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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 198r, page id 00068201:0395
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23
25
sit Aequatio X = q= p X ea exlta utrobique surdesolidata dabit
15 10
18 +3 - 109 X0
10
2
. es 1) 8.
H Aequationis 1. radices  sunt E, , , co, ergo aequationis 2 radices erunt
25, 8, X, V, c05. quas  vocemus f, g. hil, m. Eritae 5 = 54 et h fg = 109
perp divisas
et  5dh = 10 g et h f9hl = 540 pro. sunt erg, G. t quantitus ratacalis porto quod in
Ponamus jam X, radicem aequationis 1 constare ex quatuor radicibus gunde soludis
a seu esse X = a + b + C+d, quarum partium qu’et ponamus quod in X rationale est
et ponamus ex earum combinatione generali non prodire rationale, nisi cum surdesolidantur
hanm partium.
Hinc sequitur quod in X rationale est, non reperiri nisi in ipsis a +b + C + d, et
similiter quod in X rationale est non pro reperiri nisi in ipsis a et aeV, et quod in
x rationale est non reperi nisi a et ao b, et abc. - denique quod in X ratio-
nale est non reperi nisi in a 4, 
1010 a bC, a
Quod autem in X rationale est, debet sesse quinea pars ejus quod in omnilm hader
qumoset att qut porostenq quamlidet resehietijesse quinda pars ejos quod in ommilem haor
scndesolidis simul sumtis rationale estr, seu in 3. +8 +  + 4 co, quoniam quoad partem
rationalem radices diversae ejusdem aequationis non differunt inter se ergo cum rationale
in 25 aequetur rationali in G, et ita porro, sequitur rationale in Z, adeoque et in X
a simul
esse quialam partem rationalis in +9 +G  C H co, id est valoris torum quia
omnes simul componunt quantitatem rationalem ergo cum valor horum simul sit 59
iguum rationale in X5 erit 95, sed   id aequatur rationali in ae seu ipsi
reperiri nisi in _ iptonali ipsius d
aquatur ipsi a = 9 sed totum at st rahonale. Ergo ratib nale in X (seu 99 aequati ipsi a
.Nam quod in s rationale est suppono not
Poro 15.5 = 104, seu 35 - 34. etix  _  19 461. = 5. +2239
110
am
et fint 2590 = 31 + 2. 1090 seu 20 = 25 244 o ergo rabionale
10
 est. 54 25 q. In valore autem ipsius Xo habetur aF. ab. proter
alias formas quas negligimus, quia nulla pars rationalis , et habemus quid cuique
X
in
praefigatur invenie possumus fiet _x = a +.... etc + 10. 10. 1. 10. 2. 10. 3.10-4 a b + et
10
1. 2. 3.4.3
ergo q= 4 + 10. 10- t etasrursus quia a= g sit a  + 2 a b = qt
 5
c
10, 10. 9 ad st  a’b5 =
Ergo rationale in LX est a + 1. 2 ad5
C
quia jam habemus a = 4, fiet ( a +2a b = q seu a = q- 2
0
Ergo fiet q. 2ab + 10.q. adsii a
25 8365
E=
5
1. 2. ad 5
3. = Cor 1338 + 33388 .
Vi.) a..
1..N
e. Ergo fiet 315 - 12595 - 359. 1095 + 3. 14  5q = 
a + β a V + V abc Ergo hoc, =
10
10
= q Ergo ab = 0. Ergo a = 4
1c
10q. sed  85 = 5 q. rarjus 3
= (315
25
Ergo rationale in X est q5.
1
Rursus rationale, in X
est
95. ubi β et V haberi possunt, ut infra
10
jam a = q. Ergo  cubando ulrobius aje a = P1 a f - da. a b + 3 abc
sed aeV5 = 0 et a = q’ Ergo a = 9 + 34b5 superest ut inveniamus ab
a’_eu B) a = a = 3 abC = a + 3a b + 6 a jam a. Eyo
hoc loco ubi ab=ofit ao b5 = - 3 abe Ergofit q a Ergo sit
2
a3 ab 95 = 4+ 3a bc  - 3β abC +V ab5. Ergo abc -
vel 3- 3(3 +) =0
et a =a Ou a=
sit, modo
conponaunt
tommula
tatibunt