zaan penn mayberry

zaan penn mayberry (18 november 1939-19 augustu 2016) oka american ganita tatwavetta mariyu ganita shaastram yokka vilakshanhamaina aristatle tatvasaastram yokka srushtikarta, dheeniki athanu thana pustakam "dhi foundations off mathematics inn dhi theory off sets" loe vyakteekarana icchaadu. oka pihech puurti chesina taruvaata.dii. illinayislo gaisi tekuti paryaveekshanhaloo, athanu athanu bristol vishwavidyaalayam yokka ganita vibhaagamlo oka padavini chepattadu. chepattadu ganitam paatakudigaa padavee viramana chese varaku ayana akkade unnaaru.
taatvika rachana.
mayberry tatvasaastram platonic sampradaayaanni tiraskaristundi, idhi ganita saastraanni aadhyaatmikamgaa garvamgaa bhaavinche abhouthika, conny ardhamayye, vastunishtha entiteela gurinchi satyaalanu kanugonadaaniki sambandhinchina divya saastramgaa pariganistundi. eee vaikhari atanni ganita saastravettalalo bahusha "nissabda majority" drukpatham nundi vaeru chestundi. roser penros anargalamgaa oka vilakshanhamaina platonic sthaanaanni vyaktam chestundi.
marovaipu, mayberry kooda ganita shaastram gurinchi kalankita avagahananu teevramgaa tiraskaristaadu, athanu daani gurinchi aalochinchinatlugaa, kaaryaacharanavaadam dwara. ayana ilaa vraasaaru
atuvanti kaaryaacharana siddhaantaalalo atyanta praachiinamaina mariyu vishwavyaaptamgaa prakatinchabadinadi emitante, sahaja sankhyalanu 1 thoo praarambhinchi, 2 pondadaaniki 1 nii jodinchi, 3 pondadaaniki mallee 1 nii jodinchi, niravadhikamgaa konasaginchavacchu. idhi "n = 1,2,3" anae sangnaamaanam dwara vyakteekarinchabadutundi....... "ikkada chukkalu" "jodinchadam 1" "yokka niravadhika pratiruupananu suuchistaayi". deerghavruttaakaarapu eee chukkalanu angeekarinchadamlo, niravadhika punaraavrutam yokka avagahananu angeekaristaaru. eee rakamaina nirvachanam taginanta spashtamgaa undani mariyu marinta samarthana lekunda ganitamlo chaerchadaaniki haamii ivvadaaniki samayam yokka swabhaavam gurinchi amaayakatvam mariyu bahusha tappudova pattinche antar drushti nundi taginantagaa vidadeeyabadindani mayberry nammadu. ayana ilaa vraasaaru
athani vaikhari gatha konni satabdaalugaa bodhana abhyaasamtho matrame kakunda, puraatana kaalam naati sampradaayamtho kooda vibhedistundi. thana muulakaala pustakam v yokka nirvachanam nirvachanam, euclid oke rakamaina rendu parimaanaalanu, a mariyu b, "okadaanikokati nishpattini kaligi undataaniki" eee krindi vidhamgaa nirvachinchaaduh
maroe maatalo cheppalante, vaatilo okadaanini padepade jodinchadam, a anie cheppandi, daaniki marokati minchina parimaanaaniki daariteesthe, b, i anie cheppandi.ii. konni sahaja sankhya "n", "n" a> b. dheeniki viruddhamgaa a mariyu b okadaanikokati nishpattini kaligi undavu, vaatilo okadaanini niravadhikamgaa punaraavrutam cheyadam marokadaanini minchina parimaanaanni eppuduu utpatti cheyakapothe. vii euclid anae pustakamlo nishpattula yokka saadhaarana siddhaantaanni abhivruddhi chesaaru mariyu ii-IV pustakaalalo icchina utpannaalanu saralikrutam cheyadaaniki mariyu ii-IV pustakaalaloni konni siddhaantaala paridhini vistarinchadaaniki nishpatti bhavana yokka saktini pradarsinchaaru. mukhyamgaa mukhyamaina udaaharanalu book III prope. 35, ikkada ilanti tribhujaalanu upayoginchi chaalaa saralamaina rujuvu ventane andubaatulo untundi, mariyu book vi prope. 31 ikkada ayana pythagorus siddhaantaanni chaturasraala nundi saadhaarana saaruupya sankhyala varaku vistarinchaadu.
