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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 65r, page id 00068049:0129
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fomula V + CC VV + f4 cit
fiet 
a et
ee
ec
aequandos quadrato quod sit a vv + CV + fF +VC
2)a
geDHFD + 2CV3(F CBVD + 2HCo V (+ fD. et Doisi i et sublatis
se
de
+2C p2AVB 42fe v
t2eco 1s5+C + e. fiit P( e= f12)
+
+
4 2 ec vV
+ cocovv
tollendis ac divisis omnibus per 2072c0
fet vv + 
BCo trecot2V + f20
2Cd+2V
ccote
Tantum ergo opus est efficere nt cocotrecoerss sit divisibilus pe
Hoc enim obtento radix quadratica extrahenda erit a formula quam non ingreditur nis altior
gradus ipsius ed quam ocd. sed video nihil obtineri, quia ut sucecedit divisio oportet esse
f4=
e quo posito formula 1. non opus habet aequali quadrato, sed ei jum est aequata. Quod
si ergo relinquamus aequaliores, 3 qualis est, fiet v ocotr futreo+
e coconeo 5+ Sicotaecut affcoco
qecoco escoet ous
L decos. ge
4cd+ge
ay S,d imusyt  =O sit
e
co -3
o
bffccto
a2e0
ec 
ces
1bees
v-
23
(coraecoriscto
+
4c0 +40
que essot)
Sed extractionem ideo non obtinomus
yt =  ex + f. et dy = edx: 2 (ex+  et fiet
 M eX +mm D: extff. Superest jam tentari alterutrum, pro depressiono
O e (x SeCXX + 2eHX + +4
+n4
pro extrahibilitate Numeratoris debet fieri
C
utrum scilicet numerator sit possit reddi extrahibilis, an
aut si mavis, divisibilis per nominatorem, explicatione
arbitrariarum  et F
4eC. f+mmff+ n= (2) reff+mme, Nam si _ a + b() = aa + 2 ab + bb etga a bb = (2) 2ab
Ergo aeCf + Ammeess + antec 4 eef+ ammeess + mmee. sed ita fit nm ann
Et evanescunt omnes arbitrariae, adeoque nabura sese opponit successui nec succedit quaesitum
tte
nisi in certo datorum casu. Qui intercta notandus time mus
litatem numeratoris per nominatorem 
sed ita ut divisio succedat, deberet fieri
n = 0. a contra Hypothesin. itaque sese
iterum opponit natura
=WYXX
LVC
ecXX + res X + 
Si faciamus yy  XX+I3,: x + 21 fat (27: 8
mne
+s
doiit
ns
Cx + B
centemus jam divisibi
Zex +mm
syy= Lmmo 2oi A X + 13
R 20X + 213. 11. 4V
4(8
aneemnm se pr
sit  +mmyus +n=DD + nm DO +n
+mn13. 2
2
a
se 122XX + 2, 12. 13X + 132 + nn 1 2XX + nm 12. 21X + nim 13∞Y (F KCX + 2n 2I X + n 21,: I sexr
2 (113
et Aydy = 2dD - Dd8: F, = d CX (12. 20X)  +12. 21 (= 12. 20X) = 13. 208: 20X +2O. 2IX +21
(12)
e)
a
12. 21= 13.20
Et denique fiet C = s= dx L
p o
2oX +2I
 2OX +21
12X +B
(12 XX F2. 12. 13X8+ 132
mXX + mm. 12B, X + nm. 13.2)
AnEo XX +mm. 1Z. 1OX + n. 212
+24 20.2 X
Hic exitus reperiretur, si formula 12XX etc. vinculo radiciali inclusa reddi posset extrahibilis,
vel divisibilis per (20F 12X+ 13. pro extrahibilitate procuranda e debet es
4. 12+ m. 12. 20 + nt. 20. 13+mm 132) + n 21
4 le
(21, 2. 12. 13 + mm12. 21 + mm. 13. 28 + 2n. 20. 21 MH
t
4. (2. 13)+ (4. 12 mn 13. 2D + 4. 12 nF 21 + g m. 12. 20. 133)n. 12. 20. mo 13. 2144m. 12. 20. n217 an 2013897 20 n 13 2000n
2
e
20 +4n
d
202157 8 12. 13.20. 27  2m 12. 21. 13. 2044. 12.Bmm. 12. 2+ (4. 12. 13um 1320)
+4 n 20. 21 mmiz. 2D 4 4 nt 2021 mm 13.20) Et destructis destruendis, atque ordinalis secundum 21, 13, fit
A+MF. 207. 13. 13 + M+ 122, 21. 21.
4n 20..
=ap
+ (D.  + 8 nJ. 12. 20. 13, 21
= 2H4. 12, 20. 13. 21
=0 quae aequatio dividi potest
per m- 4n que 6
mirum est, cum ita datae plane evanescant et fit 20. 13 +12. 21 - 2. 20. 12. 13.21 28
(11
et fit 20. 13= 12. 2). Sed ita foret yi = 20. 13X + 21. 13,:, 20. 20X + 20. 21
et res siledit sed praeter intentur
absurdum evanescit enim indeterminata X, et fieret, yuQ  13.2 e ad huc unum brevi
ita et de divisibilitate formulae 12XX ete per 12X +. 13 obtinenda male ominor
ut A in formula 12XK et dectruaatur duo temigi primi, et fit 124 nd 12.20+ n 2020 et 11 ∞0 sci et 20
et
3. 13. + nm 20
suarado pro rata fil. 12 ae et 1t aA et 2 . 13 
ue rornr
nm 20+ 26Y m An  (+ mm 20
2130- mZ0 + haom n  47
16fftoto 3 2fl0- 1618