B C E C0I0 3H b lñ K O IM H TET no Ą E JIA M B b IC U IE H W K O Jlb l npH C H K C C C P
Í I P O r P A M M A
Kypca „B b lC U IA B M ATEM ATM K A“
(flJlH BblCLUHX te X H M H e C K H X V H eÖ H b lX 3 a B e ß e H H f O
r O C y M P C T B E H H O E H 3 A A T E J l b C T B O „ C O B E T C K A H H A y K A * M O C K B A - 1944
B C E C 0 K > 3 H b in K O M H T E T no Ä E J 1 A M B b lC U IE H I U K O J I b l n p « C H K C C C P
yn i a e p x c d e n a
B c e c o i o 3 H U M K o M u m e m o M n o d e . i a . u e u c i u e u u i k q a u t i p u C H K C C C P
Ky pea
„BbiCUIAS! M A T E M A TH K A “
(a'jih B b ic u iH X T e x H tm e c K H .x y w e ó i i b i x 3 a B e ü .e H H ñ )
O ó b c m 3 8 0 n a c o s . n 3 e u s 1 8 0 a a &
J i e K n n f î . 2 0 0 a a c . y r r p a x n o i m ñ .
r c o jte r p a a n n p o r p a jn iu n o MaTCMaiaaecKoMy , a u a - OporpawM a Kypca ßbicincB M aw M arnK acocTonT m an y x casíuCTOflTeabnbii naCTeñ:
n p o r p a in r n n o a n aa n ran e cK o fi a jra y .
c b f lE P K Í A H H E n P O r P A M M b ! A H A / IM T M H E C H A P T E O M E T P U P I. flpnMoyronbHbio KOOpysiHaTbi Ha
nnocKOCTH
HpflMoyrojiLüHo aoKapTOBtr KoopjnnaTbi n a a a o c R o c m P aecT w inne n c a tiy iB y n a
T o n K a . \ i n . II w e n n o o T o e a n a f a a n n o M o t i i o-
in e n n n . Ila o n ia ib T p e y ro a b n n a a O a p a a a e a b - noe n e p e n e c c n n e cncTexiw ¡ceopm uaT .
I !. (IpflMaR IWHHH
y p a B n e n i i e n p jiM o n a i i n n n c y r a o B b r a K o a in rn n e n T O M . y p a B i i e n n e n p s r a o S b o ó m e n b h j o n b 0T p c3i ; a x . F r o a « e s a ? i B y « n n p a i i U M n ; y c a o B a a n a p a a a e a b n o c r n n n e o - n e i u n K y a n p n o c m . D e p c c e n e n n c n p n u u x F p a B n o n a o rrp n M o fi, n p o x o i i i m e i " n e p e s a a n - n y i o T o n n y b x a r a io a t H a n p a B a e H n n ; n y a o a n p jiM b ix . y p a B n e n n e n p iiM o n , n p o x o i n n i c i f a e p o3 i s o j a n n r . i o t o b k i t . H o p ir a a b n o * y p a B n e iT H o n p m i o f i ; p a c c r o a u n e o t t o p k b j o n p s iH o n .
II I . OnpeaepHTenH BToporo h Tpèîbero nopanKa
O n p e a e a n re a n B ioporo n TpcTbero n o - P fljk a . nx CBoficTBa; miiboph a aareO pair- BôCKHe a o n o a a e n n a . CacxeMU a n n e iln b ix y paB aennfi.
I V . KpHSbie
reoMCTpanecnoe snanenne ypaBaennJł Moa:ay Koopam arasia n ypaBaonna roo- sieTpifBocKax MecT. OKpyj&iw crb, panana-, n u e Bilan ypaanenna oaDyainocTn:- o t h - CKairae nenrpa n paaayca. Oaairnc, ero ypaiłneHHe a $opMa; oKcnearpacHTCii an- peiiTpncbi. Oaannc Ear. npooEnns k p y ra . ConpiiKoniibie inaM eTpu sanmica rimepfinaa,- aciranroTLJ m nepnoabi; rapeKTpirebi. co- npaæeanbie .maM6Tpbi. flapaooaa. UnaMeTpbr napaßo.ibi. ITapaöoabi y = a x 2+ h-4- c . B b n w j (c noMombio npoapBoiabix) ypaene- nnñ icacaTeabHbix n nopiraaeñ r Baauacy, nrncpßoae a .napaßoae,
3
HoBopoT b c e fi: n n B â p n a n T H O c fb n o p a .u ;a 'í r p s . 'E o f r n p n npe<>6pa.30BainiB K oopinnaT.