euclid pustakam VII loe, thana rekha, konam mariyu bommala jyaamiteeya parimaanaalatoe paatu maroka rakamaina parimaanamgaa, "ankaganitam" anae bhavananu parichayam chesaadu. dheenini "unitla samuuhamgaa" ardham chesukovali, ikkada oka unit "manam deeninainaa okati anie pilustaamu". singletonla sthithi mariyu khaalii samiti gurinchi konni abhyantaraalatho, "arthamos" yokka greeku bhavana tappanisarigaa "sett" yokka aadhunika bhavana. euclid yokka saadhaarana bhavana 5,-"mottam bhaagam kante ekkuva"-yokka praamukhyata anedi ankaganitaaniki vartimpajesinappudu, oka ankaganitam ekaruupamgaa undadani, ikkada eee padaanni heath taruvaata "khachitamaina amarikatho unchavacchu", daani yokka edainaa saraina bhaagaaniki, ledhaa, maroe maatalo cheppalante, oka samiti parimitamainadi, aadhunika ardhamlo samiti mariyu daani yokka saraina upasamiti madhya 1-1 anuroopyam ledhu. greeku ankaganitam, mukhyamgaa euclid pustakaalu VIII-IX, nijamgaa parimita samitula adhyayanam anae vaastavam "ankaganitam" nuu "sankhya" gaa sarvavyaapta anuvaadam cheyadam dwara mariyu 17va sataabdamloo sambhavinchina daani asalu "ankaganitam" antey "nishpatti" nundi sankhya bhaavanalo parivartana dwara aspashtamgaa undhi. ardhamlo maarpunu neuton thana upanyasalalo spashtamaina vyakteekarana icchaaru.
keelaka ganita bhavanala abhivruddhilo nijamaina chaaritraka sanghatanala kramam gurinchi mayberry yokka nammakalu athani taatvika dhoraniki kendramgaa unnaayi. jacob clain yokka "greeku ganita aalochana mariyu beejaganitam yokka muulam" gurinchi chadavadam dwara athanu veetiki daariteesaadu. mariyu richard dedeckind yokka ghnaapakam "vaas sind und vaas solen dye jahlen".
17va sataabdam madhya nundi 19va sataabdam varaku sahaja sankhyalu mariyu avi aadhaarapade aparimita punaraavrutam anae bhavana ganitamlo aacharanatmakamgaa mariyu taatvikamgaa punaadi hodaanu pondindi. taatvika vaipu, kanth ankaganita pratipaadanalanu kruthrimamaina, oka praadhamika ghnaanamgaa vargeekarinchaaru, mariyu rekhaganita siddhaantaala yokka saaruupya vislaeshanhaku samaantaramgaa, athanu mana antariksha antar drushtini kanugonnadu, vaati balavantapu swabhaavaanni mana samaya antar drushtini gurtinchaadu. ankaganitaaniki sambandhinchi kanth yokka saadhaarana sthaanam 19va sataabdaaniki chendina goppa abhyasa ganita saastravettala aamodaanni pondindi. gaas kooda, jyaamiti sthithipai cont vaikhariki asammati vyaktam chesinappatiki, ankaganitampai athani vaikharini aamodinchaadu.
