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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 21r, page id 00068220:0041
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sit X + b X + CXX + dx + e aequ.0 Resolvatur in duas partes, nempe
EA X + m X + n XX + p X + 9 aequX +YX + Sx + t xx + VX + y
quinque
quarum partium utraque aequetur factis ex quluor radicibus rationalibus
prior ipsi
X +1 X + 1. 2 X3 4 12. 3 XX + 1. 2. 3. 4. X 41. 2. 3, 4,5
1iq
s
q
dis
219
1.215
3. 4
305
1. 4. 5
2. 3. 4
s
2. 4. 5
43
12.3.5
1.3. 4. 5
2. 3. 4.
Ret 1 - 3 aequ
4. 2. 3. 4
2. 3. 5
ere
F. 7. 8. 9
6. 7. 8. 10
posteror iasi
+ 6 X er.
BLsit aequa b fat. 2 5 6.78 aequ C
.
negaieu
aequ. a f1. 2 3. 4. F =  t. 47. 10, qu.
Hatum 5 qu aequationum ope inveniendae.
incognitae derem. Ergo quinque possunt assum peot
ita ut reliquae fiant rationales
Incipiamus in simplicioribus:
ExX + Px + 9 aequ. ol e fiat: + 8 2 - 6-8-8 aequB
in lieris
ec denique 2. 3. 4 =  6. 7. 8. aequ. c
a + b+C l -m - n aequ R
fier  a + 1 (aa + P Ca + 9 aequ. 0.
+ lemin
2.342.443
ab+ at bc Im ln- mn aequ . abex lmm aequ G.
25
almalurma + lmn
1t
resolvere in rationablius
Opus est tantum aequationes 1. 2. 3.
a t ago a+ tet  PiE scribantur 2a +3l +  4b +5M + 6C + 7n aequ 1
id est aequare a +b +c= l. m X cum fag +si et ab ta bC Imuta mn cmfgatBAgh.
quaenamus a litaequa f bem aequg. calaego
et fgt cum abenlua cum fgh
a + +ab aequ ee 42el 4+ l 4 2lm
Se
Eit ftgahaequ. c.
a aeqd C - b - c - l - m -n igo ex aequ. 2 fier cb - bb (bc bl - b m - bn Ccabence -cl - cn  bd
(∞)
+rab p +rim
ln - In -mn aequ. p. et ex aequ. 3. fit: ebc - bbc - b cc - bcl. -bem -ben. - Imn aequ. 9.
aequ. Smultiplicetur per c. Ope aequ.  et 6. habentur duo valores ipsius l.
aequando prodibit aequatio in qua omnes literae altius assurgent
a,l. bum + C- n aequ, C. 2a l + 3b 3m + gc - qn aequ. f  denique 54-5 l +6b -6m +7c - 7 1
3d
si quid judico optune fiet: b aequ 2a +3b + 4c, et maego 5a +6b +7C.
ocaque
et naego ea +9b+C et erit: a -3a -5a - 8a +b - 3b- 6b- 9b +C 2ohGbo
et ln erit: 25 ap 1 36bb+47cC+ 26135 ab +(7 194 ac + 374 45 bc. Qui calculus tam probatiodem
daria mulliplicabine, quam nic sene numero rum in unu additorum han 25. 36. 47. quadratorum
quesficientes faciunt a. 11. coefficientes ipsius ab sunt 8. ipsius ac a ipsius bc 10.
In aego.  5B44 164V+ 310CC t 194b8 ab + 4e 179 C 5.10478 a6 +6. 16+ 79 bc
en
124 6, 7.9
equantitates
Ei
6iG- 78765
sid 5.7-)
aequ. b
22
L.