IIp iia o K o n n e n p e o S p a a o B a iin a K O o p in n aT k y n p o m e n n io o 6 m ero ypanneH E a Kpireofi I I r io p a jK a . R a a c c n im K a n n a u n c c a e io n a H n e
KpiTBblX II H o p a iK á .
F p a s H e n n a a p i r a u x b n a p a M C T p n a o c n flil ijiopM c; y p a B i i e i i n a a a a m i c a , n E K g p n m . P3 3B C PTbu K p y r a k i p . i l o .i a p n B i e ¿ o o p i n - j m t h , CBJI3B c iBKapTOBBiMii- G n i t p a a B . R « - .’iíipuB Te ypaBH O H BB ' K fln n q e ’CKirx c c H e n n i i . S a í n a n n a c o C T a n a c u n o y p a B n e n n i l r c o - MCTpjI'iOCKnX m c c t .
V , S a e M B H T b i B B H T o p H O H a n r e G p w
Ilp a '.ro y ro .iB n P io K o o p im iaT b i b n p o c T p a n c T B e . BeKTopH a a p o c rp a n c T B e - C a o iK em ie b BW B iiTaniio BOKTopoB, y s m o K e n n o a a m ec
h o . R o a a n n c a p n o c T b u K O in u a n a p n o c T i, b c k - T«poB. K.ojinoncFTTH n n p o p K ü n n ( i ;o o p i n n a - i ú ) B e n T o p a; o p r a , p a 3 a o K e E n e RCKTopa n o opT asi p c e S ; l a n n a BCKTopa. n a n p a r .a a M - n u r e k o c e h y c h , c o o T iro n ren iic M o k iy n m arr.
H o o eK u n jr a tirre fra o n s o j r d t m a n n n b o k to p o b . P aartyc-B C K T op to m k it. R e p e x o a o t e iw r n o - n io H n fi mc k i y B e E r o p a a n k k o o d i m r a m -n tn i cb o p M y aaa. C K aaapH O c n p o ir s B e ic n n o i b v x n c u T o p o B , e r o C B o f t e m ; B b ip a K o n n e cK a- a a p n o r o n p o B iB o ie n iia a e o c a K o o p in n a T H roM H O K irreaefi. F r o a m o k i y m y mm b c r t o - p aM ti. y c .w b ito n e p n e iiin K y .T jip n o c T B R p o - o 5 p a n o B a n n e n p jra n y ro .ii.H Ł rc K o o p iR n a r b npoc-TPancT Eß. B c k to p e o o n p o n a p C ie n n e JIB y j BCKTOPOB. FcHOBEíI napa.T.TP.IMKK-TTT 5RYX boktopop. CMomannoe npoiiBBejonirp TpCX BCKTOPOB.
V I . rinocKOCTb u npBMan b npooTcaHCTse - flopMa.ibHoe ypaBECBue o í io c k w t h VpaB-
nenne
b i o c k o c t e b oSetom b e jc .y p a B n e n n e e h o c k o c t e b o i p e3K ax.. P p a c - E o n n e BpiiM ofi b n p p c T p a n c T B e . F r a u . o ö J p a a o B a H H U è i b y.mb b h o c r o c t h m b , i b j e m EP H M B nrn, irp s n io Ë n e x o c b o c t b i o : y c a o B n a n a p a a a c - T tn o - c T E h n e p E e n i E î t y a n p n M T E n p fiM H x n n a o c F o c T C H . D c n o B H b ie s a i a ' i n Hä npH M yio n naocKOCTB.
V I I . ripocTeñiiiHD nosepxHacTH
reoMOTpiiEccTioe 3naEenue oinoro s ce- ctomh myx ypaBnennñ «CKiy Koopjiraa- Taani tomok b trpocTpanCTBo. ÍIoecpihocte BpaincBiifl. niap. OrbicKaHHc ero acnipa h pain yea. Sa.nmconi spamenia, Tpexocmiö aaaEEConi; ceMcnna exockocthmh. napaa- aeabHbiME -KoopiEBaTEHM íthockoctíim. Ilapa- ooaoBi BpamenEfl. saairnniMeoREß napa- Öoaoni n ipyrne noBepxnocrn BToporo no- PElKa. IIpiiMoaEiiefinbic oopaayiomne omo- noaocTHoro rnnspdoaoaia n rEnepöoainis- CRoro napaôoaoBia. IlEairaipnEOCRiie n
U O IIE M C C K E p E O B e p X H O C T E .
n p
n
ba a o
bn. ü ., ÂnaaETHnecKau reoMCTpBE.