daadaapu oka sataabdam taruvaata payinker ilaa vraasaadu
19va sataabdamloo mukhyamaina vyaktulalo, dedecoind matrame contian ekaabhipraayaaniki vyatiraekamgaa nilabadinatlu kanipistundi. athanu challaga ilaa vraastaaduh
mayberry entho mechukunna dedeckind, samayam yokka contian antar drushti ledhaa niravadhikamgaa punaraavrutamayye karyakalapalapai aadharapadakunda sahaja sankhyalanu sthaapinchavacchani choopinchaadu. ayithe athanu anantam yokka contor suutraanni spashtamgaa angeekarinchadam aadhaaramgaa alaa chesaadu, idhi mayberry etthi chuupinatlugaa, euclid yokka saadhaarana bhavana 5 yokka viruddhamgaa ardhamoyiki vartistundi. ayithe sahaja sankhyalu mariyu punaraavruta prakriyalu chaalaa mandhi ganita saastravettalalo ghanatanu kolpovadaniki pratyeka punaadi hodaanu kaligi unnayane abhiprayanni dedeckind yokka parisoedhana kaliginchaledu. antar drushti udyamam, ganita shaastram yokka ardham gurinchi oka platonist avagahananu tiraskarinchadaanni meberrytho panchukuntu, vishayam gurinchi kaaryaacharanaatmaka avagahananu aasrayinchindi, idhi vaari aalochana yokka hrudayaaniki niravadhikamgaa sudeerghamaina punaraavruta prakriyalanu aamodinchadaaniki daariteesindi. lanchanapraya udyamam, parimita sthirathvam rujuvula dwara contor yokka siddhaantam yokka anantam yokka ganita phalitaalanu kaapaadataaniki hilbert yokka karyakramanni anusarinchi, adevidhamgaa, lanchanapraya vyavasthala nirvachanaalalo mariyu vaati lakshanaala sthaapanalo, niravadhika punaraavrutam mariyu anubandha nirvachanaalaku pratyeka hodaanu ichindi.
mayberry yokka vaikhari emitante, euclid yokka pustakam V nundi, euclid pustakaala i-IV loe udaharinchinatlugaa ganitam yokka nijamaina aatma nundi idhi oka vichalanam. athani pustakam yokka pradhana uddesyam athani sthaanaanni vivarinchadam mariyu adhi avasaramaina vishayaala gurinchi ledhaa ganita shaastram yokka aadhunika abhyasanni naasanam cheyadani choopinchadam, conny, ganitam antey emiti mariyu ardham gurinchi thana marinta avasaramaina avagahanaku tagina drudhatvam yokka pramaanam gurinchi spashtamaina aristatle avagahana gurinchi thana sifaarsuloo, athanu moodu sataabdaala laanchanapraayata taruvaata ganita saastraaniki ardhaanni punaruddharinchadaaniki contor praarambhinchina sampradaayaanni anusaristunnadu. edemaina, mayberry drushtilo, saraina taragatulu, nishpaakshikamgaa unnayani cheppe aadhunika platonic prerana pondina siddhaantam, 19 va sataabdam praarambhamlo lanchanaprayamga prerepinchabadina siddhaantam, nemali yokka "shaashwata roopaala samaanatvam yokka suutram" anie cheppadaniki, manchi ghnaanam mariyu sambhaavya nijayiti nundi nishkramana.
mayberry yokka saanukuula taatvika abhiprayalu aristatle nundi paakshikamgaa prerana pondina koddi sankhyalo taatvika siddhaantaalaku kattubadi undatam nundi mariyu paakshikamgaa daadaapu rendunnara sahasraabdaala ganita anubhavampai, mukhyamgaa 19va sataabdam pratibimbimchadam dwara pravahistaayi.
