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riENTPY NYMEPIAE 1-NTPEIJI
1. ^NtfEMN'bpî n p er1>T XToa pe.
1	. TpEEXÎNJja a!JtE»Xi,£Ka j^NTpE ciNE M^piMlAE <|>£AY-
pÎMCAOp AE CÎCT.EMţE A£ AXKpypl aCEMEN'fe , aAiKb Ka Cb «y aMECTiKtk Tpsî oaiweNÎ ky 3e«î£ miKYOcxrb, wtaci-A1T Cb a<f>AbM MIJIE NXMipî ţN aţlNC , KaCbapaTE AEO-
ccBi ne 4>ieipe Kape aAXisaps. Ama YNI1VIE cE-YN£ipe opî ne OB7KET cai AyKpx ain Kape cE-KOtyinxNe anii aAYNa-pt; xap NlîîVl'bPYA cai K/îiTrbIJ)I!VI'B apaTb k;kte AÎNTp’aHECTe OBTKf.Typî KonpÎNAf; uii ab ani b’in 3mEpiA£.: lifi*, a ol, Tphî, naTpy, hînhî, mace, raaniEj oht, not>, 3£ue, miiju[>pEAe cai' xapaK-yepi ripÎN KapE ce apatb a<i$cr£ NXMEpE.
1	2	3	4	5	6	7	8 g . .. . .
2	. A' MYATE opî BOisi Cb YMM Mal MYAre NVMEpE fî*-xp’xNXA aAÎK-b Cb a? AaynTjM . Animn» AAXNapE ce-apaTb npiN cemnya 4-m* CE-npoNytt^a3T> tIA¥C , cai
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APiTMETiK'b OMXA{{iM£ NENXMbpaTb M Nxwipî mi ae xapaimpî. Ne AEnbprbM fNCT> ae autorb kx xn mÎ/kaok cfioapTE aecne iui ÎNţiENioc; aAÎKb n e a m ^mboît ta <|> i e iu £ Kape jiirjip’b 11 x c b A’aciiKra aATÎa ci» i £ A £ 31 u e opî Mai Mape a £ k x t a a k a a p <|> i (J>0 CT |Nao-k x a a ■! e ia . Acjiapb ae altera aM a^iAaT o ijitjipb 0, ns Kape onxmî.vi NFATi, iui sape ae cîne Nxape m*i» xw îipsjj a a cb,x napriKXAap.
Iia cb CKpÎM Aap NXMbpxA 9 + 1 muapE <j>a nxmîm 3S-< «11 CKpÎM IO, npEKXM Ulî Kî + l CE- apflTb 11J aCEMEi-nT> ini Il£ A o b - c II p £ ~ 3 E 4 £ ,	T p t i - C 11 p £ - 3 £ 4 £
naTpy-CIip£-3£sI£, UNll-cnpt-SE'IE, iu a i -Cnp£*3£1E,. ... CKpÎM 12, l5, 14 , l5, 11>
^NT^MnAbpiAf. autorii aiifipa i npEfjXEqiE seue ntre-Tpx Kb ecte A’acT^Kivra .p rpTmra a Aoa .
■^NTpX 8 CEMEN'b KÎll mi A Q b - 3 £ 4 1 , AQb-3£Hl- ' Î X N 8 , AOb-3 EUÎ-Ulî AOb,.... OE-OKpîX 20,21,22	..
IlENTpy KbIji<J>pa 2 Ka .JvN 3 AOlAi) TptlTrb liptfJXtlJJE A' 3£>JlXpî. O CITlb, QCXTbXKa, OCXTb AOb.' CE-CKpix 100, JOI , 102 .... Ul'iA .
Ecte aecnf. c.b pyjjEAtţlf.M Ki) npiN aa^TOpXA auEipii
fMBOÎpi nXTEM Cb CKpÎM T03TE NXMEpIAE HEAt nXTÎNUOaCE KX 3£4E xapaKTtpî ISXMaî: (piÎNA Kb, Ka Cb MbpiM npÎN XNXA opî 4£ NXMbp , npEKXM I1E 557 5 £ AECTXA Cb IIX-NtM jvN AOKXA AX1 n , KapE ECTE +V Ap^IlTa , 11E XpMbTO-ptA cbx fN mxpxA i, 2,3,4 ... 7,8,g mi aBEM 558.
&n<a ;ţuf>pa aîn Apt rara ap <J)i g, p aokxÎ uxnem o, mi aAboiapi aj<Î xnv ce-i^ue	ut A’acŢXNr*
NYMEPE trsTPE.m	&
Ayj g . Ama |,n 55g + i , îiinem aukva asî 5 m 4, mi fN aokya avi g ’NVAa , KapE tJia'iE 5-'*o=53g4-1. A« aiisut 12999 + 1=10000 ; 999-^-1=1000.
7 . TptEvs aKVM i;1j jve c|)a4£M o AiMBb Ka cb tiytem a-pbTa ^)ΣUll-BapE NVMfcp iţlbp'b a^MMXAftî NEMbpJ.lipiÎT ISXMEAEAOp. IlENTpV a'rbcia NE^MBOIM 3 TI p O N V N-!jia ns paNA ij i <J> p e a e ie (jiaş riiNTMbp A e' t p e î xapaKrEpî, A A N A $ i E K -b p v ia kate ons-Mips K a P E C'bl apaTE TprferiT-i.
lUiauia Mai ptxTAUv auJipEAE AEa Aoa Tplînrb 4£ ce nymeck 3E41M1 av aBffCTE NVMÎpI -• IO, CE-NYMEUJE 3E4E; 20 A O li s e q î; 3o, Tpst - 3 £ 41; 40, n a t p x • 3 £ iî ; oo , li N-mÎ-se'ii; 60, iuaî-3f. hi: 70, ra a n t e-3£ 4 1 ; 80, 0J1T-SE41; 90, N O'b-3 EH1 . [IpEKVM IUI 45,87,78, g3, CE npONXNyia3t H.>TpX-3£41'lDi4iri41, 4 i N 4 1 3i î-mi-manTE, maui E-3t,4i-mi-Ao b , «oh. 3 EHl-Ioi-TpEl.
V/A,vnb airivA a^Ecra a'i rm\k npONXwjia mi m 11 , 12,
.... 3E4E mi XNX, 3E4S XIII AOI , 3E4E Uli TpU .... A«P OBÎ4E1XA A£ a A«*T 3AT£ NVINlipi, aAllvb VN cnp£3m , AOl» -CnpE3EME , TpEl CnpE3£4£ .