YHEBHblE nOGOBMfl
E io m r e E c 0. G., AnaanTniecKaa rco-
M eTPEfl.
3 A A A M H M K
U y 6 e p fi u i a o D 0 , R .. 3aaaMB n yBpaKHennH n o auaaHTHMecKofi
reoiieipua.
M A T E M A T M M E C K M R AHAJ1M 3 I . tpyHKUHH
I’a3BETEG EOHflTEE MEC.ia. H 3p6p3K eU E 0 B e racc T B c n n b ix MHcea Ha
ephmoiI;
E o eicT aB - a e n n o B c raec T B e n n b ixmec
ca lecnniM E T iM n ipbßflM E. nep3BOHCTBa. a o e o a r o r a a f l B c a n - M iina. R piróanK C H E bie a n a M c n n a B e a n M irn u . EOEJITEP. OÓ aßCOaiOTHOH E OTHOCRTOabHOßiiorpcnraocTH; mec.to bophbix 3naR0B Oek-
THBnaa TonnocTb. Coxpamcnnoe ysmoKonne n i c a c n c e n p n S a n s e H H H x MHcea. n e p e -
Mcnnwe 'ican'iMnij. î'iukeem rpa^HHocKoe E 3oôpaKOEHc ifyiiK.EEn; irpaMaà nponop-
E E O E a a b E a i i 3 a B E C H M O C T b , a E n e S n a a $ y n K - E n a . o S p a r a a a n p o n a p i i n o n a a b t i o c T b . I I o - HHTH6 O íy i l K U E E HOCKOabREX HC3 3RnCEMIJX n e p e M e n E b ix . n o E M e n c H E e roaiJiiiEO B k n p n - G a n K c n n o M y p e i n c m i i o y p a B n e n n ü 'T 'y h k - n n o n a a b n b i o n r K a a H b ( p y n K E n o n a a b n b i e c o t r e . A n a M o p d x w a r p a i i E K a l a E n o f i î> v îik - n n n n p n n o M o m n O y B K n n o ï ïa a b n o f ! c c t k i i
II. riDOM3B0flHap
EccRoHOMHo-Maabie, n p e i e a H ; H onpcpbiB - nocT b (JiynK nnñ n to m k e paripi.ir.a R a ia a i i.
EDHBOIHEIEC R E0HJITEI0 EP0E3B0ilH02. DpOv
ißEO IH aa. IlpocTftfrrane f o p a y a H . rc n a o T p n -
|è c ç o c u siexam inecK oe s n a n e n n e npoM BO j- nofi. HpaBir.ia iiidiepcm iH poB annH T p a ro n o - MCTpiraecRiie n öS p a n in ie TpiironoM PTpnao- CKiie OyHKnini: npriMepbi crray co fu am .iiB n i ß w m i i n ; n p e je ji o ra o m c H n a c irn v c a 6os- KoneaHo-Maaoö l y r n k. can o ti x y re ; n p o n 3 - . BojHhie TpnronoMCTpiinecKHx n o o p a r a tix rpiironosieTpnneeK.H x ip y aiim n i. K ncao « e » , HaTypaatH B ie • iiorapHdWbi. -.IIoK a3aTe3bnaa
$ y u K n n a n aarapRiSM iPiociiafl. h x irpoira- , B o in tie . öpiTMepw aaK onoM ennocT eänpH B O - m iiu ix K noKa3are3BHo§ (pyuE niin, IIoHflTne o rnnepSo.TnqecK nx dryHKniinx. oponaBOSHbie rim epfloanaecK nx i ty n Ä n ä .- T c x h h k í ind>e- WiHu¡ipmi;init:i, IÎpr>H3BO,TTiHe \ hpjibhbix (pyHKHnñ h ®yiiK-HHS, s a ïa m iB ix n a p a v e ip n - qecKH. KapaTe.Tf.nHe u r n p a a - w K nirocitiiM KpirBbiM. Ilo u fm re o n a c r a b ix nporoR o.inH x.
