porism

porism haah ganiteey prastav kinwa parinam aahe. tyacha vapar puravyachya thet parinamacha sandarbh denyasathi keela gela aahe, joou upasamhar ekhadya siddhantachya thet parinamacha sandarbh kassa deto yachyashi samaan aahe. aadhunik vaparat, heey eka asey naate aahe jeey mulyanchya anant shrenisathi dharan karate parantu keval jarr steinerchya porizamsarkhi vishisht aut gruheet dharali gelee tarach. haah shabd euclidchya haravalelya teen pustakanmadhun aala aahe. ekhada prastav siddha jhaala nasata, mhanoon porism heey pramey kinwa kharey asoo shakat nahee.
mool.
porizamsabaddal jeey pustak pratham bolate teey euclidche "porisms" aahe. alexandriachya 'sangrah' chya papasmadhye tyabaddal jeey mahit aahe, too itar bhaumitik granthansah tyacha ullekh karato aanee teey samajoon ghenyasathi aavashyak asalele anek shabd deto. pups mhanatoh
papus mhanale qee shevatchi vyakhya nantarchya kahee bhoomitindware badalali gelee, jyanni porismchi vyakhya (leapon hypothesy topikou thorimatos) mhanoon apghati vaishishtya mhanoon kelee, jee (kinwa tyachya) gruhitkadvare locus-prameyapeksha qamee aahe. proclusney nidarshanas aanoon dile qee 'porism' haah shabd done arthanmadhye vaparla gelah eka arth mhanje 'parinam', parinami naan magitalela parantu eka prameyavarun anusaran karnara disato. reshevar arthane, tyane "junya bhoomiti" chya vyakhyet kahihi jodale nahee, heey sangnyashivay qee vartulachya madhyabhagi shodhane aanee sarvat mothya samanya mojamapacha shodh haah porism aahe.
yuklidchya porizamvar pups.
pappusane euclidchi 'porism' chee vyakhya nakarli. aadhunik bhashet vyakt kelela eka chhidravad, assa dawa karato qee chaar saral resha dilya, jyapaiki teen tyaa chauthya bindula bhetatat jyaa binduvar tyaa valatat, jarr yaa reshanchya chhedanbindunpaiki done bindu pratyek eka nishchit saral reshevar asateel, tarr chhedanyacha urvarit bindu dekhil reshevar saral reshevar asel. samanya vyakhya saral reshanchya konatyahi sankhyela, "aine" laa lagoo hote, jyapaiki "aine" ("aine" + 1) vya varr nishchit kelelya anek bindunvar firu shakate. yaa 'aine' saral resha done aanee done gunankanna 'aine' ('aine'-1) gunankanmadhye kapatat, 'aine' ('aine'-1) hii eka trikoni sankhya aahe jyachi bajoo 'aine'-1 aahe. jarr tyanna 'aine' nishchit bindumbhovati firavale gele tarr tyanchya 'aine' ('aine'-1) chhedanbindunpaiki konatehi 'aine'-1, vishisht maryadechya adheen rahoon nivadalele, nishchit saral reshanchya aadhare 'aine'-1 varr asel, tarr chhedanyache urvarit pratyek bindu, 'aine' ('aine'-1) ('aine'-2), eka saral resheche varnan karate.
vareel goshti asha prakare vyakt kelya jaau shakatatah jarr pii aanee kyu heey done nishchit bindu, eka dilelya saral reshevar done saral reshanna bhetatat, tarr ell, aanee jarr tyapaiki ekane eka nishchit saral reshepasoon, aii. emm., haah bhag kapla, tarr aksh, sthiteet deela, dusari nishchit saral resha aanee tyavar nishchit kelela bindu bii nishchit keela jaau shakato, jenekarun bii pasoon mojalelya yaa reshevar nishchit reshevar reshevar halatya reshene banavalelya bii. emm. yaa bhagache gunottar ex teey am asey dile jaate. porizamchya sandarbhat pups jeey lemma deto teey aaheth
nantarche vishleshan.
robbert simsonne keval teen prastav spasht kele jeey papus konatyahi paripoornatesah soochit karate, jeey 1723 madhye "tatvik vyavharanmadhye" prakashit jhaale. nantar tyanni samanyatah porizamchya vishayacha tapas 'dii porismatibus tracklets; kwo doctrinum porisarnatam satis explicatum, ett inn postrum abb oblivian tutum phoor sperat aktar' yaa shirshakachya pustakat keela aanee tyanchya mrutyunantar "roberty simson aupera quaidam rileka" (glassgo, 1776) yaa khandat prakashit kele.
