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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 12v, page id 00068229:0024
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15 - 2p= l
4116p l - 2p3
2p)
. Ergo _ Ap r6lp (2p, + 15- 2lp  p p1 ps)
-- a--
Ergo  4l pe = + aB p  + l pV  7 12
- - - 1.. +V12
verus
contentius
Ponenia Ve o. erit valor ipse  pt + p, et promde valor affinuntibus ipta P omnium huic aequationi
satisfaciens erit omnium possibilium minimus. Sed quia diversi possunt esse valores ipsa p. contenti
et quia P potes habere diversas radices iDdeo et ea cujus vulor affirmativus est minimus, fore minimam
satisfacientium et si placet sic polevit dici ante divitioneme extractionem veram:
p2 + Cp
19
+ I fi +pB (+ 
Ergo diffTumma ex p. et AL erit aequalis dimidiae radici ex 4p - 3
Indeamus an ita liceat extra here radices, aequatio est: p+ - e p 5+ 12
duplicata.
+t.
conferatur L er +p a lot p + V 5, cum Ap +Vp + c7
125~
fient aequationes collatitiae duae, una inter st et P. altera inter
est fiet st  12, et l5 p +- 12
7- 210I)
(+ pt
t p 3
qus et IX- 2PF f4, id
= 21
Hin S+ . et Sp F- l ergo V ( +3- 1 +. Redasta est ergo aequatic. quadrato quad catita
Enor
Culculi
secundo termino carens ad Cubicam secundo termino statim carentem Cum contra
Methodo V. eta a Cartesio transseripta neesse  ceducatur quadrato quatiatica
ad cubicam secundo termino proeditam, eamue quod et ipsum incommodum est sub
velamine sextae dimensionis ita ut adhuc praeterea ad radicem subicam extrahenda
non tantum sublatione secundi termini, sed et radicis quadraticae ex lota aequlo radice
extractione opus sit.  1. Atqui F l5 + 12, ergo fiet B p S + ls. atue
ita reduci potest aequatio Cubica ad Quadratica bis ad duobus diversis modo
2
Y
fier 
pone tr 
ad cubicam, eamque vel secundo, vel tertio termino carentem
sumamus tertiam cubicam secundo termino. carentem. y Xim Y p p pl
rende y a la y  pl y. Unde   + lm V + Vm
+1. +mn
+ ~n+
P+ mY  4 Fnly + lp.
1 43 
7My ply+C
Eodem quo ante modo
atque ata aequatio cubica in aliam transfer
potest, quo facto puto posse mcdi in modum officer
V +lmY B V2n. Ergo 3 + (m p Isn
posteia aequationis, pars conferatur cumque
Jr21qm
+ qug0
12lZ
6
A
Len
2Im V + uln
21Z... + joqu d 1
p 2414 + qu14
vr
UmtriZ, sue jus umenZ l 4918 414 07 +4(4 nZ2+12
 Laq. y +. mY + 1pY + lp ( y + ry + l9y + 1)
+ 35)
1V + ty + qu
t
NV
+Mt
C1 + feY + eq (CDC X) (H C v) (+ = C9 (+C v) - 5C+) os (f) Ens l reveq
+by
329
sict item v ergo S. Bam et pro e korieue (hape aequationes duae talis naturae esss nosun
potius ste, fat fH h.l + F 2 k∞ + + Hq + _ 13. se
in SN tax  B g. Eyx f r li B. F ter 
TLB
fui toffrk her artiver. 1.1
inter
q ut inte le composatantur, non sit opus nisi unjus ex ipsis
factae solutonem quaerere, quia scilicet etsi possit
tunc casus evenire quo non satis faciat tamen ille casus futur
est ratus; et eace in hocegregiam artem Anahyticam
Consequentia quadam uti, quae et si non sit reciproca, est tame
sut plurimum loquendo; il est larus, autrarus in certa specie casus
est quo recproca non set, undeantisi Tale estartificium fermatio
inbe B, ia ut Ecquatio ex visse
in quibus utraque aequatio
et Is p lm+n
ut semper extrahi queat rudix
Unde gam fiat: y+  1 m + 2lm y
vr N
+ 2lm 250
Eaulmao cum ny +15 ny + Cus ffict: ple Asn
con feratur cum n es + ply (+ l m
V  my,  lp
fiet q p sIn.
14
+ Y. +1g.. tts
15.
12