II I . flHtjiepeHUHan
ÍIopaTicn ö ec kg n c a n o - a a .i f i x , paBHOcnab- Hbie SecKone-’nio-aa.TTjie. Jlm p ep em m aa n n p irp am en n e . reoMeTpnnecKafl n u e x an im o - r.Kaa raiT ep n p er a n n a a n T p ip em w aaa. I n - dipppnnna.T n apon3BO,Tna¡i- H e3aBHCHM0CTB aii4>epeinuiaaa o t Bbifíopa a p r y n e m a . T ex- HHK3 ïiidiepenniipoBa-Hroi. IIoH im re o n o a - noM n n $ e p p H n n aa e (pynK nnn necKoai.Kux nepeMCHHbix.
IV . flocnefloBaTaabHoo RHijiGpsHUHpoBaHHß.
i P o p M y n a h o h b m h l i x n p H p a i u e n n i i
Uno ns Bonn a n n a m p e p en n n a a BToporo no - P33Ka. M cxannneeK oe a n a n o m ie npoiraBoa- nnfi BTpparo nopiriK a. U p o n aiio in b ie n m -
•¡‘Cpeniiîia.Tb! Bi.rcmero n o p a in a . TeopaMa P o a a a . (P o p n y aa R o p e m ttix n p n p a m e n n S . io p M y a a Kohih. P actrpbiT ne neonpeje-T en- n o c re n no n p a n n a y J lo n n r a a n . Ach m u to th. OopMyaa T eiiao p a n A ianaopena; ocraTO't-
§ § § n a 4a.
V. MaHCHMyMb! H MHHHMyMb) R o sp acT an n e n yö b ip airae dry n an n il.
A i a K o r o i y u n miihhmym. H e o o x o j H M o e y e a o -
niie. SKCTpenyMa; . jo c ia T o n n u e ET»nrepir0- 3g i a bit n a o r a c K a n n e n a ne h ü y mob h sm- ninryMOB. H anpaB itenfre BorayTOCTB Kpn- Rofi. to h k h n ep ern ß a . flocxpoeirae rp a fn n o B no xapaKTepiiHM T o n n an ,
V I . KpHBH3Ha naocHoîT h p k b o ü
Im jropenanaa n y rn ; nanpaBafliomne no- crm y c l i KacaToabnoii, K pirenana. í>opMyaa KpnBH3Hm. K pyr K.pirBH3nbi, paxnyc h u e n rp KpnBiisnbi. HoiiHTue o5 ajoSiOTe. n s b o b b-
BcnTC. ; /
V I I . ripocTpaHciEeHHbia h p h b h b
ypaB ncnm i npo.CTpancTBCiniHX k p h b h x b napaMeTpnnecnoH n BeRTOpHo-napaMerpnne- CKofi dropne. Indrep em iiiär ¡tyra. In O e p e n - m ipnuaitne B eim pa n o cK aanpnony a p ry - .TienTy; n p aB iu a liTtpöpennnpoBaniin. E m - nnnnbiii Taiireraina.Tbiii.iri senTop, c o h p h-
Eacaiomajic-ii raocKOCTb; Kpiransna V i i l . H eon oeflen enH biii HHTerpan
O racK anue d>ynKHHn na ee npoir3Bojraoü n an in$opeirnH a.iy; n p ira e p a h b uexannKii,- rcoMeTpnn. HeonpeieneiraLifi roiTerpaa. npo-
h b b o . t b b o o . nocTonnnoe. Oópamenne diopMyx jndiopenmrpoBa.HHíT; Taóanna npocreihniix iinTerpa.TOB. OenoBHBie c b o h c t b 3 nRonpe.TR- aeiraoro nnTCrpa.Ta. lînTerpnpoBainre noi-*
cTanoBEoS. - HnTerpnpoBanne no nacTiiSi tlp ro e je n n e nB aip arao ro Tpexnaene k cyst- Me h j i h paanocTii iB yx iraaipanoB. HaTerbK- poBanne pannoiraabiiBix jp o fe ñ c nnaip aT - nHM TpexnaenoH b 3HajienaTeae; u poctóS - m ué npiDiepH na iiHTerpirpoBainie o an n o - na.Tbnbrx ąpoóeS co śąaMcnaTcaesi c re n e iis Bbime BTopofi. UnTcrpa.Tbi o t npoCTeSinHX nppannonaabnocTcS:
f m x 4 - n r — _ _ _ _ _
Ji/ 5 m i+ r ’ V ^ 3+^+c dx-
H aT orpirpoB anne npon3Bé,Teiniíi cT en en e n CHiiyca n E o cn n y ca. K pocTciiinne npHMCpu in d T epennnaabnbix y p a B n en n ñ .