ganitasastram, mukhyamgaa ankaganitam adhyayanam, keetaka shaastram ledhaa pakshula shaastram vanti itara pratyeka aasaktigala shaastreeya vishayaalatoe paatu daani sthaanaanni aakraminche sahaja shaastram anie, eee praapanchika vastuvulatoe nishpaakshikamgaa vyavaharinchaedani aristatle abhipraayamtho praathamikamgaa ekibhavinche aristatle vaastavikavaadi. aristatle ilaa vraasaadu
mariyu itara pradaesaalu
mayberry tanaku taanugaa aandolana chendutunna shaastram ankaganitam, euclid anae padam VII-ix pustakaalalo ichhe ardham yokka suddhi chesina samskaranalo ardham chesukovadam, mariyu athanu paerkonnatlugaa, contor eee padaanni icchina ardhamlo kooda. mayberry yokka pradhana sthaanaalalo modatidi aristaatiltho oppandam, ganita shaastravetta vishayalu mariyu konni vastuvula yokka bahuvachanaalanu, unitlu mariyu ankaganitam gurinchi, keetaka shaastravetta yokka vastuvula adhyayanam mariyu konni vastuvula yokka bahuvachanalu, keetakaalu mariyu keetakaala kaalaneelanu adhyayanam cheyadaaniki tappanisarigaa saaruupya maargamlo adhyayanam chestaadani. ankaganitam" nirvachanaaniki sambandhinchi taatvikamgaa atigaa load cheyabadina "" prati vishayam "gaa heath yokka anuvaadam nundi matrame" εκαστον των οντων "yokka euclid yokka lapidary nirvachananni athanu angeekaristaadu, mayberry euclid nirvachanamlo" multitude "anae padaanni mundugaane jodistundi-" ankaganitam anedi unitlatho kuudina samuuhamu "-" khachitamaina "anae padamtho. dheeni dwara ayana ardhamu emitante, ankaganitam khachitamaina nishpaakshikamgaa unikilo undhi, sarihaddulu ledhaa parimitulanu kaligi undhi-ankaganitam parimaanamlo parimitam cheyabadindani ledhaa lekkinchadam vanti edainaa kaaryaacharana prakriyaku anukuulamgaa undani ledhaa konni bhaashaasaastraparamgaa roopondinchina paristhiti kaligi unna vishayalanu khachitamgaa kaligi undani kaadu, conny adhi ankaganakaalalo undaa ledhaa anae ardhamlo matrame. saadhaarana bhavana bhavana (bhaagam kante mottam peddadi) pratyekinchi anugunamgaa undatam anedi "ankaganitam" anae bhaavanalo suuchimchabadadu, conny anni ankaganitam kaligi unna teerpu, adhi jariginappudu, eee lakshanam. konni paristhitulaku anugunamgaa ledhaa konni saadhaarana naamavaachakaalato sambandham dwara nirvachinchabadina bahuvachanaala kosam-e.zii. moodu kante ekkuva unitlu ledhaa" "gurralu" "kaligina arithmoi-mayberry aristatle padam" "jaatulu" "nuu upayogistundi". oka jaathi kevalam manam daanini oohinchagalamu kabatti unikilo undih idhi prapanchamlo oka vastunishtha vishayam kaadu, conny mana thalalalo oka aalochana, ayithe oka jaatiloki vachhe vishayalu ankaganitam thoo samanamga undavacchu ledhaa kakapovachhu. ilanti vyaakhyalu "aasti"-ii vanti itara bhavanalaku vartistaayi.zii. undatam mariyu kramabaddhamaina ledhaa "global function" e.zii. power sett mariyu union operatorlu. mayberry ilaa vraastunnaaruh
