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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 1
# Folio 7r, page id 00068214:0013
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Indem.
e
Regnuaect ueo Ero oarqul
Egusmat pest cm ess
uun
os
h mny in
troigrari
mustu ex hm er  raci. E esid
horaris.  Emmmar.
cagur E.d
et
0
b
 did e  ad  t vude
dE A a vianl.It  + ut ut ut no  n nemo
cumere i degi
ns tuvagu
 V B atum
d. u6) id + id et b0eo  rsa
hin. oen in
11t
 in
ee odo unet uat in 
cuis oenr
quont nontr in ingerenati mocto rupuli) aguem
oct + 2bav 18
digiat 6. v N u us) d   - b, ∞ 10+
40t6 oh ut in) in 
Eesse 2th ch cenou 2 i 126l tu x 18 + d uv a-  . Gurc Emonad E A
unq ib ob
a qum ven Eurmoem ee hrazt
1d+
Chor18t adt mvno trr- l buos + ut hoger
abu v1B +, duv at yt V. B mv1B + a buob +  1ot 1a mmau
cmont rrarim erpois o
us sit ldo eut lungas io ingren amnz ryag uumee
el Wertgan +dh magn) wgisaatim in uumant ess. u p ub
gr  in dewgun Emguinn monti
egB ad -ubcuvb- duvc: 10i) gnam
cant.
eud uni
v lo
sumaru
qualo n
a li
uobu
in
cagossumt u d - 9 ubcuvb- d mvE
n) n 2 + a dE + ad + a H, x
4 + a + E + a l X Zaver
o i hib
puy soyo res o orrgomas), iu in qui)  agnatio vna
uve x. duo 
dotuo. Fibuor
es
4 + a
HX
sur
Eicmress angusas in seuerguatio biu
L.
udvr (dmvtica
brove
uc
Cud
teu
u
d 2
adisca
 i o) s sio
uto r
do X C
16
Aiut
S. ) atr a
un
xs
mb.
dog eegn esch egurs nnt egnienat n
alir hat
bi
bu
u
b i Y ubrum-- xdt- ∞X
vinons dur un sunere uchnt huit nn hurgu, ingen angoreri
sed video ipsius dexplicatione nullo modo esse opus, etsi enu pt
Unde si pergamus non necesse est quidem irrationalem d reducere, attamem
optus tamen est eam saltem destini, si non reducitur, quoniam supponitur esse
Nempe aequationes sunt duae una cubica: unique in tognitae
quae est dat
altera q adratica suarum incognitarum quae est data sumta pro arbitrio,
ex eubica radicem extrahendo, fier
(3) yr 1- aq + a a4 + L, ap - 10+ 2 aq sa L ap
et ex quadntia duarum incognitarum idem y sic invenietur, nempe
exyH
Ilde
(8)
ex aq. 2. ordinita fiet:
V + Y +G.  B +  , X
a.
a
l da
4a
+ 2bd C X
+ d
1) 3 - 2X ∞+ _+  b X + td X +3
sivne brnou ligie cursas ponen bo
as
C.1 3  2bd= e h. a d afp al
abebies ra B 2. e ( d B n. tum ex aeq. 9 fiet:
(10)
y⊓ n X + n + SZX + hX + at
Crmus liberae b.c. d. e. f. non sint amplius occur surae eo quo ante sensu,
(i1
deo novos illis possea mox valores dabimus, quod neminisse intererit
ne prioribus confunduntur
Jam ponr compendi causae Radicem cubicam O, vocabimus b- Redicem
b ⊓ m X + n +  + c. quod cubando fi: et ponendo n X + n+ er f. Eibp AC
traeq
: aq) (a d)
Unde eaq - fr iocndo ar. fet.  C arafc unde ruisus Tubando
(2) C6  - f C + 35 C’ ar a3fCaeY + ar
jam exi + : aq + a d. et C + a q + a qd + ad, fier:
(3) (3) a q+ aqd iad n- f aq. f aed + 3 fara Bg C df aicide
aq. s3
in explicabilis. Interim quia  est prolixior, eum nunc quidem noaa
Asequemur; sed supponem,s ab initio loco aequationis 2, hanc.
17
er cuft
(6) = et c seu : a9 + ad  Sd + 3sd a v + sd a r + av
CX +3C X geX 13X aex + d c X
+3ca .... ae3 ... + 3a ef..
CeceCLACALCCaCE
+abpc .... - 2abd pc ... + a3d pc .. + a  pe.
ex aeq. 19. fiet sequens cubica.
ad
ebpe .. +2abd pe.. + a d pe + a d p)
8963... + alb pf.. +raebdpf.
adeoque ordivando: et  qd + f a d vocando , a Sd et f9ffa atC 21)
(1) C _ a sd + a V e a Sd + aV. meseu
yB CX + aeX + af
Cx 3CX + 3caf X 1b a et X + 3a cf L + hact X
cubicam D vocabimus C. radicem quadraticam q + L, apZ vocalitums
et aliam d X + hx + al volabimus  C. quod meminige intererit
unde ex junctis aeq. 7. et 10, fier: m X + n + (,bac. sive:
et) b seu (- : aq) ad) e f + 25c +3fC (8
(ag: ap
(7
(15
ad
+32969.. +3a90d.
+ a9d3
fx + de f. + 4d B0. In qu  cum jam absit terminus secundus.
4 4  + d sit affirmation sed hol non est in nostra porestate quil carbitraria
isset, it plao neo eamine utrue omista sestinctive teminis ultuus aqpatonis 
irrationalis quadratiea, tamen ornes ejus terparu suit cogniti
raexaf + hde ka)
af
+ 3aexa)
et + a7
t
qu
ap V ducatur
in bX Fad, cub
fiet: 9 ae e D
+ b X + ab X ad = 3bX arde t a _
Quos ipsarum y et y. vatoles substituendo in aeq. 1. fiet:
adpf
+agb ... + 3aqb3.. +3aqbd. + a  9
quad siqua porumus Essssu A e as
Tertetur au sus lato Temmin
alin aao c  ceri
(19)
O apcx apex taeps
1b= + Abd. + a d
aipc.. +adp. +ad p
+rabis t
+abpe ... + 2abdpe.. +2a6dpf.
abpf
ac X + haef X +3a e X (+ a f3
+ ab pe tabpen taebps.
In qua aequationes ponatur ultimus
quadraticam deprimetur, sed aequatio subsidiaria, per quam
terminus aequalis nihilo, tunc aequatio 20 ad
3. apbX , agbd X ibo Xrap
ultimus terminus nihilo aequalis ponitur erit cubica, si scilicet ejus ope quaevatur
mrudia arbitrariarum, nempe f vel 4. Sutius autem erit quaeri f, et fier:
 utradix cubica inde extrahi possit exprimibilitur, seu Geometrice. Ac primum si bimi
penultimus cubicae datae seu aequations
ntantum superest ut efficiamus ut