
vimaanon key santulan parr

plain () key santulan parr archimedies dwara dou khandon mein ack granth haye. pahali pustak mein leaver key niyam kaa pramaan haye aur yeh trikon aur trapezium key gurutvaakarshan key kendra parr prastaavon key saath samaapt hoti haye. doosari pustak, jisamen duss prastaav hain, paravalayik khandon key gurutvaakarshan kendron kii jaanch karati haye.
alexandaria key papus key anusaar, leaver parr archimedies key kaam aur yaantrik laabh kii unaki samajh ney unhein yeh kahane key liye prerit kiyaah "mujhe khade honey key liye ack jagah dein, aur main prithvi koo sthanantarit curr doonga" (), halanki anya pracheen pramaan iss kahawat key sandarbh key baare mein aspasht hain. 
avalokan.
leaver aur isake guna archimedies key samay seey pahale seey hii achchi tarah seey gyaat they, aur vaha shamil siddhant kaa vishleshan pradaan karane vaale pahale vyakti naheen they. pahale kii "yaantrik samasyaaen", joe kabhi aristotal koo jimmedaar thaharaati theen, lekin sambhavatah unake uttaradhikariyon mein seey ack dwara likhi gaee theen, mein gurutvaakarshan key kendra kii avadharana koo niyojit kiye binaa leaver key niyam kaa ack khula pramaan haye. euclid key liye ack aur laghu kaary haye jiska sheershak haye "santulan parr" jisamen gurutvaakarshan key kendra kaa sahaara liye binaa niyam kaa ganitiya pramaan bhee haye. 
isake vipareet, archimedies key kaam mein gurutvaakarshan key kendra kii avadharana mahatvapurna haye. "samtalon key santulan parr" i, jisamen saat abhidhaaranaaen aur pandrah prastaav hain, leaver key niyam koo sahee thaharaane key liye samatulya aur atulaniya parimaan donon key liye gurutvaakarshan key kendra kaa upayog kartaa haye, halanki kuchh loga santoshjanak roop seey tark naheen dete hain. archimedies taba samanantar chaturbhuj aur tribhuj key gurutvaakarshan kendra kaa pataa lagaane key liye aage badhata haye, joe trapezium key gurutvaakarshan key kendra parr ack pramaan key saath ack pustak koo samaapt kartaa haye. 
"onn dha equilibrium off plain" II pahali pustak key samaan vishay vastu saajha kartaa haye lekin sambhavatah baad mein likhaa gayaa thaa. isamen vishesh roop seey paravalayik khandon key gurutvaakarshan kendra key sambandh mein duss prastaav hain, aur inn khandon koo samaan kshetra key ayaton key saath pratisthaapit karke unaki jaanch kartaa haye. yeh adaan-pradaan "paravalay key chaturbhuj" mein praapt parinamon seey sambhav huaa haye, ack aisaa granth joe maanaa jaataa haye kii "vimaanon key santulan parr" pustak ack key baad prakaashit huaa thaa.""
samagri.
ack kitab.
pustak ack kaa pahala bhaag santulan key gunon aur leaver key niyam seey sambandhit haye, jabaki doosara bhaag buniyaadi samtal aakritiyon key gurutvaakarshan key kendra parr kendrit haye. leaver key niyam koo sthaapit karane vaalaa tark vishesh roop seey pahale abhidharana kaa upayog kartaa haye, joe kahata haye kii "samaan doori parr samaan vajan santulan mein hain. prastaav 4 aur 5 mein, archimidae iss abhidharana parr yeh saabit karke vistaar karate hain kii kissy bhee pranali kaa gurutvaakarshan kendra, jisamen samaan bhaar kii summ sankhya hoti haye, samaan roop seey vitarit, dou kendra bhaar key beach key madhya bindu parr sthit hoga. archimedies taba inn pramey kaa upayog prastaav 6 (anuroop mamalon key liye) aur prastaav 7 (asangat mamalon key liye) mein leaver key niyam koo saabit karane key liye kartaa haye.
saboot
dou asman, lekin tulaniya, bhaar aur ack leaver bhuja koo dou asman, lekin tulaniya, bhaagon mein vibhajit kiya gayaa haye (vipareet rekhaachitra dekhein), yadi parimaan a aur b koo kramshah bindu e aur d parr lagu kiya jaataa haye, tou pranali santulan mein hogi yadi bhaar lambai key vipareet aanupaatik hainh
maan leejiye kii rekhaaon aur bhaar kaa nirmaan ack samanya maap (yaa ikai) aine kaa upayog karke niyam kaa paalan karane key liye kiya jaataa haye, aur chaar seey teen key anupaat mein. abb, baain or lambi bhuja aur daaeen or chhoti bhuja koo dohrakar aid kii lambai koo doguna karein.
pradarshan key liye, rekhaaon koo phir seey krambaddh karein taaki cd leey (dou laal rekhaaon koo ack saath) key nikat hoe, aur mool key saath judaav (neeche diye gaye anusaar):
yeh spasht haye kii donon rekhaaen mool rekha aid kii lambai seey doguni hain, kii lh kaa kendra ee parr haye, aur usa echake kaa kendra dee parr haye. isake alawa, dhyaan dein kii aih (joe see. dee. key barabar haye) samanya maap (yaa ikai) aine koo sateek sankhya mein baar leey jaataa haye, jaisa kii ee. see. aur vistaar seey, chaa. taba yeh saabit karna baaki rahata haye kii ee parr lagu kiya gayaa aeye, aur dee parr lagu kiya gayaa bee, kaa gurutvaakarshan kaa kendra see parr hoga.