IJi^pa TpEfiTi A’aTptia cav a cXTiMÎAop ce-nxmujie kx s'mep'fe Gxrb; ama 245 ce-hIteuie A«b cxte naTpx 3E4Î mi HÎN41 205 (|)a4E AOb CVTfi 4ÎN4Î; 074 TpEi CVTE uismE 3£4i mi naipv. Bb3vp>M Aap kvm ce-hiteijie opî 4£ NV-M"bp 4£ CE-KOMITXNE AW TpEi jjîc|)pE.
iap Aana NXMbpXA ap£ Maî mxat ae kikt TpEi ijiiţipE, npÎN fMBoips ţ.A |MnbpyÎM , |K4tn*NA AtAa Ap^rua
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6	APITMETIIxb
cnpe Cf^Nra Ascnbpjjipt as Tpet fâi(f>p£ uii ne <J>ie Ka-|	pt O NVmÎM KY YN ASOCEB1T NYMEaACbY.	A Ana, a 2-a
j	Ascnijpjjipg hi «yme as Mii; a 5-a AsMiAioaNE; a.
J	4-a AeBiAioaNE; a5-a asTpiaîoarte 1
|	fsi 546; î ni; i5oi6; 8 oo4;' io 200 701;
j	5o 001 000; 17537100227.
|	Ce<uteck: Aob 3ecu mi visa aemu iiîn<ii cyte naTpy 3E-
J	yî mi uiatjs; o mu o crrb yiscnpE3E<ie; i5 mîi 16; 8 siiî na-
I	Tpv; 10 MÎAioarî 200 as Mii 7 cyte yny; 5o as MiAioaru o
|	Mie; 17 BÎAioaNS 307 MÎAioaNE ioqaemu 227.
I	lipi pap CE-fNTfiMUAb Cb 3BSM NYMfpE M31 Mapî AS
I	k^t ae aot> crips 3£ae ^i(J)p£ ; Aap a-mmî ae npoN?- isgi-
j	EM ^S Kaps ASCIIipaipS <|»bpb a O NYMÎ ; HETpY Kb NY-
MEAEjyxnOaTE Cb NE A^ ÎSlllî O ÎA'-E ASYNNYMbp 3 KbpYJ MbpÎME KOBSpiUâlţlE XOTapYA ‘IE AUNtI) N08CTpb HOaXE cij’a Konpiîfă’b . Am ^MBbjjax Aap a 3Î4E yn nymt»p j	CKpic /^n jji(|)p£ uii aîn nporiBb, apix&iETÎKa 3 £ h i —
1	M a A 'b 1.
i
5 • n £ N T p Y A A Y N a p E .
•	S. A'^YAYCE Mat MVSTE NXMEpE, AÎN Kaps tf>*£ KaP£ C£a~
|	parb NVMaî ky o yĂ+pb , ecte a^tya oÎNryp obiieiva rb
b’.-. .jvMIîeue a at^Aa cxua ; kt>>ii iu aisEM xpsEYÎNyb ae Nmî o psrYAb ripiiiNa aiicTa.
Cb AYb.U aiîYM NYMEp’lAE..........................
070 > 4-0 19+12487+54. Ecte psiBEASpar Kb ae bom sjlA'lE AE OCEBl CSMd YfUJUAOp, ăE'liMlAOp , CXTÎMÎAOp ... *
NYMEPE tNTPEI.II	7
■a,(£CTt smirvpi cav pF3YATaTxpi .pinpESiNaTE ne cop yot aiB cxMb. Aiua bom atjiAti i5m.u + i4 c»tf.+20 AE3EBÎM1 + 21, cav l5 OOO+ l4o0 + 200 + 2i: AYKplRNA anoi ae a ao'h'B acvnpa autcTOp Avne xpMb NXMEpE, a-BEM 1 3EH1ME AE NU+ 6 MU + 6 CVTE + 2 SEHlVpî + 1 Ca?
i6 621 , cxjia BEpxrb.
Alicii cokot"£atj c-noaie cfiais Mai ky 5j3i AtCNÎpe nxiisA, A*nb kym ^NnpOTiBb ce- 34g beae, NYMEpiAE ynya cyet aAi ya, ac<|£A Ka 12487 Sic})p£A£ AE a'JE'Bmî TpIjnTb Cb CE-KOppb-	54
CflYN3b YNa CYBT aATa ApEllT j,N SOC ; AVOb	16621
a'i'IscTa CKpÎAi aÎn socya (jjifi- i;bpia koao-NE CYwa Emîrb, Aana aaBcTb cxaib ny aa TpHS npECTE g; KbMÎ aTYNiî nvrsEitf NYMaî yni’mÎae ini 3EinMUf. ae jjînem Ka cb ae aAborbM Aa KoAONa vpMbToape mi n£NTpY an’B-cra ^NHEIIEM AYKpap'i) AEA3 KOAON3 YNiMÎAOp .
Tatb Mai MYAT6 EKCEMIIAYpi A£ BAYNapE j
5	783	77	^56 10	376	786	5 784	201
4	028	3	388	'789	632	r74g	832
5	987	9	763		58g	i4 078	55g
8	5a î	9°	267		75	20 g 12	672
24	6ig	181	16 i 11	167	O 00 0		
		4.	[7 E N T p y	Ck	b A£p	E . !	
6. EcTEipÎYT Kb AE ORf (Jli KYNOCKVT NYMbpYA KîlpE «1-AboraT ayî 243 cb a*6 6g5 ; ap <|>i tpebyît kq ykimîae AY1 + 5 Cb A’k 5 , 3EBÎJUAE AY1-f 4 = g } CYTÎMi/E Abl + 2 — 6. Gkp'im Aap nymephe aste Ka iui Aa aA^fiapEj
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APITMETlub
^nctj !i£ HtK Mai Miu aînîkoc, m xpMb CKoa-, 6g3 tem f|)i£-i;apf. fii^pb aîn tkoc aIn ql5 a in cvcya	243
11, iui 3Î>iem 5—5=2, g— i=5, 6;—2=4	452
mi ama bbem 452 p'hMbmifib,
Ce /jvNTa&MnATj ^Nct na fii(|)pa aîn cxc cb <J»îe Mai mîki»
Af K-ST H'fe AÎN JKOC npEKVM CE-BEAE f ÎS EKCtMnAVA VpMb-TOp , **'AE NV HVTEM CKljA'fe 8 A1N 7 . EctE pMBEAEpaT K"b 8TVNHI NVMbpXA MEpVT K3p£ TpEBVE Cb C£*aAa01J£ AVI
8 NEnvTMNA A» 7 , arptEvir cb a'S 17 Aa cv-Mb, uii Kb sEniaii c’a jjînvt na cb C£-aAaoi,t£ 36147 Aa EOAONa ypMbTOapE: VpMl)3b Aap Kb TpeEXE îg 3.28 cb 31H1 m nv 7—--8, 41 17—8=g, ini cb CEpiM 16 8 ig g Tp^inTa vN’miAop ; ne ypMb 4—5=i ,
mi Ni" 4----2 , mNTpV Kb O AtqiME 3M 1|ÎNVT Ka Cb CE-
aAaoi,îE Aa eoaonh KOMiixcb ae 2 mi ae fiic]>pa nikv-kockvtI); 4 Aap ecte cxMa aqtmit fiic|)p£ miaAxî 2 + 1
cav 5.
