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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 115v, page id 00068201:0230
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 116r); this page is its left half.
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C  bX, ac
 + d X +ac
X4 + bN LacX
+ d... + db.. +dac X
tac.. +aebo eaeac ah. adeoque.
X + fN 9X rahX xad
et fiei novissima aequatio:
ag - df +d
agdtis ute a fo
X H =x x n +_Y,
+ v f
v f f
f. e
H erga haec ex priore suppositione eunt
falsce q quatior falsae.
Y +0X  - X +0 X + X + Y
f 4. falsa, unavera.
X -0x = X - 0 X + x +
 v f f. v. f  nes false due verae
X +0 X  = X7 - 0 X + X + r.
f V f v f
X - 0 X  - X + 0 X + X +Y
tes false dureverae
tresfalse dus vers
Hud sequatur ejusmodi aequationem ds habere
radices reales falsas; unam realem veram, et
unam imaginariam. Omnes enim positiones n
consint dicunt tres  falsas, et unam veram,
etsi aliquae ad falsus aliquae ad veras unicam
unam adjiciunt.
X - ap X raer  ar
 X  - rap X + + ap N - ar Bo
Tolteado terminum secundum fier: Scribatur ejus loco
2 X = 24Z + Ap Z a a po ponmus Z., s +P
Co (+n co to +
 p at . Apco ip, 
lubg at  P A 72B
p 0 ap, 2t
Xe sed na + 10 Ana
XF) na 3+D = nat + 31) nt a + + na
sive Xs na
+3ans S0na +sna
xnsona + se tna.
X e na + na   n a +3 nassiae
hiic XH na  + han  X.
Xes er
+ sq X
sit jam aequatio dati:
conferendo erit een ces curmmmis. n p T q. quem
valorem secunda aequationi inserendo, fiet:
aa ,  qu  Y, nir g+ .
N4 +3 _ qarf sr a.
sive N 9ra s +
122 fugae) orra ria
quod est redire ad scipianis Ferrti est
pigno, atque ita
Mutenda nonnihil scena est:
ax cVona + d sona. Ergo
ax ena + d’na +3edna vona + 3Cd Sina
jam videamus an 3 cdna (3) na + 3cdna 1B) na f
exare dividi posit per Ec 1 na  4 d na lcanca
fer. 3ea 3Cdna 10 a 4 3cdna +3cdnao
8 c N9oa
 n a B
procedit ergo divisio feliciter, et fita x  Ca + 3cdnaX
ex aruns  colur. ).  + aX aXH N ra + Naque X
fiet Cne 1. N9. uq Ng
quos valores inserendo in aequa
oedtionem ex purorum terminorum
collatione
X APX - ar. hioc X  p X apX  ar
snibam XZ -p X trap - ar 0
C0 +, eZ +3 Z+
2 tat fat talga
+rapYZ Acap La
+ rapr 20 t 
1ga += p
nerpe da + 4 a gea o ra p coe q  3d aga
sive grac d se  Cq s + dga, sive:
Hac ergo mutilia sunto neglecta si fiet e Dra
si possuissemus - Cd  N, fuiesset n+ - 4. et n  4
et fuiset aequatio. C39a + d a  Cdera tcd
v ponamus qu p 1. qu. erit 47 ta, quod semper
est qantiodo egndiva. Sed pissumus etim facere semper
in aequatio   quae est. aequatio inter tres cubos
Unum a c. alterum a d,  tercium a cd Bra
ponc iin se . e S3ra Sed e  c - d
fiet : C - d’ 2  - 30d + 3d - d,
sed haec imutilia.
CB ora + 81 Y a- n4a et nH 3
sive ne 
gra = SBrra-iqa et  virae 8ra 2qu
gra + Spira = 12g a
sat axe se =, oa Y su  +4 103 1  ia forrariuria
quae consentunt Huddeniaris.
graduum ad hanc quae duos tantum habet teruinos incognitae X. Y AY
quadcando reducituur ad altioam nium terminoram ergo per regossium
exinmpli causa: X6 - 2a(XY a p St X
Xe X + r. dant: X  4X + 2gY X +V
jam xCp, qse X + X 29Y A X + Y5
cu: X B B X + AC X + d. Ergo
soita confrendo r N  d. coanescunt mibitrariae
+g s, Si radq 2d ga ut aute
gra da , 4 +3d qa
207 a  n arpN atr. X 3 obtineri potest in data aequationa  negati i 4
Xp 
ni adis nddilur
ni nvatioaem paudami
be) f - d. ex secundis.
ac ag - df +d- ae extertiis
BaaB. Erga ex quarti
dag = df +d- dac, + aef- aed 
aets à h.   dag 43 f.d
adeoque res non procedet. Nota omnis aequatio quaa omnium
duorum terminorae
culius aequationis cundus terminus tulli potest: sed hunc credo tertius fici affirmation