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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 95v, page id 00068197:0190
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Liberiores erimus hoc modo: X = 1O + 1D,: 8. erta dx = = _+ 18: 10= 10: 185.
dx n- Loxredabit YD8 - 91 (D: 8) + 10Y - D B: 8
 2(5 - Q10: 1 7 + 91 (. D 9 13. 1 9. tE
Y8: 1D - VD: 1E, st
ita nunquam excedimusbi
miplum
 sit ego  K: a = (OF (D 3:) 8. fiet XX + ab, XX rac = 8 + 210D + Ab , 8 + 20DrcL, :
c
F
et X + aCKX + aabC; a a+ 0 +6∞D 400F
ab)
aequ.
qu (a9 +f107
aa8)
Tab G VoD tbiB + bc48
X
l
et
aaepe+
otine ut comparentur pumum irrationalia coincidentientur, fiet
E8
  = (8+C)C4 a (O+ D), : _b) quo valore substi tatio in
equatione rationalia identificante, habemus ad huc tres literas O, D, 
subi c ad se habetemr  et ita quantum apparet camplm ampliorem praestandi quaesitum
2
Et ix icado et per 100410D+ videbimus an ope le et  talli possint 60+ 3D, et OD
ila restabit solum. C +.. D +..  =0 seu vale quaesitum fritasse nec est apus ipso 11
ut ergotollamus CO + DD, et C habelimus aa cB +b aa OD + bC 4Y + etc = 4 ad  +   Ov + OD , etceru 1
(+41B abre  (Or) b) )
 aa qu (er1) + ZMl , 4 jusb NBrb  
ex + Baa (br Deustre
Etese
aaq te
etfer odan  o a(t)  1oobe   a. H et  600. 0u aa t 200  a (bre) 12 1onolc - e)  H
 aaqu bi) asbe queaque t)q)
 + abi Cs(o OrL 1O~)
od
( 00. 00a  ,00 aa
B
ergo fiet (00, 00 aa) 1 00. alb. c) 10 + 10 1obc (00. D0aa) et fiet 10 =- 00 a (b+9)ibc
et fiet se
d
aa C3 sint 1t V uqu (btC) 26) g FasorC   ((C31 1) 8 + 16a qu (B11) - 24070d.
fiet denique fiit abtra (OrD) + bes _ by2DC, 
- bc 5+
unde sin Q + h (C+ D) _
C
1f
=a (b+C)
99
4f
Laa)
et radie deb et ex seu Z+ h (9+D) = . Y (Chh - 4 l9) qu (915) - 49m OD)
C
+ H
fiet schtr Alg = d om om quod  sub vinculo ridicali est, potest
is
esse m 9 an qu (O+D) = 4n OD, ita enim fit O - D, Van Ent ego
agm (= aan) Lahh- 4 lg et explicando aqu-aagu (bu c)- 4bc A
et ahh = 16a4  qu (b+C),  4,  (+ e H 4a + f jage
a l= 4 a3 - at, f et 9 = aqu (H) ; e
et 4alq = 4a qu (b1C) - 16abc ff = a Y u(b+C) + 4 af bc : 454
nost
Aqustrc  be
et fiet aagusbec - a. H bc 1st raa - a qu (bre)  qu (2aa = )  i an vi va   )
AaA
na gu (O+) +2aaBD +bC Q8 + a (b+C, C1D) 8, 4f = a 4 8  ( (C)
fiet 88 + 8a (b +C, O+ D) Y + (16d - aaas) qu (3 + L A (H- 2a a) DX
 O
= - gats..
+4C
taa
2a (ea. ) (b+ cser D) + YAaa qu(an ff, boc, 3) - (aaqus btc) - +C)a
aaqu (btC) - afbc
ua
ubi quod sub vinculo radicali invenitur, compendio sic enuntiabimus: Y(al =  ma) u (O.D): = mI OY)
seu b
aa qub+c)- 4fbc
positis  = aaqu (b+C) - abets, et al = gaa qu Cna -H, bnc,  D n = 2ita (Bda 2H) p= HX
vel abetesse A Daa b debet esse mp = aaq et al-mn = aq seu  Aal am t mo seu
in 16a4 qu (3aa -ff b+ C) - B Laasna-) (aa qu lb 19)- ib. H)  4 sis ( aq Ibe
sa Sbi) e    ga (aa qu bre - 4+ beff) -. Z 4 ff (B araa) (a ( mibre)  qu H)
unde fiet vel aa qu (b+C)- 4bCf = 0 vel - 8a = 4 f 8aaH. seu 2y5~ na H()
vel sif = a f = a(b+C): 2bC, sed uta destorveretur QZ, sed hoc videtur non licere,
fiat f5- 2aa +0 evanescet OD,  evanescet etiam. _ simplex, et siet
18
=
2
34 qu (6+D)
6. (8pabe a abb raabe
o
(Or
ancc
abata
Aberaa= aaqu (b+ C) (bc- qu 3bb- CR
si b et C sunt rinsem figutres est possibilis, sia minus veritur ad inapitaras, sod tunc faciemn
B et D ettam imuninalias
fsl) +2a5116)