mayberry yokka pradhana taatvika siddhaantaalalo rendavadi emitante, vishayalu mariyu vishayaala ankaganitam nishpaakshikamgaa unnaayi mariyu bahya vaastavikata yokka fabricto bhaagamainavi. ankaganitam yokka antological aadharalu sarigga daani bhagalu. ayithe, aakaasamlo meghalu, erupu rangulu, maanava bhavodvega sthithulu, 22va sataabdaaniki chendina purushulu vanti oka jaatilo padee vastuvulu saadhyamayye ankaganitam yokka unitlanu yerparachadaaniki taginanta spashtamgaa vaeru cheyabadinda ledhaa vastuvula bahulatvaala sarihaddulu-udhaa.zii. centaurs mariyu matsyakaarulanu "maanava jaathi" loe padatam anie manam pariganinchaalaa? erupu chivarala shades mariyu oodaa shades eppudu praarambhamavutaayo khachitamgaa nirnayinchabadutundaa?- oka ankaganitam erpadataaniki taginanta spashtamgaa varninchabaddaayi. ankaganitavetta yokka pani, athanu ankaganitam gaa teesukogala vastuvula yokka unitlu mariyu khachitamaina bahuvachanaluga teesukogala vastunishtamaina spashtamgaa vyaktigatamaina vishayalu unnayani saralamaina oohatho praarambhinchavacchu. mayberry ilaa vraastunnaaruh
mariyu, konchem taruvatah
mayberry yokka pradhana taatvika siddhaantaalalo moodavadi emitante, prati quantifier yokka paridhi khachitamaina ankaganitanku parimitam cheyabadithe, "andarikee" mariyu "unikilo undhi" anae parimaanaalanu upayoginchi roopondinchina nirvachanalu, nirvachinchina lakshanaalu mariyu vaadanalu matrame ardhamavuthaayi, vastunishtha vaastavam yokka prakatanalugaa. kabatti, udaaharanaku, manam ammayilu, kwa unitlatho vyavaharistunte, aastiki sambandhinchi iddaru ammayilanu elaa polchaalo teliste "telivaina" aastiki sambandhinchi "john thana taragatiloni telivaina ammai" anie manam telivigaa cheppagalam, conny "john telivaina ammai" anie kaadu, endukante taruvaati prakatana "ammai" jaatiki chendina anni vishayaalapai lekkinchadaaniki uddesinchabadindi. eee vaikhari ataniki peeno ankaganitam mariyu germelo-frankel sett siddhaantam yokka rendu shaastreeya modati arder swayamsiddha vyavasthala punaadi natnalanu tiraskarinchadaaniki adanapu kaaranaanni istundi. atuvanti adhikaarika vyavasthala nirmaanamloo antarleenamgaa unna kaaryaacharanavaadaanni ayana vyatirekinchadame kakunda, prerana mariyu pratyaamnaaya suutram yokka suutram yokka saaraamsamlo predicatela erpaatulo aniyantrita quantifierlanu swechchagaa upayoginchadaanni kooda ayana ippudu tiraskarinchaaru.
mayberry yokka nalgava pradhana siddhaantam athani moodava siddhaantamtoe mudipadi undhi. unitlu mariyu ankaganitam-i thoo vyavaharinchadamlo ayana dhruveekarinchaaru.ii. vastuvulatoe-manam shaastreeya tarkaanni samasyaatmakamgaa upayoginchavacchu, ayithe aalochanalatho vyavaharinchetappudu-jaatulu, prapancha vidhulu, saadhaarana nirmaana lakshanaalu modalainavi. - tagina tarkam antar drushti. mukhyamgaa "a ankaganitamloni sabhyulandaruu p lakshanaanni kaligi unnaaru" anae ooha asambaddhatanu suuchistumdani manaku teliste, appudu manam chattabaddhamgaa oohinchavachhu "a, x loe kontamandi sabhyulu unnaaru, dheeni kosam p (x) kaligi undadu". ayithe, manam oka jaatipai parimaanakaanni upayoginchi oka prakatana chesthe e.zii. "anni vishayaalalo p" ledhaa p kaligi unna edho undhi "memu ikapai oka vastunishtha vaastavaanni nivedinchadam ledhu, adhi kesu ayi undaali ledhaa kakudadu. atuvanti prakatnanu samarthinche vyakti thana manasulo daani samarthana undani vaadana chestunnatluga ardham chesukovali-i.ii. saarvatrika parimaanakam vishayamlo, p