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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 299v, page id 00068194:0598
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pag. 1.
te
(imo) bXX+ cCX + d3, xte reddutui depressive extrahibilis per expliationem ipsiu X.
Fiat ergo () X = Lgy + mimus + n3 : yap2. t Explicetur bxx + ccX+ d ut fcat
extrahibilis  Ergo a _Fp, bxx + Cx +d, erit extabi  fiat extrahibilis
fiet
bp= Cbly + Eblmmus + ablryy
+BM.. + 2bmmry + bn
Ccip. X sel l.. t ec mm. + cc. n:
+2ec lp +2cc Bmp. 4 2cc Wp.
+ccl pp. . + cemmppo + p
dyap= d. +4dp. +6d pp.. +4d p3. + d pt
at pet . . . (uo  tid s(, 2 (tos  Cids
Agg X + 2ag gy X; + at
quae formula
aequetur quadrato
a quutrry+t
Ilgymmus+n
ducto in a. quanqu vel
ubi tamen compendii
causa poni potest, Y =0
Habemus quinque identificatrices, per quas E; m, n,  P, quantum opus potemnt
inveniri. Faciamus n = ppV et (7mo) nm = Wp.
Ex 1. fi et (Bvo)q = Tabll + accl + ad.: a et ex aqu2 per 6 sintu f- p sabvotacevt ad: a
Ex 3. fit (0mo) 2bW + ce10 + 2cc L + 4d3 = 0 seusum) W = - 2cc l - 4d3, :, 2bl + ec
Ex 4 fit (nmo) QuW +ec N + 2CCV + 4d = 9, seu (1340) WV = - 2cc v - 4d3, :, 2b0 + cc
iti
quos duos ipsius W valores aequando, fiet. Cel + 2d, 2bv + ec = ccv + 28, ib. l+ ec
vel (41o) L, (+ 2ccd)4 2bcc lv) + 2ldv = cv2ad 2bc lv) + 2bd l,
seu (16to) Ct - 2bd, l- v = 8, et quia e  b, c, d sunt datae, ideo
subitituendo lpro 
fiet l - v = 0 seu(17md) l = v
Restat aequatio Sta, secundam quam fiet 
18V0) 2bH + bwW + cel + 2cW + cel +6d = + bl 4 ccl + . ubi si faciamus
(19no) + ∞ + fiet rom) brous + 2ccW +4d = 0 bbro1o + 2bcW0 + ct = c - 4bd
seu (2no) W LC 4b0 DC,: b quem volorem aquando vulori aeq. 1. fiet
2bcct + 4b33 = + i rbael +4d = Eblu a aro, eeu l-. un tbd3 ala
burr- e D E aeq. U est (22do) 2blus F ccW = - 2cel = 4d sen   = - cc W - 4d: 211o +2cc
cer.. +C - 4db. seu per ax fila = - cc W - 48, : 2C+ - 4 bd sin per 11 fit (28t.) (= cc  et 4 bd  seu
2bs.
eb 2brA abd3
fietaot = - + rcc + sC- abd 1: 2b Ergo sigmo) fieret l (B =)  W
ujo x-
WV y- rtop + ropp
2 yt
pae
seu  (igno), X = F2tfo
+p
Ergoserros
Ergo. (187) e Fer op2. per 6, 1, 27 fiat a 1 8r0) x = i W0 9y + W0 p 3. + L ppro
unde demique fiet 1X = , W yy + 2W p yfepp seu denque s
se
est contra desiderata, fieret enim x constans, quod non licet
R edeamus ergo ad aequ. 18, et sit (19no) + ∞ = et e q. 1s fiet
(20mo) 4bH + b101 + 4 al 4 2cc W + 8d seu bbtoW + 2ccbW + C =c = bH- 4bcel = 31d3
seu (21 mo) W = ct - 4bb = 4bcel - 8bd - cc,: b qui  u exv. 11. est; fit
(22do) set -4 bbll - 4bcl - 8bd = (+ 2b1cd) + c+ = 2bc. D - 4d3:, xbl + cc et quadrando atrobius
toltendoque  fractionem, hel (C ba 4bc- 9bC d+ alb C16b1 - 16b cel -- Bd U (+4bc D 16b a B
= 161b E I - 32 bbcc d3l = (C) 8bcd) + 16b6d seu unde
3t
fiet
241) B 1 + 2cc 13 + H E H + 2 b cc d L + d6 = 0 et extutando fu (6) bl+ ul + d3 = 0
et a +2cc 8. 17d)
+2b
adeoque bbIl + cbl A+  C = + C (03. seu  = C -9bd - cc
Ego (quod mium) pervenitur ad eundem valorem ipsius, l qui supra seu fit l-u
quod fieri non debet, itaque huic calculo sese opponit rerum natura
Curiosum et notabilet pit abll + Ecel + bloWo+ necto +6d = + 2bll + rccl + 2d3, faeri
et W - 2ccl - 4d3:, ibl +cc. fieri El = W = 5- 4bd = ce : b; sive ponames + esse +
sive 4 esse =
bll +. ee l +d quadeti fit 2.
bb ( F2bccB+ 2B
gy + 2p y + ps
lis + mmy t rgy
+2lpa t, Hp. + rp)
+ lpsout amfese