
lambert kii samasya

khagoliya yantriki mein, lambert kii samasya dou sthiti vactors seey ack kaksha key nirdhaaran aur udaan key samay seey sambandhit haye, joe 18 veen shatabdi mein johann heinrich lambert dwara prastut kiya gayaa thaa aur aupchaarik roop seey joseph-luis lagrange dwara ganitiya pramaan key saath hull kiya gayaa thaa. iska millen sthal, lakshyikaran, margadarshan aur praarambhik kaksha nirdhaaran key kshetron mein mahatvapurna anuprayog hain.
maan leejiye kii ack kendriya gurutvaakarshan bull key prabhaav mein ack pind koo apane shanku prakshepavakra parr bindu "pee" 1 seey ack samay "tii" mein ack bindu "pee" 2 taka yatra karane key liye dekhaa jaataa haye. udaan kaa samay lambert kii pramey dwara anya charon seey sambandhit haye, joe kahata haih
ack anya tareeke seey kahaa gayaa haye, lambert kii samasya antar sameekaran key liye seema moolya samasya haye.
sootra _ 1
dou-pind samasya kaa jaba ack pind kaa dravyamaan aseem hotaa haye; dou-pind samasya key iss upasamuchchay koo capler kaksha key roop mein jaanaa jaataa haye.
lambert kii samasya kaa sateek sutrikaran iss prakaar haih
dou alag-alag baar sootra _ 2 aur dou sthiti vactor sootra _ 3 diye gaye hain.
samadhan sootra _ 4 kaa pataa lagaaen joe oopar diye gaye vibhedak sameekaran koo santusht kartaa haye.
sootra _ 5
praarambhik jyaamitiya vishleshan.
teen ank
samtal mein ack trikon kaa nirmaan karein joe vactor sootra _ 8 aur sootra _ 10 dwara paribhaashit haye jaisa kii chitra 1 mein darshaaya gayaa haye. binduon key sootra _ 7 aur sootra _ 9 key beach kii doori sootra _ 15 haye, binduon key sootra _ 7 aur sootra _ 6 key beach kii doori sootra _ 18 haye aur binduon key sootra _ 9 aur sootra _ 6 key beach kii doori sootra _ 21 haye. moolya sootra _ 22 sakaratmak yaa nakaratmak haye joe iss baat parr nirbhar kartaa haye kii sootra _ 7 aur sootra _ 9 mein seey kaun saa bindu sootra _ 6 seey sabse door haye. hull karane key liye jyaamitiya samasya sabhi deerghavritt koo khojana haye joe bindu sootra _ 7 aur sootra _ 9 seey gujarate hain aur bindu sootra _ 6 parr dhyaan kendrit karate hain.
bindu sootra _ 6, sootra _ 7 aur sootra _ 9 ack hyperbola koo paribhaashit karate hain joe bindu sootra _ 6 seey gujarta haye aur bindu sootra _ 7 aur sootra _ 9 parr kendra key saath. bindu sootra _ 6 yaa tou sootra _ 22 key sanket key aadhar parr hyperbola kii baain yaa daaeen shakha parr haye. iss hyperbola kaa ardh-pramukh aksh sootra _ 37 haye aur vikendrata sootra _ 38 sootra _ 39 haye. yeh hyperbola chitra 2 mein sachitra haye.
saapeksh samanya vihit nirdeshank pranali joe atidhruv key pramukh aur laghu aksh dwara paribhaashit haye, iska sameekaran haye
key saath
sootra _ 6 key roop mein hyperbola kii ack hii shakha parr kissy bhee bindu key liye doori sootra _ 41 seey bindu sootra _ 9 aur sootra _ 43 seey bindu sootra _ 7 key beach kaa antar haye
hyperbola sambandhit sambandh kii doosari shakha parr kissy bhee bindu sootra key liye _ 45 haye
aaee.ee.
lekin iska matlab haye kii bindu sootra _ 7 aur sootra _ 9 donon deerghavritt parr hain jinake kendra bindu sootra _ 6 aur sootra _ 45 aur ardh-pramukh aksh hain.
ack manmaane dhang seey chayanit bindu sootra _ 45 key anuroop deerghavritt chitra 3 mein pradarshit hotaa haye.
ack anumit deerghvrittiya sthanantaran kaksha key liye samadhan.
pahala sootra _ 51 yaa disha sootra _ 52 mein kakshiya dhruv honey key mamalon koo alag kartaa haye. pahale mamle mein sootra _ 54 key madhyam seey pahale maarg key liye sthanantaran konn sootra _ 53 antaral sootra _ 55 mein hoga aur dusare mamle mein yeh antaral sootra _ 56 mein hoga. phir sootra _ 57 sootra _ 10 seey gujarta rahega.
yadi sootra _ 59 shoonya haye, tou i.ee. sootra _ 60 aur sootra _ 61 kii vipareet dishaaen hain, sabhi kakshiya vimaan jinamen sambandhit rekha hoti haye, samaan roop seey paryaapt hain aur sootra _ 10 key madhyam seey pahale maarg key liye sthanantaran konn sootra _ 53 sootra _ 64 hoga.
sootra 66 key saath kissy bhee sootra _ 53 key liye sootra _ 7 dwara gathit trikon, sootra _ 9 aur sootra _ 6 key saath chitra 1 mein hain.
aur ardh-pramukh aksh (sanket key saath!) oopar charcha kii gaee hyperbola haye
vilakshanta (sanket key saath!) hyperbola key liye haye
aur ardh-laghu aksh haye
bindu sootra key nirdeshank _ 6 saapeksh hyperbola key liye vihit nirdeshank pranali hain (dhyaan dein kii sootra _ 71 mein sootra _ 72 kaa sanket haye)

