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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 92r, page id 00068197:0183
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ciats
proponitur Y((X+ ab, XXFa) ax, = aydx formula summanda quadratura rationali
+L X: a = 1O+ SD, : SG, fat XX:aa = 0+D f210D: V. et proinde
Ax = 12dB: 36∞ - 10d8: 18 +18AD : sD - 1D1G: 183 : 28.d ponatur
valor ipsius y extrahibilis, re redacta ad bimam tantum in endem formula sub esdem vinculo
irrationalitatem, fiet et fiat Ay = aG + f16D,: 8, fietque t + D =t per
usa et te
L
etbr
fet gy =  at +bQF 2d 10D, aZ + bB + 2440D,: 44 = ad 4 + ACD + 2af2 1CD: YG
H
n Ah + bc Q8 + aetrZ + 4 aa 
a9
abc
t+
C +24 
NOD ~ aa 9+ fOD +2afe 10)
ut jam conci identificentur irrationates siet se = 2at, + eg. Etque ut etiam
identificentur rationales sut aat h + bc TL + act, 5B, ff = aassqu+ 0D, adeoque
ff, aatit + bc 84 + a et  = 4 atitu + 4a et q aec ZY + f OD. sit quaaf = ag
l
 qu
 sit, aegts fagH0D + aghZ+ auegqF + (aaee -bc f) B Y = 0 sit avec bst dh
(D. 1)
quaOD
Et puit 
ii a eq
+4
et + 9th - dts OD = 0 est autem D= u et DD-
24 at
bil
F aat
 et adextractionem ordinando ∞8 + eg et + eego
sat
seu Q+
2
Z- (eegg - 9aah9) Gt + 2hatt 0
att gaathL
Auath
e9+ A(eegu-taang) th + ahy stOD), 2at
HEF Reddamus quod in vinculo est, tale, ut varians quantitas in ec non manet, quod
duplia modo fieri potest, vel reddendo formulam sub vinculo extrahitotemel
re salva variabilitate, vel redient
am constantem, priorem modum
est velor
il
ota tentabimus explicetur D per t-O; fint B egh  rec fiet OD = Ot- 00, e
formula ex in qua variantes sunt avirulo liberandae est ((eega-anahus ht + Anqeti  
ic
E et ponendo eeAaat = aaque sit a
Eah
d Ach +  tO - 4uH00)- egF
ill aaq
 id quod in vincule est identifietur hunc Gh + 2mO + mm BC
seu
Eatin
1
2= 1
a
aaque
et s
= mn = = 4h
pa
 na A aaque
aaque
ratL
et fiet 2n= aaH
a rpa
fiet ff = - 1, sen Hf - -
eaque
et fro ah, et anqe ponendo valoies siet lanee ff- bc f - -59+ 4a tr = (expli-
antetenalic E Cundo g eth) , Caec taa  ace ff + Aaana ed- 4aab 55 fuo f +aa = 0
fieti Aaa = H = 0=9
e seu H = aa ex : bc = gaa et ee = 4bc ude  b -c =0 quod non ficet
5
Ergo a non licet reddere quod sub vinculo est reddere extrahibile
salve vrationalitate variabili, sed oportebit reddere aequale constanti
Nempe in aaqttu + anfftO anffOd sit C = , ot +na, : 00
et fit 0000gagtqe + 4. 00. 1)h titr. + 400. uHat - 4. 10 00 t Zh. go uisff at
 at tollatur titu fiet
60300 aaque + 4. 00 10 f - 4 10. hfs = 0
= 4. V1. 1 hffaa
t ut tollatur ati firt 4.00. 1hH = 8. 10. H hff = 0. seu 10 = 00 +2
i
ex aequatione tollente ttu fiet oera sis seH
seu
ago at, seu s  = aa   eah
E+ 2HaY gh rat
f. gae9-agaut,: gaa ec -8bcf
saceg dum ah= (ee Aua) - eett (- qua ee + bc f = H. Gu (b- c)
se abe et sied = ff qu (b- c). Dhaee - bcff) et 
 et 78bcf-8 ade =  aa qu (b =C) adebque
L (a (bC) + 8aa qu (bfC): DbC
00. 00 aaqe +2. 00. 00 ffh - 00. 00 ffh seu aaq. + ffh = 0 seu
a) it +Hah = 0 seu a eeg- quh + faeh = 0 s
eg-
seu
agt 20 seumee at, seu aaee = aaee- beff
et fieret, bcff =0. quod non licet. Ergo nec haec via succedit
esset 0D = ht
6O + (2 -1) OD+
Haequidemm succedunt
2
seu r0D =0O+D) +20γ(i vereF
Ergiro) = dela-a trr = 4BD sin O 2 (72 + ((or -41)) 
a
scorta tnt 5: d constant et G: B, onstai
bs 2 qpot XC
en
10c
+
et
C
a
E
e i
10 ++
EEx 
i
u
e
te
e
AC
6
er
v