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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 92v, page id 00068197:0184
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unt
Aranitur exxetabus Ax+aC) dX ay dx, formula summa riondita rtioali
siat X: a = sO + D,: VZ, jam dsC = d0: 210. et similiter in d SD et a VE
erit t lx: a = 18 +C: 10 - 10 de: H +BaD: s-(Dd8 14 :28
Sit y = aQ + f+DP: Q, patet ydx non continere rat irationalem trimam, et proinde
pendere a quadratura rationalis, si duo ipsiusy valores sidentificentur. Quod ita tentubimus
Ryy = x tab, 22 tac - a 8 + b8 + 2a 1OD, ad + cQ + 2arD a an 82 + AOD + 2afG 1OD
te
aa
per compendium sit 0+8 =k. et fiet
autiq +ab  + bcB8 + iaatu 10D + 4au BD) = aa ZQ + HOD + 2af4 (OD
AC
 +2ab28. . compradio sit Aaa -H = ag et b+c =C
ut jam identiticentur irrationales, erit 4aatue + 2a Z = 2at Q seu 58 =2at + e Z
nicd 
Et ut identificentur rationales, substituto valore ipsius f) fiet
a
2
aahh + aetr Z +bc 8 + ag0D, ff = 4 ag H99=) 2a +4aetr Q  ee
5E
4
seu aephh + aaegte + (aa e bSf) ZY  agfOD = o rt, agee = bs Hsit F a h
th. ahg D-t.
88 + eg. t8 + ees th = ee gghit - gatraoh h + 4htOHCD
C
4aatitr
Itaque ut procedat extractio utrobique, faciamus eegqe- 4agh = -ontif seu reg9
fiet
X
an T Anaph
seu eeg t 4aah 3: h et seu et ontrando sit h fict et seu ueque  ds
seu eeaque. 4aeh --aliss,  et ulcando pet 4
seu et seu eeg a ceu- taah=- hH, sen eeq = hag  et ee = ah.
et seu aa ee = ah = anee bcff, seduta fint baff = o, quod est absurdum,
Ergo non licet hoc modo procurare extrahibilitatem ipsius numeratoris in perte latere
dextro, ut C) et D nantant simil vgiantes. Auligo Itaque opus crit ut faciamus
D constantem, A et pro D substituamus est erit B = C+ l et OD = 10
et tZ = 00 + 2l0 + I,  habemus (ee99- 4 aahus) (9O + 2lO +U) + ahg fflC
sed nec hoc prodest. An explicamus 3). per  10O + na, erit O+ D = (00 +10) O F1a =h
itaque ex seegu -gaahqs t + at gff0D fict (elug- taahis) (20 00 + 2. 70. na O + i1 a) tahgffioetru
ubi ut tillutur DC fiet ubi ut procuretum ormphibititur, sul et ordingudo
compendio M OC Y CAnaC+ paa, seu
d- 2. 20.  +ghg +  4 1ihia ff.) a0)
egai
(+ (regus gaahus) ita
jam mn OD + MnaC +mpaa, ut sit extrahibide debet esse um = 2tm M D tal
mn= 2m imp, et n = 2simp, seu nn = +m
iid
seu gu quigg qu (20e59 20. 4 dah + 2hff)= 
n
20 C99-, 20 a eegt -4, 20 Cgh ff
+20. 66a B) = (5). 20. qui H t ( t f4
es
8
mmoaet orpaa
+2mimp a0
roeeg-490 aah + 4. 1olff eegu auh
(20g420 ahec  1ol trus H
=E eegauti (+ 4. 20 ahhs (.  acclilit
e
fiet 2. 1 ee Ha
2 2020) g = 6. 26 a h +2 (4. 20 - 10) aasph; + 2hf
seu (2. 10 + 20 eB 4aa- ee +4) = C,  6. 20 a 2 (420- 10) ff. + 252) (a bct f)
loupendios elgg. qaagh = acgq, siit tiz + A fff C3G - AhtsOC) fiat  - 8+ 31a,
el
Kesser 21+20200
firt 9030. O0 + 230. 31 ap + 31. Haa + 4 l.B
aa
aaque
eaaque
00. 3000 + 4hH. ao. 3t a0  + hf6B
aaque
fiat 22 + AbH RD. 30aq F 4hHf. 00. 30 = Ahff0d
=O et R. 30. 31 aa9 + 4hff. 00. 31
fit 30 =. 2. 00hf: aaque et fit 0ff8100. 200R ag- 65. 00 aaq f. aff = 3aa9
seu ahs= 30q seu nae- bc54
l day= ac caih fraee + pe hcet
tet 4aa ee= 12 2a bc = bc B
Chragauus tercabets