yi,£ OEtpE , KiENAJiit^piAtCSC B a cj) î M H 1 II i *
Kb, o MbpiM k y 3 E *î E , nexpMb fi i n e m y n a Ka c’o vsisi Kyfii^pa 'îs ypM^3b n v m a î . AaTb cupe cTAsra. Aiua bom vpwa coKox’fcAa AEcyc Avnb aiEcx mîkaok: i-=-5 nx ce-noaTE, 11—5=8; 6 — io nv cE-noaxE ,	16 — io = 6 , j>N c^nspuiiT
3—2=1 .
AeiMEflii mi pN EKCEMHAV A1N npOTlIVb SÎiem g — 5 = 6;	2 — 7 isv CEjiioa-
te , 12 — 7 = 5;	4 — 6 nx c£-noaTE
>4—5=8; o—q îsv ce-no-te io—q=t;
o ooo 429 2 578 573 421 856
NtfMEPE fNTPEl.II	9
—8, nv ra-noaTE, io—8=2; o — 6 îs* ce-noaie; io—6=4, mi pi c<|>*pmiT 3 — 5 = o , Kape nv $a-
*i£ TpEBKiNJJTi a CE-CKpi.
Iaxb K*T£ Ba EKCEM1IAC AE CKbAEpE .
3ooo	6000	6000	i5o 001	375 83i
i296_	4ooo	5999	76 385	186 g43
1704	2000	i	73 616	188 888
10. KxN* BpEM Cb CKbAEM YNNYMbp AÎNTp’aATY KOM-HVC A£ o YNÎME YpMaTb A£ aTXT'fe NXAE, K*T£ Jp<|>pE CASNT ’ f N MEA A1N TiKH? , £ AfCTSA aCKOarC Y N i M i A £ A 1 N IO iap tl£A£,AaiAT£ jj i 4> P £ A î N 9 Uli CE-NYMtlţlE K.OM-il A i N i p E a p i T M £ T î Kt a a«lEAYÎ NYMbp . AaIktj ....
i ooo ooo — 279 g55 at> 720047 mNTpy pbMiuiijb. Anficrb coRorbAb ecte ama aeaecne, pi K.CTNi'rî kt> nv. tem cb o nvm’im AYKpaps: o <J>a>i£M pcb KacbaAV’ieM O CKbAEpE fN aAVNapE .
Cb <f>i£ HEpYT 3487 —259: ECTE i>NBEA£paT Kb flVTEM
aAbora mi cshA^ iooo, Kaps t|>a'iE.........................
3487-fiooo — 25g —iooo: aehî KOMriAiiviplj avi 25g ecte 7'h = iooo—259; mi ama 3bem Ai<J>£p£Nj4a 4tpy-Tb 5'*$7 + 74i—1000; cav 4228—1000 = 3228. Bs-
AEM Kb fNAOK Cb CKbAEM YN NYMbp, I1YTEM aAbOIB KOM-IlAINÎp'b, CKb3/KNA NYMaî UE YpMb O YMME A*1N Ap'ftnta ^6 BÎN£ pAUTb Mai CY.C A£ NYMbpYA ’IE ECTE Cb C£-CKa3b ,
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10	APITMET1K1}
AvKpap'fc ce-c^he wni kxm ce-beas fN npOTÎBt, apt» TXlU.npiN T Kt Ijicjipa 1 TptBVE Ct C£-CKa3t; 3487 |.NTp’aMECT Kin , NKMtpn >J£ C£-CKplE T74l ac^EE a^iorar KSTtuiMEÎ aeckTjsvt 5228 fi a!> nx*.t> n e n t p ¥ cxmi; T741 + 269=0.
AntcTl COKOTfcAt ECTE Mai MVAŢ TpEElÎN- 3 2 7 3 l noact k<rna CE-Aai Mai mxate aAiNtpî mi KNa A*nt aATa ; +'ie cnpe niAAt, 32731+5729 — 371—4854; 4-NTpEBviNIitM T.» 66 i.OMiiAimpiAE /x1 §71 iui 485^ Kaps cxnt T629 332.55 hut5i66 mi aBEM riENTpy ptMtuiijjt 53255.
5. ritKTpx MvATinAiKajjie.cay dbMMVAijips.
11. AAtorxNA m 7 a« 5 opî, mi he 5 ae 7 opî, a^>AT»M iot he aMEAaui npoAYKT 35; ama 2,ap 7 X 5 = 5X7) aCEM£N"fe C.E-^NTfiM-JlAt mi Aa TOaTE <I£AE ABATE NIMEpE ţ .....
oAint nvTEM ciţNToapuM ....................A
pXNOA c[>t KtTOpi AO p <J) t pt............
acE-cKÎMBa npoixRTu. Ct 4>a-	.........
mem cnps ’niAAt TaBAa A as 5 Aitm ,
a’in Kaps <|>i£ K3P£ cl> KonpiN3t 7	....
niNTipi; NXMtpyA ny.NfyptAOp ECTE ......
7X5; mp ae bom ^NToapne ................
Aint kim ct beae fN B , NiMtpyA......... B
nvNTipiAOp Ba <|)i tot a^EAa aptraT .....
XipiN 5X7> AE «NAE ypM”i53b Kt..........
5X 7=7X5.	....
