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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 215r, page id 00068196:0425
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depressive.
id agitur ut bXX+CX+ d, xte, reddatur spbiitr extrahibilis per explicatione
ipsius X, fiat ergo X = lyy + mnus + n,: ( y+p
fip a = bl s + 2blmmys + 2blnyy
+ b m.. + 2bmmny +
CCPX = Ca + CEmm. + CC n..
+ 2cc lp.. + 2cemmp.. + 2CCB p ..
+ celpp .. + cemmpp. + cer pp
= d. + 4d p.. +6d pp. + 4d p3.. + d pt
d
aqqus + 2a grry + 2agt yy
tart. trarrey + at
sit Y =0.  et sit n3 = ppY.
Et ex aeq 2)
Ex H Ilfil Exaeq. companato identificatrice i sit g = sbl + ccl + d: a p(t = pp rbWBCBa
Et ex aeq. 3, fit - mmip = 2ccl + 4d3:, 2bl + cC q unde (4bcc lD+ 8bd v + 2C2  cd) (ab celvusbdltumaud
Et ex aeq. 4 mmip = 2ccB + 4d3:, 2bv + cc) seu 4b 8bd L. v = 2c4 L- v = 0
seu firt bd - et l - B = 0. sed non licet facere 468 =c = 0. ergo fit l = v
superest aeg. 5. unde sit m: pp C + Eemm: p + 2bI +, cC l + 6d aequ + 2bll + rcl + 203
Ergo si F + ∞ + fiet bm: pp + rcemm: p + 4d =0 seu fiet
bb m : pp + 2CC b mm: p + C = c+ - 4 bd. seu b mm: p = e + cc B Sct - 4bd3 l
faccendo W0 =mmip et fit: Ecc l +4d3 :, 2bl + Cc. = c ccob - (ct -4bd: b -H
et fiet Eccl + 4d3 = 2blW + ccW fit l = ccW = 4d,: 2cc - 2bW ergo per valorem t
sit t= cc + 4d3 1y l = ceW - 4d:, 2sc - 4bd = v q- F: pp = Aurcl+ d: a
W seu - mm: p = cc: b - Sc- 4bd: b et
et fiet X
tam ceto -4d3=
et
2 Y1- 4bd3
sit
X=
cco- qd yy  - pV y +  ccl- +d
2 Set- 4b0
yyt 2py + pp
2YcF- 4683
pr
cSc abd - C + 4bccd NL pH e abd = sC
2b, c - 4bd3
(e Se abd - C + abccd) yy
C
1- 4bd
et pl 2b, ct- 4bd = - 2 ccp. + 2psC. 4ld
( - abd - Bcc) (1. 16d) py)
(C C - 1bd - c + 4bccd3) yy. + (C - 4b93 - CC) C - 4bd 2py + (C Set - 4b8 - C + 4bucd3) pp
2b, c - 4bd31 + p
vel compendio X = lyy = pa y + lpP, :, y + p, posito (= curv - 4d et W = cc - sc - 4bd
2 Sci a 4bd
ubi si esset =HyD 1, + Upp et IpW = ellp sin W = 2l, esset etiam x extrahbies, quod tamen hic
non licet licebi pou pro xte, ut fiat extrahibilis  poddibit +lgy - ploy + lpP: yp
+rep. + epp
ubi si fat -pco +rep,: lte = 2p sieiet rursus aliquid non est in potestate
quia evanescit p. Itaque hac methorto obtiaere non licet ut tres
formulae Cubicae radices una vice fiant extrahibiles obsine bitui tamen per
gradus  quod suficit
l = c -  c Sct - 4bd - 4bd Sc - 4bd - Cc -W
2b Set - 4bd
lyy +mmy+ n3
gy+ 2py + pp
= lppgus t mmppy n pp
+dp1) F2map. F 21 p.
Lly. Fmn. 7 13.
a gyyerrytt
Oyip
vis
s 2
e