isaliye, jaise kii lh aur hk key anupaat ney mool doori cd aur ec koo doguna curr diyaa haye, isi tarah parimaan a aur b koo aathh seey chhah key anupaat mein vibhajit karein (ack parivartan joe unake chaar seey teen key mool anupaat koo sanrakshit kartaa haye), aur unhein sanrekhit karein taaki a ikaaiyaan (laal) e parr kendrit houn, jabaki b ikaaiyaan (neeli) d parr kendrit houn.
abb, choonki samaan bhaar kii ack summ sankhya, samaan doori parr, dou madhya bhaar key beach gurutvaakarshan kaa kendra haye, a vaastav mein e parr lagu hotaa haye, aur b d parr, jaisa kii prastaav kii aavashyakta hoti haye. isake alawa, kull pranali mein samaan roop seey vitarit samaan bhaar kii ack summ sankhya hoti haye, aur isaliye, usee niyam kaa paalan karate hue, c koo poorna pranali kaa gurutvaakarshan kendra honah chaahiye. iss prakaar, pranali dhalaan naheen haye, balki santulan mein haye.
kitab dou.
samtalon key santulan parr" kii pustak dou kaa mukhya uddeshya ack paravalayik khand key kissy bhee hisse key gurutvaakarshan kendra kaa nirdhaaran haye, jaisa kii prastaav 8 mein dikhaaya gayaa haye. 
pustak prastaav 1 mein leaver key niyam key ack saral pramaan key saath shuru hoti haye, joe "paravalay key chaturbhuj" mein paae jaane vaale parinamon kaa sandarbh detee haye. archimedies gurutvaakarshan key kendra kii avadharana aur paravalay key gunon koo "samtalon key santulan parr" pahale paae gaye parinamon key saath jodkar agale saat prastaavon koo saabit kartaa haye. isase bhee mahatvapurna baat yeh haye kii way anuman lagaate hain kii dou paravalay joe kshetra mein barabar hain, unakaa gurutvaakarshan kendra kissy bindu seey samaan doori parr haye, aur baad mein unake kshetron koo samaan kshetra key ayaton key saath pratisthaapit kartaa haye.
antim dou prastaav, prastaav 9 aur 10, kaafee aspasht hain, lekin kissy bhee paravalayik khand seey ack nirasha dwara cutt gaye aakriti key gurutvaakarshan kendra key nirdhaaran parr dhyaan kendrit karate hain.
viraasat.
archimedies key yaantrik kaary, jinamen "vimaanon key santulan parr" shamil hain, gyaat they lekin pracheen kaal mein bahut cumm padhe gaye they. naayak aur pappu donon yantriki parr apane kaam mein archimedies kaa sandarbh dete hain, jyaadaatar gurutvaakarshan aur yaantrik laabh key kendra key baare mein apani charchaon mein. vitruvius jaise kuchh roman lekhakon koo spasht roop seey archimedies key kaam kaa bhee kuchh gyaan thaa.
madhya yug mein, kuchh arabi lekhak santulan aur gurutvaakarshan key kendra parr archimidae key kaam seey parichit they aur vistaarit they; haalaanki, lattin paschim mein, yeye vichaar mutthi bhar seemit mamalon koo chhodkar lagbhag agyaat they. yeh kewal punarjagaran key anta mein haye kii "vimaanon key santulan parr" paae gaye parinam vyaapak roop seey failane lagey. archimedies kaa bhautiki key prati ganitiya drishtikon, vishesh roop seey, baad key vaigyaanikon jaise kii guidobaldo dell monte, bernardino baldi, saiman stevin aur galileo galile key liye ack model bunn gayaa.
satrahavin shatabdi key poorvaardh mein gurutvaakarshan kendra kii avadharana parishkaar key uchch star taka pahunch gaee, vishesh roop seey evangelista torricelli aur christian husense key karyon mein, aur tarksangat yantriki key vikas mein ack mahatvapurna bhoomika nibhai.
aalochana.
kaee shodhkartaon ney "onn dha equilibrium off plain" kii pahali pustak mein visangatiyon parr prakaash daala haye. bergren pahali pustak key lagbhag aadhe hisse kii pramanikta parr sawal uthaate hain, udaaharan key liye prastaavon kii atirekta 1-3 aur 11-12 koo dhyaan mein rakhate hue. haalaanki, vaha prastaav 6 kii mack kii aalochana koo aswikar karane mein discusterhuis kaa anusaran karate hain, joe vaastav mein saabit kartaa haye kii "yadi santulan kiran parr nilambit bhaar kii ack pranali santulan mein haye jaba kissy vishesh bindu parr samarthit hoti haye, tou inn bhaaron kaa koee bhee punarvitaran, joe unake gurutvaakarshan key samanya kendra koo sanrakshit kartaa haye, santulan koo bhee sanrakshit kartaa haye." 
isake alawa, pustak ack kaa prastaav 7 apane vartamaan roop mein adhura prateet hotaa haye, taaki pahali pustak mein sakhti seey kahane parr archimedies kewal tulaniya parimaan key liye leaver key niyam koo pradarshit kartaa haye. vimaanon key santulan parr" kii doosari pustak inn kamiyon seey prabhaavit naheen haye kyonki, pahale prastaav key apavaad key saath, leaver kaa bilkul bhee ilaaj naheen kiya jaataa haye. archimedies key maujooda karyon mein kaheen bhee gurutvaakarshan key kendra kii koee paribhasha naheen haye, jisake baare mein kuchh vidvaanon kaa tark haye kii "samtalon key santulan parr" unake kuchh tarkon kii taarkik sanrachana kaa paalan karna (yaa usey uchit thaharaana) mushkil hoe jaataa haye.