5739
T629
NYMfcPE lNTPEyi	11
. ApT>TT>M nplN 7X0X2 Kb A^Hb 4£ BOM fMMSAlp npE 7 npÎN 5, TpEBTE Cb pEXMMXAljiM npOASKTVA 35 npÎN 2 ; Aap npoA^KT^A axi 7X0 ny ecte aATa ae k«t 7 + 7 + 7 + 7 + 7 > iui Ka ct>’a fMMVAQiM np’m 2 e~
CTS AECTVA Cb AYbM AE 2 Opl II£ <J)i£ K3p£ napTE , CaY
i4 + i4 + i4 + i4 + i4 . &z »na6 vpsi'faw, Kb.... 7 X 5 X 2=7X2X5. Ae BpEME «16 n»T£M CKIMBa AO-KVA am.CTOp AOl (|)bKbTOpî AIN YpMb, npEKXM ufmeAOp AOl AÎNTasre, lipi) AECNE IIXTEM fNJAfAEţtf KbpXNAYA a-HfCTOp Tpu ţ[)bKbTOpl Aa ^MMVAgipS H03TE tf>i ^NTOpC AXnbBOfc. AceMEnIj CE*^NT£MIlAl# mi nESTp» YN NXMbp UaÎMapE AE 4>bKl>TOpi.
Ct> a pbTbM cnpe iia: Kb 7X5X2 X'4=4 X 5 X 2 X 7 î
'<J)iiNA Kb CE-noaiE ţKTOapiE pXNAXA «JEAOp aîn X*Hf Tpet ^JbKbTOpt , £ AECTXA «Vb apbTbM Kb...........
5X2X7X4=5X2XtiX7> ay 10X7X*=ioX4X7î
tui au bcTa xpwÎ3b aîn meae ae cvc .
12 . K^NA tot 346a NYMbp 6CTE Sjaî A« MYAT6 Opl <£b^ Kbrop, kyivj5X3X5Xo, 3i4EM Kb5scr£ apAisair a a a 4-a IIHTEPE, mi npOAVKTXA CE-fNCEMNliAb fipjN 54. A'i'fecTb ui<£pb 4 ce - NVMtiţis CiJXNElNT K.ap£ cnyNE aekxte opt n y m b p y a ecte 4> b k b.T o p . AcemenIi mi 23 = 2XsX2 = 8. IlYTEpfe 2 ce-nvme-ipe mi lEbTPAT, mi umpli a 3% K¥fiK : kxbsntxa a4ECTopa bom beaIs Mai T.Kp3ix ^25i, 3o6). Ama 4;* ecte nVrpaT Avt 7, cav 7X7 = 7®, mi 216 ecte kybya **16» cav 6X6X6=63.
tipOTÎBb NYMbpYA Ktipt noaprb YN eilYKţf! r ţi
9
12	APlTMETIRT»
NYMeqie PbA/lîTfN'b, aAÎKt 7 ecte pbAVUNa irbrparşţ avi 4g, KYBiK'b avi 343, ae a 4-a avi a4oiv... nENTpv k>,
72=4g, 73=345, 74=24oi.............. Afecte pi>Ab-
3ÎN1 ce-aparb kv cemnva \f ;	7^=:3y/343 = 4y/'2 toi .
KfiţJA Tp'fenTa ptATjHÎNi NV C£-yjvNC£MN'fe3T», 3TXN4I pb~ Abiirca cE-coKorgipe ae nbTparb . Aaîki> 3Î4em kt> 7 e-cte p^bAfiiNa avi 4g , iui cE-cupis 7=ry'ig .
31 . (J)iiNA KTj , Ka Cb ^MMYAJpM VN NVMlp E AECTTA
ci>’a aAborbM avj ^rcvuii ae haite opî bom ţoi (3),
npt AtCNE ECTE a C£-a(J)Aa IlpOAXKTVA K*NA 4>bKtTOpi
ax NVMaî o jii<f>pb. TaBAa vpMbToapE ce-([>opiM'fc3b a-AbOrSNA AE g opî AE p*NA n£ NVMbpVA I AVI f NCVIUI AÎsia AW TSK 0pi30NT3 Ab , nE NVMbpVA 2 aH-^
Aoa, m’arna Mai j,nkoaao .
TaBAa axî ITiiaropa.
1	2	5	4	5	6	7	8	g
2	4	6	8	IO	12	i4	16	.8
3	6	9_	12	»5	18	2 1	24	27
	8	12	16	20	24	28	32	36
.*>	IO	i5	20	20	OO	35	40	45
6	11	18	24	3o	56	4-2	48	54
7	i4	21	28	35	42	4g	56	|65
8	16	24	32	4o	48	5ţ>	64	72
9	18	27	36	45	5<»	63	72	8i
BpEM CbaiţtAbM npOAXKTVA AVI 7^^ yb>|.|> m
AN AlNia h1> AÎN TJKIV 0pi30ISTaAλ,| Îhî ’	'	^
*	r	* X« KOEOpSM AE aii
NTTMEPE iNTPEyi	*3
pe aînîe *oc n«Nb kaîna benIm Aa NSWhpVa 55 , Ka-pe c£-ac[)Ab AÎNia se ce ^nieiie aea8 5 uiiatua a bem ne 7X5=55.	ţ
Ecre np1> ae TpEEviNipb cb ne AEnpÎNAEM kv npoAVRiE-AE Ny.MipiA0p ciMflAE, K3 Ci NV 4**“ CJAijil a a/spi’a TOT A’aXNH Aa TaB/,a I JiTaropiKb .
44. Ap <J)i 4>oct np'B <j.n npsAyNţiipE nsNTpy NyMEpi-
A£ ME/£ Mai Miipt a AÎKpa /[vMMXAJiip'fe aAb(>r*NA nE f w-MXAXjÎTif A AE BT;Rt1> opi KjRTt y.N’iMI r£-K01ipÎNA fN plMlfA* JjJT.op Axnt k*m- c’a aptraT ţ n AE^ÎNiji'ia (5^: At«*i bom apbTa NÎipE MiîKAoaaE Mai .jN/.EC^iroapE cnp£ a c£-n»ci npOAXKTXA,
1°. Ka ci> fMMy/ji’iM tu 2957 npiN 8 cb ne fNKÎnyÎM AS O KâM A3Tb Kb 3AbOrbM A£ 8 opî n£ 2g57 ; KOAONa ifNiwiAOp C£-Ba cfjopMa ae jil<j)pa 7 ae 8 opî aAborart iui cjfMa Ba ,<|>î 7X8 av 56; hxnem Aap ns 6, uiigÎNiM ne 5 KaCT>’A*NÎM Ky KOAONa 3EMÎMÎAOP . AqliCTbb KO/O-Nb CE-KOMriVNE AS Iji^îpa 5 CKpicb AE 8 opî ; 3ÎqEM AaP
5 X 8 = 4o, aAtor^NA nf 5 HEapbwac, a bem 45, mi jap hvnim 5 flilwA ne 4, uiha: Beaem Aap RbaitcTb a». KpapE cs-^ais-pi MYAjjiNA «f**6 Kap'e jji-(|>pb a f m my a jjiTVAV 1 npiN ^MMyAiji-	2967
Top, mi f n q £ rix n a A £ a a y n i m î, c k p i m	8
cve 4>iE kap e iji tţ) p 1» y n imi ae npniv-	25656
jt t v a y î ie aM atjuaT xu i y i n e m 3 £ q i m i-f £ KaCbAEVNiM KynpOAyKTVA ypMbTOp.