I X . Onpeae/ieHHbiñ n m e rp a n
B u n n ciien n e n.Toniain spaBuanneñilofc dinrypH n ip y r n e aaaann. npnBojflnine fe nnrerpaabnH M e y jm s f h nx npeieaasr, Otrpeac.Teniibifi imTerpajj nan npeie.T c y n - MBi. reoMeTpnnocKoe snanenne o n p e je a e n - noro HHTerpa.ia. reopena o cpejne:« sn a n e - n n n . flopiuyaa Jlefiôimna-iïbioTona BaacHA nepeMeiraoro b onpeieaeinroM HHTerpaxe.
IIonjiTTic o necoocTBcnabix H nrerpaaaX i 5
X . ílp H /io w eH H H o n p e fle n e H H b ix MHTerpanoB
B r > n n c i e n n o n i o m a j e i i b ic K ap T O B b rx u n ó i a p H H x K O o p ü H u a T a x ; oÓT>eji í e i a B p a- n ie H iiB , B u n i r c i e n n e r ó n e n a T w ia n o e r o n o n e p e n n m r c e n c n n a i > : n a r r a r y m : n i o - m a i b n o n e p x n o c r n B p a m o n n a . B a j a bit ira
MOxaiTHKn, J n r a n n n .
X I . npn6n>iweHHoc BbmncneHHo MHTSrpanOB
(I>opMyaa Tpancnnił (Jiopjryia Cu«ncoua.
rpaíitnteeiíoe iraTerpnpoBanne. Ilo n a m c o
n a a n i r a o T p e .
" X I !. KoMnneKCHbie MHcna. HcKOTopbte CBS3BKHB H3 BblCLUE¡3 5fir&6o b l.
ripH/ÎOlHCHHa H TeXHHHB MHTerRMpOSaHHfl
I io m n io E c á b ie n u c í a , T p iíro n o M e rp n n e - CKan (popMa no.o iaeK C H o ro n i r c i a líeñcT B nfl i i a j E oirnaertcH biM ii n n c i a i í n . f t o p n y i a M y a B p a. O o p n y i a T e f a o p a u n « n n r o n i e - n a . ' lío p n ii n o isrn o M a . E p a m u e E o p n a . c o - n p a a ie n n o c T i. E oonefr. r a r n o m e r n ic n o aim o M a n a MTioiKHTeaii. ü p ir ô iH æ e n H o e p o m o n n e a a r e f in a a n e c K iix n r p a n c u e m e u T iiM x y p a n -
n e n n ñ .
P aaao acen n o p a m io n a ib iro fl ip eS n n a npocT efim ne: m rrerp irp o B a'rap p a n n o n a ib - nrnx $ y im n irff. R irrerpnixtnaH iie na s e r r a r a * K aæ coB nppannoTtaabnocTeS n T p an c n e n - ic r m ib ix (¡lynniriiff nprrBoieireeM noiim -Tcr- p a a n n o ro B b ip aatcn n n k . p a n n o n a ib n o ity B n j y .
X I I I . BscKOHSM Hbie p a f lw . O o p M y n a Tew nopa
B ecK o n em n jo p n j u . B n ciO E u e p a i u . C paB iienno píiio b, npiranaK c x o im io c r a H aaaieóepa, KHTerpaibBbrfi n pn3naE K o m r.
npiranaK .le iió n n n a j a a snaEonepeMenHHX POJOB. A ß c o n o ra a ir cxoihmoctb. lefrcT B nn n a j p f lja a n . ( íy in c n n o n a ib iiu c pa.na.
