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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 327r, page id 00068196:0649
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Nemoratile est
V+b, v+C) posse reduci ad rrationalem
al + mo
pC): ant p
aat  pco). atis
et v+C = +aen + CpCo:, an +pcc. sit am + bp = 0 siet m - -  bp: a
si sit etiam al + en = 0 seu l = - cn: a, quibus valoribus l, et m
taal + amco
substitutis in Y, fiet: B - e-paen = +bpco, et fiet
ean + pee
sic a
V+b, v+c = V + ab 2
p
antpo
ita duplex irrationalis reducitur ad simplicem, an forte eodem
Sed quia ex alia
methodo re oritur spes hoc modo posse reduci quatrip
modo ut quadruplex ad triplicem?
 ergo eodem modo fvi undo o Vortab, vntac
posse et onicam
immandum fiet hoc ipso calculo tantum pro B substitu
endo PD et pro b et c substituendo ab, ac fiet inquam
al + mao
ab - ac S- anpco et quia vB = aa antpco
tamco seu-aa cn tabpa sed hinc. dv habe in se duplice
vetab, ertac = an tpco
an + pco 
ita redimus ad triplices irrationalitates
an+ pco
Aliter sit
rrationlem
Eltimeo
antped
triplices irrationalitates
pet v+b, v+C, V = ro cbcd p+ epto
t pro co substituamus coco. seu t quaeratur (de V, vtb, vtc, v
sed video sic rursis rediri ad
fiat v- al tam vco,: aan + pcoco, et fiet fiat m- - bp: aet
aatltuloco
sal +mcoco,d gaantapcoco
et l= - en: a, ut auto; fiet que
cos-p, aan + paro
b.c
de R, V +b, v+C, V = an +pcoco
do V, vib, v+C, V, teulemus sic explicare
V =
am co taq eoeo
aann + 2apCo + ppcoeo
taabum +rabup co + bpp c0co 7:, aannt zanp + ppeoco
V + b = au nna ra + a + a Meo + agod
in priore festmantur duo termini summi, in posteriore duo infi
compendio na a + B a ∞ t idoe in 20aa + 21 aco  22 
V + C = + aaenn + 2aenpco +C pp cvco)
fiet produotum 102042 4 10. 21 a) et + 10. 22 cc a d cd + 11. 22 a cd
+ 11. 20 43 c0 4 11. H1 aa cdco + 11. 22 ald
+ 12 20 aacoco F122A a co +12. 22C0
net mini duo infimi
sit 2029 10 =0 et 22 -0 et n = 0, et 24 = 0
ter  cnn: aa
in priore dessimantur termini duo summi, in posteriore,
= 2a b X p + 2 ac =0 sed hoc non Ecet
= - bpp: aa m = - 2pbnp. aa
a +  aall + 2al mco + inmavco
aF d  aann+ ranpco +ps cved
restat  am + 2a enp =0 seu
fiet v+ b = + aa+ 2aa lmeo + a mm eocd,: aann +ranpco + ppcoco
Ergo faciemus V quadratum seu V=
+aabun +rabup a  b ppcocc
LH XXXV, XIII 1 337
v+C = aI + zaalma + a mn coco: aann + 2anpa + pp coc 
Hic pates tollendo in uno summum in altero imum rediri ad triplicen irratioraltalem
 aaennt raenpco + C pp cv eo
unum ergo Ergo in uno tollamus duo summa, sit
ps- 1
amm+ bpp =0 filt, sna (p a tab sa
n: L-
porro 2aa l p -b: a) +rabup = 0
sit 2aalm Lhabup =c. fiet f4a L ib: a ) pF. 1 + fqbn  
fet v = -a1
seu 2aa p: a) tab f- 1 + 2ab ap = 0
seu alfs -1 +n Tab. seu l= - n Tab
l= an tab_: as-1se
tab
sa quia
:a)Tab -1. sed
tamis natiproco, t ppeocea
asta ld n, ut Pm ab p. pute o  fieoc heremiralta
1
ita cad n ad P