AhCCT MBKAOK «’aps NlHl o AEOCEBÎpE A£ SAVNapE, arş-
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14	APITMETim»
ra NVMaî Kb NY CKplM Mat AS MYATE opî TIS NYMbpYA «IEA AC iUwaT.
15. 2°. Ivi c»» fMWYAijtM ns 2327 np'iN 532 ecte npti f.NBEAp3T Kb TpEEYE a »Ab'»ra ns 2327 A£ 2 Op^A* 3o AS opî, ae 500 ac <»pî, lainsypMb cbaAYNbu TorvA.
SÎ Mat ^NTAUY fMMYAyiM H£ 2 >27 ÎIp’lN 2 AYIIb KYM a» pbTiipbW UII a BEM 48)4. flsYp.lb IIEYTpY 2 >27 X’3c» ; f^aisu aqbcrb GbrapE A£ek\ib, Kb ae bom aAVNa a£ 3c» A£ opî îiE Nif.vibpXA 2527, av ae 2027 A£opi na 3», ko-aotj x.xi.MiAop bj Aa iYXAa, mi a3-lÎAiiAop 2027X5, cav 6j8i ; ama Aap beaem Kb TpEBys cb KbVTb.M npoAvsrxA 6481 aA f MMVAyiryAXÎ 2 S27 9827 iipiN 3, micb*A c^piM csct 465* sţy- 53a Ţ/Knay.ye kx oTpfeiirb cupe cT.ţxra. Acewe- 4 634 Wfe mi na cb ^MyAyisi ns 2027 npiN 5oo 6381, Ţp.BVE Cb CKpivf llpOAYK fYA 23 f] X5,	1 163 5
cav i i6)3, MyT^MAVJ<£ KY AOb. xpEim 1 237 q64
pnp£ cT*sra.
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«I £ A Y 1 A a AX ; Cb CKplM npOAYKXYpÎAE Ka Y~
wiMiAEt{)i£-Kbp.va c b <|> i e n y ce cYBTyic{jpa f M M Y A y i X O p y A y î K 3 p e a n p i >i i n y i t nt HpO' Ay « r , mi ue y p« b cbiAvsbH r o tya.
TpEBYE Cb NE AEIIplNAEM npT) BINE Aa a’I^CTb pEI'VAbJ utsrpy Kape mi Maî nyNEM aii Tp£Î. ekcemiiae •
NYMEPE iNTPEI.II
889 633
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16.	Iîjbna $T>Ki>Topi, rax rai xnya imiat, Bop anii *a djijsprair nxa£, aTXNiî cKoaiEM nx/£ae iui'pwbM Klp AVIIl) pETXAi/E A1N a"lNTt, Kip npOATKTXAM ll£ XpWb a-AlOrbM ¥N aClM'tvi) RXMl>p A£ NXAf. V *T£ 8M (| OCT TpaC‘ thCf.MlIAX : 406X2 =10962: A 11 4060X27 >0 At TOT maiEA upoAXKTXA vpmâT AtTptî ny/e cav io 962 ooo. 8f£M£Ncb rai «a c"b a^)Ai>M m 1000 X 100 000, iixhem 8 mxae OExpMa aVÎ i , uii aBtM ioc ooo ooo.
6. fi t ntp v	ib i3ie cax 1-m m> p jjip e.
17.	A£ BpEME H£ lîpOAXKTXA CE-(^OpRlT^l) AIN fMMTA-
ft’iT aA^oiaT a® aT*iii opî, r*te ypiiiviî ce nonpia'A ff* JJvMMXAjJ'TOp , ypMtiâi KbaiECT IipOAXKf KOnptNAt UE v-KVa ain (|n>KiTopt ae k*t£ opî c£-apaTl> npi& iea sabat . Ama katu aparii A £ kaste opî ce-ko-npinae ^MnbpyiTopvA fNfRim>pijiT; aexrae Tp\lî)3'b Kl> IlTTEM «cjlAa mK*T AEBOM CKOHTE UE ţMlfbp-BlTOp AÎN .JvMlTbpjiiT AE KXTE Opl CE-Ba niTT'fe .
ilENTpV Bltcrb |NCXUlipE c’aif a^JAaT NYMÎpUE |M~
16	APITMETIKTj
itbpjjiT, iţ.MiiijpjiiTop ini kmt ; nE«Tpx kt» Ka cTj cpaHEiyi
Mal MXATE nbfijji IlOTpiBiTE AiNTp’o KXTbJjiME TpEBXS Cb 0|MiibpaiM ripiN N*Mbp*A nbpjiÎAOp, ini kxtxa cb a-parc Mnpivi'fe 4>ÎE-K>pia.
AcemenIj Ci-B£AE Kb npOAXKTXA 35 ah axÎ 7 npÎN 5: E A£ 7 opt Mat toaps ae K/Kt 5 uii Kb kxtxa 5 aA ax! 55 iţiMnbpijii* npÎN 7 ecte ae 7 opt Mat mik ae kxt 35 .
48.	35 = 7X5» ^.NJJEAETJEM Kb 35 f.MirbpiliT
npiîX 7, AT>5 IlENTpy KXr: lap A»Ka BpSM Cb^MIIbpam m> 38 npiîx 7, cxntem c’iAÎnt cb A^cnbpţiiM ne -pinbpiji-txa 38 fN AOb Iibput, aîn Kap£ XNa ct (Jiîe 7X5; ama 58=7 X 5 + 3 ; 3 ce-ăiie P b m b in i a ^ m n b p a i p i» Kaps nx noaTe AtCbBxpmiT a ct-<|>aq£ Qn nxvibp -ţvNTpEr).