rio n aT n e o paB H oaepnoS c x o a n a o c r a p a i a ; n p ira n a s B e S e p im p a c c a . O onaeH noe n m c - rp n p o B an n e n m fte p e n n n p o B a n n e pajoB . O ro n en n b ie p a ib i, nHTepßaa cxojhmo-
cth. P i n u T eü ao p a a M an a o p en a . P a 3 io - 6
. n e n n e fliymcnnfl b c f e n e n n b i o p a i t a ; p a a - a o s e n n o n o K a a a T e . n n e S ij> y n n n n n , ‘ T p n r o n o - u c T p n n e c K n x . a o r a p n d m a , ß a n o a a . t l p i i - 6a n a : e n n i . r e B t i n n c a e n n a n o c p e i C T B o a p a - jo B p n p i i O a n n e n i i b i e Oopsryibi c t o h - h o c t b i o 10 u a a o f i B t i c m e r o n o p a i a a 1 1h - T c rp irp o E a T m e n i w S e p e n n i m c B a n n e c / r e i i m - n t i x p a a o B ; i m T e r p i r p o B a n n e n o e p e a r r a n « p a a o B . P h j l t c E o i r n a e K c n t n i n n a e n a M i t . C r o n e m n a e p a i b i b K o m risK C H o ii o f i a a c r u , n o n a T n e o o a m v e e r x m i m c r a . l î o r a a a - T C ib U b ie . T p irro íío M e T p irn c o F ite h n w e p f m u i - n e c K n e (íw iT K nint b K o n n i e K c n o f i o6.ia r .T n ; i i o p i i ÿ a a B f u e p a : c B ira b r i m e p f i o a n n e r K i t x (jiyH K rtnn c T p n r o p o iro T p ir n e c r t t m i r .
X I V . MacTKbie ppow3B05Kb¡e u noriHbia nmpepeHUManw
’lacTObie np o n sB M n w c riepnoro n b i»i c- ran x nopaiKOB. [ lo a p u o iinJicpeH nnaar.r.
Ilp n p a m e n n e (pynKiinn n ee n o jin w p s k -
$ e p e n n n a i. I n è e p e m in p o B a m ie c io a fñ b ix n iie a B n u x $ y n K n m Í. K a c a r a ib n a a nm pK ocTb n n o p a a i b k noBepxnocTH. n o n i o s e u n e n o in o ro in ijte p e m in a ia b npnó.m»;enKi,Tx R u n n r ie m r a x . H o n a r a e o iwoMyar, T p fn o p a l i a (S ynunnn i s y x n e p c a e n n b ix . 9 sc fp eM y -
iibi iJivfTKnirn n ecK o ib E n x nepeM errnux f n e - o ó x o im tb T O y c i o B n a V ¥ e i m n i a S SK C Tpe-
nvM. O co6ue T onw i. O rn n a io m a a.
r p a f m o c K o e iraoßpaatcnne OynK nim ïp v x nepcM eimbix n p n noM^mn eeM eñcraa ro p n - s o irra a e fi. Ccraararc H o n o r p a ^ n b i V p a R n e - IIno c r p e n a nepeM ennbian. C iy a a ii eoMPft- c r a a npastbTX i n n m l — '¡paM oinnevm w rt a ó a n . e ro npeoóM ROBanne e s n i y homo- rpüMMH na n b ip ran o T m u x roneR . ü p o c T e ü - ra n e b h i h t.ie itx noaorpasiM .
X V . flmSepeHunajibHbif! ypaBHeHHB ripiiM rpu m $ e p o in in a .ib n b ix yp aB n en n ri.
ilopaioK ypaBHeHna, irn»irapo.n,nH f no- CToamibie. o ô m n e n n a c r a b ie o e m e n n a ; o n p e ie ie n n e n p o n s B o ib n u x n o c fo a n n b ix no n a n a ib n b r a n m annnnbiM y cao B É aa. Iln - ie p o n n n a ib E b ie ypaB ironna n e p ro ra n o - -paTna. Pa n c i e n n e neop.Memibix O ra o p o in o e
irn îw p eïïH n aib n o e y p a ß n e n n o nepnoro no- paiKa.. jln n e fm o o ypaB iiennp nepBoro no- p a iE a . JlniSppoim naibnbTe vpatm ennfl b t o-
poro n o p a jK a; c a y n a ä nonm r.enixa n o p a i -
S ä . 3 a-,v i n n a c o m t u e n n o n p e m e n n « jniiepoiiruia.V iH bix ypaB n en n S h3 w e x an n n n , reoMCTpiin h itH3niiH S7p a m ie ni i s b t o h h h s jm tte p e n n n a a a x , HHTerpnpyiom nfi snoacE -
r m .
