369
TOPIC2133287010064133194229286
4.244128701005982
RENAISSANCE2545287010066124193257292343395460528584642
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10028878014010860120180
operations567769012870141203249312351389459530584
on1186769012886156
finite1377769012863102172210249312
numbers,1723769012886156266334396443498533
and2292769012878147217
we25447690128118180
have2759769012885148217280
established3074769012879132172233304342380436505568637
that3746769012856126188226
all4008769012879116155
these4198769012856126188242305
finite4538769012863101170210248311
numbers4884769012886155265333395442497
are5671011012862109171
possible7741011012874145199254292362401464
only12721011012876146184255
in15601011012845115
the17111011012843113176
single1922101101285998168237277340
case22961011012868130183246
of25771011012875122
infinity,27341011012843113160199269308347421455
i.e.,3224101101284479142177211
an34701011012868138
infinite36441011012843113160199269307347409
number.40871011012876146255323386433468
Therefore,45951011012886156219265328374444491553588
we522410110128101162
have5671253012870133202265
arrived8671253012886133178217287350419
at13211253012886124
this14811253012861132170225
infinity17411253012861132179217286326364435
in22091253012863133
a23781253012886
completely24981253012886155264332372434473535574645
rational31761253012871133172211281351414453
way.366312530128125187257290
It39891253012870109
is41331253012863117
nothing42851253012893163202273311381451
other47711253012894132202265311
than51171253012862132194264
common5671494012862133242350418489
sense10911494012859122192247309
that14351494012844113176215
requires16861494012851112182252291338401454
us21761494012874128
to23401494012843113
recognize24881494012851114176245315386424486548
infinity30711494012844114161200269309347418
as35221494012867121
the36791494012843114177
coincidence38911494012867136175245307346416478548610672
of45981494012875122
all47551494012867105144
existing49351494012867136174229268307377446
opposites.5671735012870141210280335374413475529565
This11671735012885155194249
is1451173501283893
the15791735012838107170
first1784173501284585132186225
type20441735012839110178241
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infinity.24711735012839109156195266305344415448
This8501977012886155195249
type11341977012858129197260
of14291977012889136
infinity16001977012857127174213283321360431
is20641977012858113
followed,22131977012865134173212282384445516551
and27991977012881150220
cannot30541977012882144213284353392
fail34811977012866128167206
to37221977012857127
be38851977012888150
followed,40701977012866135174213283384445515551
by46561977012889159
a48491977012881
limited4965197701285897207244283346416
type5672219012839110178241
of8432219012879127
infinity,10052219012847116163203272311350421454
i.e.,1494221901284883146181215
one17452219012879149211
in19912219012848118
which215422190128101169209272341
we253922190128102163
already27382219012870109156217279349420
distinguish31912219012879119173212251321391460500554624
separate38502219012864126196259304366405467
parts43522219012879141188226281
and46682219012871140211
separate49142219012863126195258304367405466
moments,56724600128109177288349419459514549
the11512460012852122184
limit1371246001285190199236276
set16822460012867130169
of18872460012883130
which206524600128101171209272341
forms24422460012859129177286338
the28162460012851122184
first3035246001285999146200239
and33092460012875146215
already35602460012875114161222285355426
indivisible40192460012852122192231301340395433504542605
infinity46592460012852121169206277316355426
with513124600128101146186255
which56727020128101171210273342
we95227020128101163
began.11492702012877139208271340376
In15602702012853122
other17182702012876114185247293
words,205327020128101171217287341377
we247127020128102164
are26702702012868114177
faced28822702012853115176238308
with323327020128101138178247
the35162702012845114177
transition3728270201284592154223278317355395464534
of42982702012875123
absolute44562702012869138192262301371410473
infinity49632702012846115162200271309348418
into5672943012839110148219
its821294301284181135
otherness,9912943012874112182245291360423478532567
into15932943012842112151221
a18502943012865
limited1950294301284281191227267329400
infinity23852943012843112159197268306346416
that28352943012842113174213
is3084294301284296
not32162943012873143182
simply3434294301285696206273313383
a38512943012865
coincidence39512943012866136176245308347417480549611674
of46602943012872119
opposites,48142943012874143213284338376416478532566
but5673185012870141179
also7823185012867106160229
their10473185012843113176213261
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This22223185012886156195249
is2507318501284397
already26403185012866104151214276345415
an30903185012866136
ordered32623185012875122191254300363432
infinity,37303185012843113160198268307346417450
in42153185012843114
which436931850128101171209277347
not47513185012875144184
just49703185012844113167206
the52113185012844113176
infinity5673426012839110157195264304342413
itself10133426012874113168231269316
comes13643426012897167277337391
to17913426012873144
the19713426012873143205
fore,22123426012881151198259294
but254234260128104175213
its27913426012873111166
internal29923426012873144183245292362424463
separateness,34913426012889150221284329392431492563625679733769
its42953426012873112166
orderliness,449734260128104152221283330368408477540593648684
its52163426012873112166
figurateness.567366801284786156226273336373436505568622677712
But13143668012893162202
even15513668012863131194263
this18503668012839108147201
is2087366801283993
not22153668012870140178
enough.24293668012862132202271342411447
There8503909012886155218265327
is1212390901284095
also13433909012864102157227
a16053909012865
third17053909012840109149196265
type20053909012840110178241
of22813909012872119
