est oospiee