XV!. JlH H eiÍH bie jH ip c p e H U M a /ib H b io ypaBH CH H fl
O anoporaoo J u n i c n n c e i H $ e p o i i n n a n b n o e y p a .n i i e n n e . E r o o6m e e p o m e s n e F p a B H e - iiH o n e o i n o p o j n i o e . Mp t o j B a p H a n n n rrp o n a - B o . i b n m n o cT O H F iH tix . F p a n n e f in e c n o - rjo H iiiiL iM n K O B i i i m n f t i m i i n . O T b iC K an n e
’i a e T n o r o p c m o n n n n e o i n o p o m o r o y p a B n e - n n a (b np& C T e’u r m x c . i y n v i i ) c n o c o ö o a J i c o r i ç è i P .i p n i i b i x K n aip m u ien T O B K n a c ß a r o j i i .-
n o e .T B iT iK cn m O m vreM H TB H ofiH U x y p a B - n e r n m c n o c T o a n n H « P K o s i i n n n n m n v n .
IloiiHTKe 06 R n w o n p o n a n n n im je p e n - n n n .iM iu x ypaB E onnii d o c o t ic t b o m pa j o b. IloTiHTire o ripníijiíiatoirnoy nTiTerpnpoBannii x n $epcnnna.ibm > re rp a p n e rra fi.
X V II. ¿¡BOHHbie H TPOKHblO HHTETpanU S á i a t í a . B B rro c -ie n n fl oSb b m o b. Ibo&h o ïï n n f e r p a a n a n irp e x e a c y x n r a . B t m n c a e n n e jB o S n o r o r m i e r p a j i a d o c pb jc tb o m <reyx h h- T e r p a n n S . -H nofinofi n n r c r p a ji b n o M p n t i x E o o p j i m a ï a x . B i v r a c n e n n e n n T o r p a i a f l y a c - c o n a .
Iin T e rp irp o B a im p n xm&epeHiiBDOBaime ÔTipejeJieHHoro m rré n > a Jia n o n a p a y e r p y . rio M T R o ó T p o f b m i t n r r e n m e . S a i a n n r a iifix a n u K íi, reoM CTpnn Ha j B o n n u o n Tpofi- JiLio n n -re rp a jib i.
|3CVIII. KpHBonHHeÜHbiñ HHTerpan
. BuHHCJICHHe paßO TB I, K p H B oaB H eñH U f) t í n r c r p a a . O opxrv.ia T p ira a . Fcjio b tip n e s a - cnctíMoCTH K pirB oairnoffiroro n ir re r p a J in o t
nyT H r n i T e r p a n n u . ÍIp n a n a K n o a n o r o j i r - ííe p e n H H a a a , tn r re rp H p o B a n u e n o - ra tix xh - Caperm na.ioB. ,
X IX . P a n u (Jiy p b e
‘ P n .l < 5 y p te . B b n m o a c H n p KngÿnnireHTOB.
Iiputt.iHdicHiio O yH K A ufi rp n ro n p n o T p iiu.e-
CKHM tí no,JHíiOMÍ,Mn c nanMenLineíí cp o itícS K najpam oH ofi norpentnacT Ł io. Ilo n irm e o XocTaTOtíHiix yoaoBHsix n p eiC T ap n iro cfn (JiynKniTH p jrjo y <I>ypie. Pä33oateHHe iJtyiiK- h h h b p ó j $ y p r,e n npoM PxyTKe% T — l Ï M + 1 o t 0 10 n. K o aeS an n a c r p y n u . IlonaTHc o TTpar.TimecKOM rap y o n n n ec K o « a n ajn rae.
O p n n e n a n n o . l a s BTy30B, r j e no yneSnoxry t m n y waTeMaiirKe o tb o x h tc h Mename 380 nacoB. nporpajiw a m o k o t 6 f j t l coK pam ena 3a c h o t m c jy r a m n x oa3xe.iOB.
B o a H j a a T H i e c s o f i r e o s i e i p n n :
a ) MeiieHTbi b c k to o e o íí aarefipbi. a p o n e c.io m en n n n BbnnrraffEn BertTopoB h n o n a -
tbji o c n a -iap n o a npon3B eiennH ;
6) ConpflHOHTBle IH3MOTDH:
b ) H ccaeaoB anne b ynpom etín« oóm ero y p annenns! apim oil BToporo n o p n jK a ;
r ) nptfMoaimeiiHLTe oS paayiom ne.