infinity.24363909012841110157196266304344415448
Let29213909012885147186
us31433909012872127
ask33043909012865119190
ourselves:35303909012871140187242304343412475529568
if4134390901283987
we425839090128101163
have44563909012871134203266
established47573909012864117157220289327367421491553623
that5674150012839110172210
infinity8134150012855125172210281319359429
is12754150012856111
indivisible,14214150012856127196235305344398437509548610645
and21014150012879149219
now23554150012887157259
we264941500128118179
have28634150012887149219282
established31804150012879133172235304343382436506568638
that38544150012855125188226
it4115415001285694
consists42454150012878149218273312367405459
of47404150012886134
separate49094150012871134203265312374413475
elements5674393012862101164273333404443498
or11014393012874121
finite1257439301285392162200239302
things,15944393012844114153222293347383
does20124393012875145208261
this23094393012844114153207
not25524393012876145185
mean277843930128109169231302
that31154393012845115177215
the33664393012844114177
entire35784393012868137176215262324
infinity39374393012845115162200269309347418
is43884393012845100
present45234393012876123186239302371411
in49694393012843114
each51194393012868130191260
of5674634012870117
these7194634012854124186241303
divisible10564634012885124194233287326396435497
parts?15894634012884147193231286348
If19724634012862109
infinity21154634012854124171209279318357428
is25764634012854108
divisible,27204634012884123193232287325396434497532
then32874634012853123185255
it3577463401285493
is37054634012853107
not38484634012884154193
present40764634012885132193248310380419
in45304634012854123
the46894634012853122185
separate49094634012869132201264310373411472
things5674875012839110148219288342
that9454875012860130193230
make121148750128130191261324
up15704875012892162
infinity,17684875012859129177215284324362433466
and22694875012883154224
if25294875012860107
it2671487501285999
is28054875012859114
truly29554875012859105175215285
indivisible,32744875012860130200240309348403441512550613648
then39574875012859130192261
it42534875012860100
is43884875012860114
clear45384875012883121184246293
that48664875012859130192231
it5132487501285999
is52664875012859114
indivisible5675116012839110179219288327382420490529592
and11935116012872141211
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in18875116012848118
each20405116012872133196266
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its2501511601284887141
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elements,31805116012870109172281341411451505540
parts,37555116012878141188226281316
and41065116012871141210
things.43525116012848118156227296350386
This47735116012895164203258
is50655116012849103
the52035116012847118180
basis5675359012870133188226280
of8835359012889136
Nicholas105453590128120159221290361399462516
of16055359012889136
Cusa's177553590128113183238301326380
doctrine21905359012889159221259307346415478
that27035359012858128190228
"any"29665359012876138208279335
exists33365359012881152191245285339
in37105359012858128
"any"38735359012876139209280335
and42445359012881151221
that45005359012858129191230
everything47655359012881150213260330367438477547617
exists5675600012862133172226265320
in9225600012849119
everything.10775600012873142205250320358428468537608644
Of176556000128101147
course,19475600012873143214261315377412
this23945600012849119158213
is26425600012848102
a27805600012873
third28885600012849119158205274
type31985600012848119187250
of34835600012881128
infinity,36465600012849119166204275313353423456
one41385600012880150212
that43855600012850119182221
is46425600012848102
indivisible47795600012850120190229298338392431501539601
and5675841012862133202
whole80558410128101170241280342
in11825841012838109
each13265841012862123186256
individual16185841012837107176216285325395464527565
element22185841012863102164273334404443
of26955841012871118
such28485841012854124187256
an31395841012862133
infinity33075841012838108155193263302341412
<…>.37555841012879219298334
Source:5676867011067127187227280333366
N.9676867011086116
Cusanus,11136867011080140187240300360407437
On15806867011087146
Learned17576867011074126179219279333392
Ignorance,21796867011041100160220260314373427479509
Moscow:271868670110107167213268327414447
Academic31956867011087140193252307400433487
Project,37116867011067107167201254307339369
2020,41106867011062122182242274
(excerpt).4414686701104093152207259299359392432462
When85072500128133201264334
I12207250012871
am13267250012887197
about15557250012887158228299337
to19287250012863133
speak20967250012879150211274344
of24757250012895142
the26527250012863132195
highest28827250012894133203273335390428
(maxima)33467250012871181241311350460520567
art39487250012887134173
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ignorance,43347250012862133202273320381452513576611
I49807250012871
must508672500128135202257296
necessarily5677491012870133195258311366428475514552623
examine12237491012863133196306342413476
the17347491012840109172
nature19417491012870133172242289351
of23277491012870117
maximality247974910128109169239279388448487528568638
itself.3151749101283979133195233281316
By35027491012894164
maximality370174910128110170240279389449488529568639
I43737491012848
mean445774910128109169231301
that47947491012840110173211
which504174910128101171210272341
59162740204438
Philosophical11616215012074145183219288343411483555593649713751
text19386215012044108170214
(Primary21796215012049123178214320385440504
Source27106215012061129200256312376
Excerpt)31136215012069132189253308379423472
N.11616359014195127
Cusanus13196359014181164229304389472536
on18866359014179165
the20816359014151135210
absolute23206359014175158223302345429480555
maximum290563590141125200274318442526649
and35856359014175160243
learned38606359014145120193258342417500
ignorance11616522014144117202281347420506571646
652196343012670