anedi edainaa oohinchadagina vishayam kaligi undani nammadaniki aadharalu, ledhaa astitva parimaanakam vishayamlo, p kaligi unna jaatula udaaharana gurinchi ataniki telusu. aniyantrita parimaanakaalanu kaligi unna prakatanalanu aatmaasrayamgaa ardham chesukovali kabatti, minahaayinchina madhya suutram appudu chellubaatu kaadani spashtamavutundi. udaaharanaku, "p kaligi unna anni vishayaalaku" anae ardham "prati vishayaniki p kaligi unna vaadananu utpatti cheyadaaniki oka saadhaarana nirmaanam naa manassulo unte" mariyu "p kaligi laeni vishayam undhi" anae ardham "p pattukovadamlo viphalamaina vastuvunu utpatti cheyadaaniki oka nirmaanam naa manassulo undhi.appudu neenu tappanisarigaa vibhajana nijamani nokki cheppalenu, endukante udaaharanaku, naa manassulo etuvanti nirmaanaalu undavu. eee amsampai mayberry ilaa vraastunnaaruh
mayberry yokka aidava pradhana siddhaantam emitante, jyaamiti kosam euclid yokka pratipaadanalatoe vistrutamgaa saaruupyataloo, ankaganitam kosam pratipaadanalanu nirdesinchavacchu, idhi moolakaalalo manchi lopaanni kaligistundi, idhi jyaamiti kosam saadhaarana bhavanala mariyu pratipaadanala dwara srushtinchabadina anchanaalaku viruddhamgaa, atuvanti pratipaadanalu aevee kaligi undavu. mayberry thana pustakamloni 4va adhyaayamlo eee karyakramanni nirvahistaadu. athani pratipaadanalu kontavaraku euclid roopamlo anusaristaayi, conny 19va mariyu 20va sataabdaala prarambham nundi vidudala chesina setla gurinchi swayamsiddha aalochanalu contentlo untaayi. oka binduvu mariyu oka rekha icchina vruttam nirmaanampai euclid yokka pratipaadanalaku vistrutamgaa saaruupyata ledhaa rendu binduvulu icchina pratyaekamaina sarala rekha nirmaanaaniki sambandhinchi pratipaadanalu union, power sett mariyu cartician utpattitoe sambandham kaligi untaayi, ivi okati ledhaa anthakante ekkuva icchina vaati nundi kotta ardhamoyni utpatti chese prapancha nirmaanaalanu suuchistaayi. ayithe, pratyaamnaayam mariyu grahanaseelatapai ayana pratipaadanalu kontha bhinnamgaa unnaayi. ivi kevalam grahinchavalasina vyaktigata nirmaanaalanu nirdesinchavu, conny saadhyamayye anni nirmaanaalu mariyu anni oohinchadagina lakshanaala gurinchi dhruveekaranalu chestaayi. oka konamlo, aalochanala nundi vastuvulaku saadhaarana vantenala unikini dhruvikaristunnatlu vaatini ardham chesukovacchu. ayithe, nirdishta nirmaanaalaku sambandhinchina pratipaadanala maadirigaane, rendintinee kotta ankaganitam unikini dhruveekarinche "parimita suutraalu" gaa ardham chesukovacchu. mayberry yokka "sarididdabadina" euclid jyaamiti mariyu ankaganitam yokka sodari vibhaagaalanu, rendintikee vartinche saadhaarana bhaavanalatho, rendu setla abhidhaaranaa suutraalatoe, prati vibhaagaaniki okadaanitoe anubandhistundi. nijaaniki, jyaamiti ankaganitam yokka bhaavanapai aadhaarapadinanta varaku-idhi tribhujaalu, chaturbhujaalu, pentagonlu modalaina vaatini nirvachinchadamlo kooda alaa chestundi., conny konni pratipaadanalalo marinta spashtamgaa, udhaa.zii.. pustakam vi prope. 31, idhi saadhaarana bahubhujalu gurinchi dhruveekaranalu chestundi-"sarididdabadina" euclid jyaamiti kante mundu ankaganitam yokka adhyayananni unchutundi.
