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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 11r, page id 00068197:0021
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x compendio a S erit XX +. ab = aa suN F. ab X 
n Xx + ab = 9a _ S + aC 74. et
a N + adi H
et XX +ab, XX raC R.
si esset at a2 = - 5Z foret 5 Z rationalis
et ∞t (, OOVV, 40 OD+60DF, +46 Lor.t
de e si ess fura  vel  etiam sC+
si f4 - aabe,
Et mira retare plantum qu rahonalis. sed pam
ffXX + 2f9X + gg
sed si fiat 2a . f2, + bt = - f2, B-c
2
seu 25= - (b +c)h seu t Z  tC
productum eut ratinale aequandum quadrato
rationali, in quo tres C t, et 2
Post vania tentata pro quadratura ira
tionali conica ad rationatem reducenda, sed per
partes diversae rationalilatis seu ita ul quadratura
irrationalis reducatur ad duas singulatim rationdes
sed incommensurabiles inter se, hic modus
aforet ratio
nalis etiam Ns + 2+ firet rationales.
foret etim se
ad prodest
destuatur in eo COro,  et ponatur 2
nd hsses u mou uri
Quaeritur (dx (xx Fbb, XX FAC)
Fiat
et fiet
= aa qu (b+ cY - 4 aabc.
fL a(b + C) =  a (b +C seu ff- a (b + C)
noconicis ubi sunt negatiou  antaccattollere
opus. A i siligi vestien iptiue e0qe ductus in
aequatuqe quartae parti quadrati
a coefficiente ipsius C). Hoc videtur in potesta te
 n 4
seu i
si f+ ae + a(b+c) + aabc = 0
0B, et si simul 2 et h
ponantur constantes plurimum
contrehetur calculus, omnibus
variantibus a majore latere
redactis ad CDD. sed ita
quo polcumi posso aarba
t e 2 esse constantis, etiam d vel 
fiat constans) non posset pars ene
rationale prius habens solum C aequ
9899 quia
cum in hoc anus solum terminus altine
posteriori 3804+
assurgat non pote possuat in e
tolli duo temini supremi ut deprimatur
1
licot tolere ocnnintim
Si
Ier sermod tisui
45y
reducetur, le
et 8 s. .
b+ c)k
i malist
ad 24, et 2p voliti ad 
 an 4
et gu
42  a
CD+Z panetarias designari
xformulas ratiopales integras simplices secun
duim unam variantem, verb. gr. D= motar;a
5dD +a a 427
dnls rednbrtr 4
+2af7
+2t10
ab cD + abtih
XX + ab
+2a b_1O7
D + G +2G VOY
+f5O7 + aa 2 2 + 2 a f2 VC
XXF _ Aac eD + aCtt +2a6F, 1O)
X X + aC
CD + hZ +2G 16)
et preductum ex xx + ab in XX +aC, 
erit
scopulo
aaaistac h
F0B fab. 5BDC eCC 
a4 4) ac. L. trh
ffonicabis 05
C_CBM t Eaaff0∞44+44 X aa r lc 
aab FOCVF FabC Onttt aabct
(4 aa 5s quabe t hp a 4n.
1. 7 55() af2 (OD + 4sC D Jaabet r0
Eth
pff (3D)G ab2 BICD +   1 ab L aF2t YCY
Jaa +H
2haa tq S2achC
ex
EBF) La3
biquadrat. (se) D +F
Tepsetur an duins valinit prodncti in hoc producti ex
XX + ab, in XX tac valote per fractionem
expresso. Numerator  sit extrahibilis quadha
vice, quemadmodum denominator: et eam
in rem cideatur an identificari possit qadrato
a Latere aa 6 10 + aa 8  tdZ
a
8502+  2418 + 24405210)
irrationali Et videntur plures esse literqe quam es
S, b ut patet. Si nuba
Et timul nam X fieret constans
permissum nan (d, ,
ACo  (Coco +  V) = 4c YZZ  Co  Hton hctut Nec aubae t Hes
s alterntra ipsarum
ac
fk. (3P + aa 2. 2 = 24f210)
B.
i
iventificando partem rationalem rntionali, et itrationalem
(0+ l = Z C Z = Co + 4C3( +6 cocoH
Ergo  10 + (c0
177 -2 ci co4
l
Notundum hic perte
- min a m v +n
pro
et
et f=  (a b + aC) sed hoc non procedit in eamon
quanlittes
 Sed Glneral iter unica solum equatones
 constantem
10D+ a  Alnotus planetarias I
Notandum hic per non
XX 
Erit XX
constans et fret de Oy + nistans = quadrato 60
quod iidetur possibile. sunt enim  sufficientes
ABN
uttolatur f alba C) s + L aaqu (b+c)
arbitrarii
rgo ne
D
Alteratia ex ipsis,   videtur posse poni aequalis nihilo
verbi gratiatu. Quod si licet calculus redigetur p ad minus
quam mediatatem. Hoc posito sequitur exidentipibatione
irrationalium partium, aliquam exhis d,E
constante ad 2t, seu reduci ad  ged non evet esse
esse in ratione
alioqui el
vadratura rationalis simplicior, quam haberiposse aliunde consta
AOD deveret dividi per 2
Inempe
lea
du ad