A,E OBtJIS KJKNA fMMXAIliNA XN NXMbp np’lN 1,2,5.......
aff)AbM yJ»NTp£ llpOAKXTfA6 CXKCECÎBE O KJRTbJjiME AaTb, aTVNHt O NXMIM A E-f M X A JJ 1 T 3A 3BEAX1 NXMbp CaX AE“ 4>MllbpjjÎT Mp’lN aHEA NXMbp: 35 £CT£ AE-'t'MXAJpT AXl
7, cav AE /fMnbpjiiT npix 7. A*e-.j.m«ya^tiae axÎ 2. cjknt NXMl.pt KXCO^X; (J) b p b A&COIJX CXNT aMEA'fe KapE NXC.KNT AE-fMflbp^lTE np‘lN 2. lap NXMbp A IN TA IX CBX npÎMiTÎB ECTE aBEAa KapE NX ECTc AE-fMIlbpjjiT ^A£ KfiT
npÎN th ^Ncxint mi npÎN xnîme .
AxXNA AOb NXMEpe xnxa fMrrbpjjÎT mi satxa ^.m-ITbpijiTOp, TpEBXE CbSiltM Kb KAiTXA M M X A{J i T îipipt n b p ij i x o p AbXN npoAXKT KapE aA"bor*N-AX C E P b M b in i îi X , apECXMb ÎI f f M 11 b p JJ1 T X A « Pb-MbUliga ECTE Mat MlSb AE K»T f 5inbpu’tTOpXA ţ nsN«
NYMEPE *NTPEţn	if
Tpv Ki as nv Ba <|>i aina, m au» irbpftiie ţa ££pc c*a A£cni>puiT ^MnipsiTVA NYBa$i wa Mal stsprs pg,t. jjît aA pvimpjiiTopsAKÎ.
19.	TaBAa niiaropiRii «^>at>m kstya as Ba <|>i ac Ofti^tpT) npEKXM mi ^MnipjjiTopyA. Bptw cnps iiIaat» cTi fMntp^M ns 35 npÎN 7 ? NEKOBop^se fjt jeoc ns KOAona KXMipjr/yî 7 iisnt> Aa 35. Kapc ectc aiala opisoira-Ai HE C£--fimn£ A«*a 5 . 5 Aap CCW KilTYA 96 06 RaîTTb , av Al — 5 . Ka ct $MirfcpijiM m 65 npii» g, newTpy Kt f n a g-a ko/ont> my a^tAitM nc 65, 9Î imeat 63, a bem 65 = 7 X 9 +2» 7 scts xstta mi a pircarai©*. Tpe-bye orb ne AsnpiivASM ripi bine Aa a’Met* cionae £wm>p-
Iiipj, KanpiN jiiNEpi asmuto c& as ewsb A«cpa $T>pi>
a aAEpra Aa TaBAa IliTaropiKi.
20.	Ka ci> ce ciBspmacKa vut Aa&« gic^tpppî, a-
pT)TT)M AOT> MiXAOaţIE ; 8AlKi KjERA ftZRtp^pVOpVA 8pE
o jjic^pT» cay Mai myate .
1°. Ci. fMn-bpy'iMnpE 4o 761 nph? f| aiS «ptin ace a^)Aa yn NyMip Kaps ^MMYAjjfo npie 7 ao îoySi; AaKa kmtya a teci a ap <|>i KYifocKTi 'abo gfpi.fi ^mjttabîna yNÎMi/E atÎ npiN 7, Kape ap TpÎBsi ct>Al> npOAYKTYA 1, JliÎNA 3EHÎMÎAE . ITpOAYKTYA 3E9ÎMÎAOp KatTAYÎ npÎN 7 yMT KY 'IE/E JpNYTE ap TpEEji aCEMEPCS CT) &Ti 6 J CTTlMi-ae 7 mi 4.N c<|>«pmiT mîîae 4o . K^tva ny apt 3ehî ac Miî; nsNTpY KT) 10000 X 7 Ai 70 ooo > 4o 761: *6 w*
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18	APITMETIKT)
Ae ■ypMfe'b Eli 4o EonpiNAB npoA^KTXA avi 7 npiN jji-
^»pa MUAOp KS.TVA.Tii A1N npEWT) KX ansli ie aM jjînxt A£Aa cmMÎ . tIea Mai Maps AS-'I'MlfAJJlT aA AVI 7 «IE C£-
soripiiue fN 4o ecte 35 cax 7X5, nxi ^>iiifA 4o ecte ţmpE npoAVKTxpiAE avi 7 npir» 5 rai npin 6, mi estva a-ceaEsii TpczvE cî» $is ^mpe 5ooo rai 6)ooo, nsnrptf KbaqccTE NXMtpt MTAgixe npii» 7 Aax npoATSTxpiAE v-hya <, rai slatva > 4o 000 cax v-nva < rai &axya > a« k^t jjum»pni-txa . Ama Aap «a uai Maps ab^mmxahît aA axi 7, he ce-KonpinAS |N 4o ai» 5 nsNTpx yi^pa MiiAop kstxaxi; a-noî, ckoqsna 55 aîn4o, ipT>Mi»mijja 5 ecte toî hz aM jjiNxr ^MMXAyip'fi cxxiMÎAop kstxaxx npin 7, kx sape AEBOM XM nE'iEAE ABATE JJl(|>pE 761 aAE |Mm>p|jiTyAXl,
576i Ba 4>i npoAXKTVA axi 7 npi« ntpuÎAE heae nekxno-
CEXTE aAE KfiTXAXÎ .
<|)nNA Kt asxM ptMXNE cb ^MnbpîiiM ns 5761 npiN
7,-0 HEpEpS aCEMEÎii KV qi npOnXCb , ypM'fcsii CT) AX-spi>M tot kx a>x£Aam kxbjknt . ♦MnipjjiM Aap ne 57 npiN 7, rais^TXA 8 Ba tj)i jji(|>pa cxTiMÎAop: 7X8=56, sape ckoc aîn 57, ptjmsne 1; ama 161 ecte npoAXKTXA axi 7 npiN vnîmiae , iui sebimiae kxtxaxî. 16 ^MnipuiT npiN 7 at> a nENTpv sEmiaiAS kxtxaxi 52X7=14, sape TpacAiNi6, pT>MSNE 2 ^n c<|xxpmiT 21 i:3 Jii$Pa XNiuiAOp, AE1Î KfilVA HEpXT ECTE 5823• i
40761 ( -7
55... V 58s3
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56..