mayberry yokka pradhana tatvasaastram yokka chivari amsam emitante, euclid saadhaarana bhavana 5 yokka saktini gurtinchadamlo viphalamainappudu-ardhamoyiki vartimpajesinappudu oka goppa chaaritraka avakaasam kolpoyindani, punaraavrutam dwara tananu taanu nirvachinchukovadamlo, oka bhaarii tappu adugu veyabadindi, dheeni parinaamaalu ganita charitralo vistarinchaayi. saadhaarana bhavana 5 yokka saraina prasamsa mariyu punaraavrutaanni vidichipettadam, oka "sarididdabadina" euclid parimititoe sambandham unna ganitamlooni aaa bhaagaalanu anusarinchi untundi-7-9 pustakaala vaastava niraadambaramaina vishayaalatoe paatu, sahaja sankhya siddhaantam, parimita samyogam, parimita samuuham mariyu kshetra siddhaantam mariyu marinta saadhaaranamgaa parimita nirmaanaala adhyayanam. maberries eee amsaanni euclidean ankaganitam anie pilustaaru mariyu thana pustakamlo gananeeyamaina bhaganni daani praadhamikaalanu abhivruddhi cheyadaaniki ankitam chesaaru. prerana dwara rujuvu mariyu punaraavrutam dwara nirvachanam yea sthaayilo samarthinchabadathaayo sthaapinchadamlo athanu mukhyamgaa shraddha vahistaadu. euclidean ganita siddhaantam aadhunika sahaja sankhya siddhaantam yokka chinna punarnirmaanam kakunda, vaastavaaniki euclidean ganitamlo sahaja sankhyala gurinchi aacharaneeyamaina bhavananu sthaapinchalaemani ayana chuupimchaaru. euclidean ankaganitampai thana abhiprayanni puurti chestu, mayberry abhiprayam emitante, euclid yokka samaantara suutraanni tiraskarinchadam dwara pratyaamnaaya jyaamitulu srushtinchabadinatle, saadhaarana bhavana bhavana tiraskarinchadam dwara mariyu kaneesam oka ankaganitam unikini dhruveekarinchadam dwara pratyaamnaaya ankaganitam srushtinchabadutundi, dheeni kosam mottam oka bhaagamtho 1-1 anuroopamlo unchavacchu. eee siddhaantam, dheeniki contorian ankaganitam anie paeru pettadaniki ishtapadataaru, idhi aadhunika samiti siddhaantam, idhi mottam ganitaanni mariyu mukhyamgaa jyaamitini vileenam cheyagala saamarthyaanni (vaadayogyamgaa) choopinchindi, idhi euclidean pampinheelo saadhaarana bhavana bhavana kattubadi undatam, idhi ankaganitam yokka pratyeka sodari vibhagam.
mayberry yokka tatvasaastram, contorian ganitasastram nundi euclidean nuu kramabaddhamgaa vaeru chese karyakramam dwara modati sandarbhamlo saadhinchaalsina ganita saastrampai spashtata mariyu drudhatvam yokka kotta pramaanaanni vidhinchadaaniki prayatnistundi, idhi athani antological mariyu semantic nammakaala nundi pravahistundi. euclidean vishayamlo eee pramaanaaniki jyaamiti mariyu ankaganitam rendinti abhyaasakulu punaraavruta prakriyalaku anni aakarshanhalanu nivaarinchaalsina avasaram untundi. jyaamitiloo paryavasanamga atyanta takshana savaalu emitante, i-IV pustakaala paddhatulu mariyu paddhatula aadhaaramgaa pustakam vi yokka siddhaantaalanu sthaapinchadam dwara euclidnu "saricheyadam", idhi pustakam v loe pravesapettina nishpatti bhavananu upayoginchadaanni nivaarinchadam. ankaganitam kosam sambandhita savaalu emitante, gunakaaram yokka nirvachanamlo euclid tananu taanu anumatinche punaraavruta prakriyanu aasrayinchakundaa pustakam VIII-IX yokka phalitaalanu sthaapinchadam. (pustakam VII, nirvachanam 15.) contorian ankaganitam kosam pradhana savaalu emitante, ananta ganita shaastram yokka goppa bhaagam-calculus nundi oka vidhamgaa ledhaa maroka vidhamgaa pravahinche vibhaagaalaku-aparimita parimaanaalu avasaram ledani choopinchadam, tatphalitamgaa atuvanti parimaanakaalatoe kuudina samiti siddhaantam kosam germelo-frankel suutraala yokka pratyaamnaaya pathakam yokka sandarbhaalu, alaage mayberry yokka saadhaarana tatvasaastram dwara anumatinchabadavu, yea sandarbhamloonainaa saanketikamgaa anavasaramainavi.