simsoncha 'dii porismatibus' haah grunth, pramey, samasya, daytum, porism aanee locus yanchya vyakhyanpasun suru hoto. saymanne lihile qee papaschi vyakhya khoop samanya aahe aanee tyane tee ashee badalalih
porismas ist proposio inn kwa proponitur demonstrey raim alikam, well plures deta ese, qe, well quibus, utt ett culibate ex ribus inumeris, naun quidem datis, sede kwe edd ea kwe deta sunt endem habent rationame, convir austendam est fafessionum kwandam communim inn prapoji discriptum. porismya etium heey eka samasya mhanoon annuntiary potest, see nimiram ex quibus deta demonstranda sunt, invenienda proponentur yaa swarupat aahe.
simsanane mhatale qee locus hii porismchi eka prajati aahe. tyanantar, porizamvaril papaschya nondiche lattin bhashantar aanee granthatil bahutansh bhag tayar ghoshit prastavanche anusaran kele jaate.
johnn playfairche sansmaran ("trans". roy. ess. oo. see. edin.", 1794, khand. 3.), simsonchya granthacha eka prakarcha pudhcha bhag, porizamchya sambhavya utpatticha kinwa pracheen bhoomitila tyancha shodh lavnyas karanibhoot karanibhoot tharananya shodh ghetala. playfairne tippani kelee qee prastavachya serve sambhavya vishisht prakaranancha kaljipurvak tapas kelyas asey disun yeil qee 
yaa prakarananchi swatantrapane vyakhya kelee jaau shakate, teey pramey aanee samasyanmadhil madhyavarti paddhatine hote aanee tyanna "porism" mhatale jaat asey."playfairne porismchi vyakhya ashee kelee aahe qee" "[aaa] prastav asha paristhiti shodhanyachya shakyatechi pushti karato jyamule vishisht samasya anishchit kinwa asankhya upay karnyas saksham hoil"."
jaree playfairchi porismchi vyakhya englandmadhye sarvat jaast pasantichi asali taree, simsonche mutt paradeshat sarvat jaast sweekarle gele aahe aanee tyala michel chesalacha pathimba hota. tathapi, leovilchya 'journal dii mathematics pures ett applicis' madhye (khand. XX., julai, 1855), pru. bretonne 'rechairs novels suur leesa porismus dii' euclid 'prakashit kele, jyamadhye tyane papaschya majkuracha naveen anuvad deela aanee papaschya vyakhyeshi adhik jawalun jawalun porizamchya swarupache drushya aadharit karnyacha prayatna keela. tyanantar tyach niyatkalikat aanee 'laa science' madhye breton aanee aaa yanchyatil vaad jhaala. jeey. etch. papaschya pahilya majkurane dilelya vyakhyevar aakshep aakshep aanee france vanne scootonchya kalpanechya bajoone asalyache ghoshit ghoshit vincentne tyachya 'mathematatics' abhyasamadhye (1657) pudhe thewale. scootonchya matey, jarr aakrutitil saral reshanmadhil vividh sambandh samikarane kinwa pramananchya swarupat lihile gele, tarr yaa samikarananche serve sambhavya marganni sanyojan aanee asha prakare tyanchyakadun midavalelya naveen samikarananmule aakrutiche asankhya naveen gunadharm shodhale jaatat.
breton aanee vincent yanchyatil charcha, jee see. hausel sameel jhaala, yuklidchya 'porism' chya punarsanchayanache kaam pudhe nele nahee, jeey chasselsathi sodale hote. tyanche kaam ('leesa trois liveres dii porismus dii' euclide ', parris, 1860) papasmadhye papasmadhye serve samagricha purn vapar karate.
porismsvishayi eka manoranjak gruhitak etch neey pudhe thewale hote. jee. zyuthen ("dye lehre wonn dayne kgelsnitten iim ultertum", 1886, chaa. VIII.). udaharanarth, jarr done nishchit bindu shankuchya tokavar asateel aanee tyanchyamadhun kadhalelya saral resha nishchit saral resheaivaji shankuchya tokala chhedatat, tarr intercept-porism ajunahi kharey aahe. tyanni assa andaj vartavala qee chhidra heey shankuchya purnapane vikasit prakshepak bhoomitiche up-utpadan aahe.
sandarbh.
gunvisheshanah

