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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 115r, page id 00068195:0229
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bigomin sgacte iprationalibus chibalende popemodu mellis videri s hartus ad aquades edeatur posse nosi stamen hem ed
e ses arb= a ea ib + e eta b ut es eve al2 ( + ee t er e. 3 a 6 etc
siter  fit  a sit a = 1 et B - L. fiet
e  i b = 1+ + b  t ( B13. ( - 13. 5 f 1316.7
sit.
2,2
1. 2.3. 45, 3
123, 2  L.1.213431
Sit a = 1 et 6= 3i fa vel 3, et
2.3
BS ero
1ab. = 1+ 2 b - B2 1 2 = 82 5 13 92 58 17, a25. 21 = b
1
1.237
I2. 3. 1.55.
123, 5= 12 345 3
1.213, 4
1.2.21, 
 b’en
applicemus ad rudices ex binomiis extrahendas et quidem ad 3fii gradus aequationes
ubi intercurmat imaginaviae quia tunc communis extractio non succedit.
 sit aequatio cubica _. _ pro producta mcultiplicando ex + bX + ec per x - b., et fiat.
X X +CeX = b cC =0 generaliter  X + ppX + q = 0 siet _   Y 
fiei X = L. +  , + 4 + Y.  - tib, 1 g
q ( ) - 9(. ) + 3pp X L ( = - 1reX 1 1p A + 9
t b+ habund
seu X = 3 beC + ct ) acto - (. bbe + istae - s u 3 toc
Sed praestati compendii causa rem, traducero ad numeras
Mulliplicentur invicem X. 1, rA, p et (et X -  3 - 1, X~ 2, X+ 
X + - 7X + 6 = 0 et X = - 3 + Y . 323F9 + 2 - 3 = V. 3B 19
seu X. 1.3 4 + es. 3 + - 3 - 19 f.3 se n- 1  91 20 62 4.62 19 30
seu X = 8 L Y. 54 + 30 f. 3 + 3 - 54 - 303
Vaeratur radix cubica ex L64 + 30F3. vel si matumue
faciamus X . , Y
seu ex a + b
et qu at b =. saa +  b  2 
ergo radcum sit X = 3 Xatb +  Vanb fiet
Naa
4. 2. 5.
12; avaa
l
1. 259 aVaa 1di V7 daista, 12. h. +i 8t a fac
X= Va - = b  3aax - a - 2
a
+
Hic tanon ut serviat considerenus  seu. de seu 8 quam fabibo appropiaquent 1
2.48 b
Methodu ut ad isum sit aptior caoem condemus nempe
1
10, 11 14
squ 9 1 
2.5. 8. 10. 145
3i e
dd seu S n tinlem ad ibidem ad decimabes
accurate salis producamus, ejusque potentiam quaeramu sed Eaeci ora
fallor prolixcora
bac + Ytos aute = 18C. +. Y Le - se auo  1t =
3 cenbus = 8. = C bb+ 3ccF = b. Hini 4C - 12 C bb. + nccb = + b + 27 bbC AC + 15 cbl fueb
1.. 275
1
4. 27
H im + Van = n + 5m an + 3m san seu 2 M + Z nun + ou an + bntani 4 aN
an
X = b + sav + b - VaV seu X =   b + 3bav + 3bb  + av Lav +  3t oig ar tat
debet conferri lum
seu suba  quam villorem pnori comparando cum lig sonaitur
coquita habebitur  av, nam feb b + nbaB = bec seu bb + 12 a0 = c0
sed rursus debet esse 3bb a An aequari 1) 2 bbrav aB  ese =  sc b 2it
4. 27
quod an consentiat videndum pro cc substituto valore siu hmol minus contentu
X = L + 9. sav + b - ibie, N YP + b s quo + 1b. + gu lv = ) B  po a t og iso
videndum quae causa
debet p ao esse datar b t bjoav 6bl 48d . ond lefon   Capr artao  ep. aq sab
b2
Ce ap debet esse dinosalis per quantamab, u et facta sivisione fet D Bb  12gg aB = qua dapa imalliplicetur eC
Penficiter Ddap. aq F  6bb + b yuggav = 48 ap
hinc auferatur aq fiet 48a  - aq = 539aV sam habetur av,
uod
nullus
habebitur 9g, sed si non sumedit alius ipsius  diveser jurcendus est 
totur vera analus tam literalis quam numerita
no est in fent
3 Eser v Z
31.-83
a
n
t divi sieis pera