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NTfMEPE ♦NTPEţH	|9
Ce-BU£ fN AVKpap'S HE CE- (JjtKX , Kt |N AOK A£ a CKpi AXNrb 4>Σ - KapE p’bM’blniu'h nE HEAE A3ATE fiic^ps 3AE
^MntpjiiTXATÎ, e Xectxa ct> KOBopsM ns uii Maî aîn txw
AÎN EAE KaCTj$OpMT>M iishea^n napTE ^Mni>pgiT.
Beasm îapt kt> fN a^tcrb ^NTXMnAaps, <|oapTS cîm-hat» xnas fMmjpaÎTopvA N’aps Mai mxat'aekxt o iji<|)pt, nvimiaî KînmM CKtA'b <^ie-Kaps .ps napTE npoAVRT ^)Tjpi> a’A CKpi, iap aTjCTiM acEMENi tui 4>is-KapE pi-
Mtffligt NECKpicb . ^Mll’bpjiipli XNX1 NXMtp nplN 7 , 5,2, ecte tot a'iE'fe Ka mi hiena c’ap Axa a 7-a, a 5«a,
cav a 2-a napTE.nps kxm cEBaBEA’fe ixects nxxjiN £3o).
Iarb llli aATE EKCEMIIAXpi AS ^MllTjpjjipE.
12 558	8765	97 587
------= 6269; -----= 1753;------------ i3g4i
257
2°. Ct nvNEM aux.M aCE-^Mn-bpu,i îgi 478 npiN 329:
KXBXNTXA Ba	NErpEXCIT TOT aiEAa AS Mal KaiNTE , IIen-
TpV KT» KXTXA iftMMYAJţlT np'lN 32g TpEEXE C"b A^> 1Q1 478 npOAKKT, XpM’ţ>31> K"b, ^MMXAJj'lNA ]1£ 329 npi« TNIMIAE KSTXAX1 mi HUNA 3EaiMÎA£ aBEM 8 XN1M1 :	aOEMENi) mi
SEuiMtAE mi CXTlMiAE a'lECTXl KXT NEKXNOCKXT , ^MMXAlţl-
te ripiN 829 Aav 7 mi igx4. Kxtxa nx ap£ m'iî, mNTpx KT> A£ ap (f>î (J>OCT lOOONVMaî, ^.MMXAJiiNAx’A npiN 329 a&x tjii 3bxt 529 000 nENTpx ^MmjpyiT.
Ama igi4 KonpiNAS npOAXKrxA ^MntpijiTopxAxî 329 npiN uicjipa cxTiftUAOp k,ktxaxi ; KonpiNAS -put mi a-ud> BE BM {j'lNXT AEAa HEAE AUATE npOA'XKTXpl . Ci» CO-KOTÎM aKXM Kt IţllM a B(|)Aa nEHEA Mat MapE AS ■ţ-MTAJJIT
*0	APITMETIKTj
*A AYÎ 399Ce-KOnpiNA£ fN igl4, iui Kb £CT£ 5 X ^9 î 5 Aap Ba <|>i jjî<j>pa cvriMiAop, nem-py ki> igi4 <J>iiNA ^NTpe 5 mi 6 opî 32g, ecie mi4*MnbpjjiTXA fNTper îgi 473» fNTpe 5oo mi 600 opî 3ag, nii kauxa fNTpe 5oo uii 600. Ct fMMXAîjiM *ap 3ăg npiN 5, mi cb TpaţKM npOAXKTXA i645 AiNigi4; igi 478 ( 329 pbMbiuiga 269 ecte aqffe HEaM jjînxt i64 5 •. 1 58a
AEAa MEAE A3ATE. IipOAXKTXpî 3AE KK- 26 97 .
tvaxÎ npÎN fMnbpjjÎTop; xnîna anoî 26 32 . mi H’ujipeAS 78, KapE pbMXN Aa fM-	658
irbpgiTVA 26978 .pviirbpgiT npiN	658
329 , TpEBYE Cb a'λ KAITXAXΠXINIMIAE	O
mi 3EMÎMÎAS NEKXNOCKXTE .
IHi ama nmu beaÎ> Kb ^MrrbpgÎNA npE 2697 npiw 329 giiftpa 8 q£ OBa Aa au^cTb ASfKpapE, Ba $1 a3EMJMiAop mi 4>iÎNA Kb 329 X 8 = 2632, Kape perpac aîn 2697 , Ab pbMbmigb 65, BEAEM Kb 113., TpEGXfc Cb A"fe XNiMl-AE 2 KXTXAXX MEpXT, KBpE ECTE 582 .
^6 XNAE XpMfeb Kb, KaCb(J>aMEM OfMIIbpjjîpE TpiBXE Cb AEClXbpgiM ASCtipE C T Al N T 3 fM-nbpgiTXAXl ţ^i cj) p £ A £ HEBOp nXT'fe Cb ROII p i N 3 b nt ^MnbpgÎTOp; MEA Mai MapE AS ^mmyajjît a a ^MnbpyiTO px a yî ie ce Konpin-AEfNa'i’ScTb napTE, Abgi^xpa ut a i n tai k a £ -cnpE CTSNra a kaitxaxÎ; ^mmyaijim tie ypMb nE^MnbpgiropyA iipinTpAsnca, pETpayiEM AÎN fMnbpuÎTXA MEA j.MtiapTE IIE lipOAXKTÎ O E O p ASM fNC^AipiuiT gi(J>pa XpMbTOapEa
NYMEPE tNTPEyi	Ui 21
^M’m>pHiT*ASÎ nponvc AX.nr'b plMtai», uii
pEfNHEIIEM fMII'bpi|ip'fe aCSMEN^ I1SN1 K£Si
bom Tp e h e npiN ToaTE {ji<J>p£AE ^Mntpjji-
T 'SAS'].
^aKa Bp’yNVA ,aîn hei napTE ■pvrrhpyiyî, m noaTE Korip'iNAE n£ ^MntpyiTop aTXNHÎ iinnem nvat> Aa kxt, a-a'iktj kxm : -1-4-73 3t = 4o7.