D o M a r e M a T H B B C E O w y S H ä » ï ï3 y :
a ) runepóo.iirnocK ne (pyniOTiin;
8 ) o6t.om T e a a n o n o n c p e 'J E b n i c e n o n n a » : b) paaaea X ïï (kpoîA npnS xnT .iH noro p e m e n n a y p a p n o n m l);
r ) H nfoi’p a ab m .iñ rrpnmitre cxoïbmooth pajoB . paBHoMepHaa o y o ïm io cT b ; BUTerpii- poB anne h HHiteMnmrpoBaHiîo p b î o b; d ju ei b Koirn-iBECHoil ofi.iacTn:
j > b p a a j M e -’ Jlim rü n ije iB^opcim Haab- Rbie ypaB B ennay oct3bhtb jhthb i n n e S - Hbie ypaBHBHtra b to w fo nop s ikm c no - CTOiinm nin KcwîifmireiiTaMK. o jn o t^ in w e h n e o in o p o iH K e, n n o H iim e 0 c h c to m c y p a s- n e n n fî:
c l ycjiOBHWÜ aK cro eirv y : o cn ô tre t o h k h ; k) HHTcrpHpoBanne n jnüiepcintiiipoBanHe o n p c ie jie n n o ro m fTorpa.ia no n a p av e T p y ;
3) b p a aiw re o E pm o v reetH O M n irre rp a - .ie 0CT3RHTŁ .Tiraib n o n irra e 0 E puB oairaeô- noM n u f c rp a a e h Bi.mnc.rorrac o b R o th :
h ) b pa33eae 0 p iîja x ® v p te ocTaBnTL jinm i, " i.n n c .ie n iie K03$nn.neET0B i* y p te n n p n a e p u .
7
B c a y ia e , e c a n cneam |niKa yncßnoro m o i o n n a TaKOBaí w o an n ac T c a nooSxojn- MBiM im o æ e n n e noKOTopi« bohpocob sia- TOMaTHKn, ho eohioihihx b nporpasiMy, b pa3steî>e no c b b o to 2 0 naco®, to bto ho-
k c t ôbiTB n p o B e x e n o 3a c h o t c o K p a r a c n i i a
yKa3aHHBTj bbüiiö p a s j c J i o B .
Y H E 5 H H K
r p B H B H H B H Æ y 3 H H , K ypc HHlJe- pemmonaa photo h HUTorpaatnoro Hcnncae- niM.
Y H E S H b i E R O C O B H fl
1. ü o c c e K n p n n a a o b , K y p c j j i -
§opcH nnonaaB H oro n im ie rp a n B iio ro iicn iic- a e m u i.
2. 0 si n p h o b B . H ., K y p c B u .c m e fl
«aTOM aTHKH, TT. I H I I .
3. K y p a n T , K y p c ï i n p o p c . n m i o n a a u i o i u h H H T c rp a JiB n o ro n c n r o i e B H i i .
3 A A A 4 H M K
4 . F ro n T o p n I ï y 3 B H H n , Côophhkh
3a ^ a H n o B B iciH eñ s i a m i a r a K e .
3 A M E H E H H H E O n E 4 A T K H
C/rp. CrpoKa HanenaiaHo Æojikho 6bitb Flo nbeH
BHiie
3 4 CHii3y V = a x 2 + b -f- c y = a x 2 -f- b x + c T H n o rp a^ m i
5 14 CHH3y f ] / a x 2 + b x + c • d x f | / a x 2 + b x + c • d x TunorpacJniH
PcÄaKTop H. H. Aôpauoe. llen a 60 k o i ï.
JI3SÖ54. Oôbcm Yi n. a. 3/< 3bt. ji. TËpask 10)00. rioan. k nen. 25/11—44 r. 3aK. 584.
H a ô p a H o h c M a T p i m u p o B a n o b t h i i . « K p a c H a a 3 B e 3 H a » , M . Ü M i i t p o B K a , 16.
OrnenaTaHO c siaTpim a Tiin. Ftpo^ nsaaTa. M oc Ksa, K p yra u K H Ö Baa, 18. 3 an. 3447.