3 6 2
Ecte Mai aecne as a (fme [tot ae OAart mi ^MMyAjjip'b ini CKtAEp1^» aAÎKTj KMNA aBEM CT> ^MMVAJiiM n£ 329 , npÎN 5, ini CT> CKOaTEM npOAXKTOA AÎN igi4, IIXTEM 3Î-he: 5X9=45, Kap£ ap TpEsyi ct ce cKoajrb aîn 4, Aap <|>una kt, anfeera nx c£-noaT£, vmm k* 4 in nv-
Mtp KKBUKHOC AE 3EH1M1 , mi aBEM
54—45=g, ns KapE jji nvNEM ckbt 1914.78 f 329 4; mi ^îîna KtTiE igi4 ’/aw MtpÎT 269.7 I 58a kv5o, TpEBXE nENTpx noTpiaipE a- 6.58
CEMEWfe CbMtpÎM mi IIE NXM’bpVA HEA	O
AECKTjSvt; yiNEM Aap 5, nEKapE <^a inîm KxnpoAYKTVA ypMtTOp 2 x 5 ai 10 : TpEBXE aCEMEN'fe a CE-CKOaT£ l5 aIn i , cav Mai bîne aIn 21 , mi ptMM’. e 6; fn c<|)xpimT 5X3 + 2=17, 19—17=2 mi ptMtmijia ecte 269.
Ce cKaAfi ac£M£Ni> aîn 2697 npoAXKTXA 329X8, 3*1-KXNA 8 x 9 = 72 , CROC AÎN 77 , ptMXN 5 • mi CE JjiNE 7 . 8X2=16 Mai MXAT 7 H£ 3M {jiNXT . (|>aHE 23 ; CROC aîn 29 ptMXNE 6,mi ce jjiNE 2; ps c<J)xpmiT 8X3 + 2=26 ckoc aîn 26 ptMSNE o, mi ama pfcMtin^a ecte 65 uiha.
22
APITMETIKT)
21. pbMSNE 3KVM a ipi Cb* a(|)AbM KXTVA ^Mnbpîjipi avi 1914 npiw 329. Ct> iivnem kt> anECT est ectekvno-ckvt , ap TpsBvi ctj’a fMMVAjiÎM npiN 329, a^iRb npiN 9 vnimÎ , 3 3E4ÎMÎ, mi 3 cmMÎ: antcT npoAVKT a^bo* rar Aa pbMbinipb, TpEEVE cb a”6 1914 AVnb anicTa e-CTE AECNE a BEAi Kb ig CE-^OpMfcb 1-B , AW npOA*-KTVA AVI 3 IipiN EST VA KbVTaT , 2-AÎ , A1N SEnijliAS u’l-NVTE AEAa npOAVKTVA AVI 29 Hli aÎN a'IEAi KapE <|>aK UE igi4 Cb NV <|>i£ VN ripOAVKT AECbBSpimT (EKCaKT) . (J)iiNA Kb NV nVTEM Cb CK03TEM AÎN ig a^ECTE 3£<îiMÎ
npicociToaps mi nekvnockvte , ^Mnbpa'iM iie ig npiN 3, KapE at> 6, mi <J>iiNA Kb fNTpEEviNjjap'6 vnvi ^Miibp-ji'iT np'b aiaps, noaTE cb aAVKb vn kst rpEmiT npiN KOBspmips, Kacb’A %pKbM KbVTbM ns 329X6=1974; a«i£CT npOAVKr e Mai Maps acest 1914, miauia beaem Kb 6 ECTE npli SiapE; HEpKbM AaP n£ 5 KapE CE-KVBiN£ Aa ^NTSMnAapi ai'bcTa.
A vbm Aap AECiipE CTSNra gi(f>pa ni ain T£» a ^MnbpjjiTOpvAvî, mi AbcbM n e n e a e abate: AbcbM acemenî miAEcnps ApinTa ^MnbJiiTVAVÎ VN N V M b p A’onOTpiBb $pE; ^Mnbppipi anECTOpAObnbpjjÎBaA» vn kst KapE noaTE cb <|>i£ npi Maps, Aap ^ N V p M b fA n £ p K b M 3.
Ani TpEBVE Cb EbTbM ciMa 1°: Kb NVM3X fMnbpjjipi AÎN anECTE naTpv pErvAE ^NHEnE Atcnps crsNra.
2®: (J)ie - KapE pbMbmijjb ecte Mai MiKb ae kst |,m-
N1TMEPE *NTPEţII	23
ntipuiTVA ; <J>ie-Kap£ jji napTE punbpjjÎT ce KOMnynE ăîn npoA*KTVA jvMn’bpu’iTopyAxî npÎN {j'njipa KoppecnyN-sbroape a KMTXAyi oii aîw pbMbimjja ca? Air» anii hz hm îi’mxT A£Aa h£a6 abate npoAVKrypî: ac *nae ypMiab Kb TptBW tot fi,’axm cb <£îe Mai mîkt» ac kmt .j,MnbpijiTO-P»a, mi px|Mirbpîjip'b ai pN napTE nît noaTE cbiacb o npi Mape jpcjipa Aa kmt .
3°: (J)ie - Kape jţi<|>pb be o KOjsopxM AMri pbMbrni-gb Ab o jji(|>pb k-st^avi’; npi aecne Aap mrreM ci» ţn-
J£CA£ţ[£M AC KMTE ip<f>p£ TpEBlfE cb 4>is KOMnyc.
4°: <|>ie - sape	napTE kxt mr noaTE cb Tpiab npe-
CTE g KapE ECTE a£A Maî Mape AII» TOaTE NVMEpiAE aEAE AC
o	ui^pi».
5°: IIe <J>ie-Kap£ jji<î>pb ac OKOBpxM rpecve cbo
^NCEMNbM Ky VN nVNT Ka Cb NIT KbAEM rpEUIBAb .
6°: Ecte npi ^.NBEAcpaT, Kb acbom ^naoî ca?^mpei nps A£fMMyAiiiTyA,npoAVKTyA Ba <|>ipNAoiT ini propti t...
pbMsiNA ^MMVAJiÎTOpyA NEdUMEaT . TIy T£ M A ap pM-
Mya]}i ne ^Mnip jjitta	mi pMnbpjjiiopyA
npiifTp’vN aaEAamî NyMp, <|bpb a ce-c’kimba rm-tta; nytem ac emenIj mi cb ae pMnbp jjîm, ini Esmcb pbmme lapbmî tot aaeAa: aAiKb, âJŞ a-pe tot aaEAlKST na mi -2-|, na mi Kmna pMnbpiji-tta ini pMribpy'iTopyA a? cnps CTMma ntae , rnrrEM aîn eae aAbca yw wyMbp A’onoTpiBb A£Aa <£ie-KapEî
24
APITMETIK1)
Iarb oape KapE EKCEMiiAXpî as fMm»pgipe,
fhjMwuiji'b. 5 986
386 782.67 87 121 6 7 212 07
pbMbmiijb... 219 g8
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i7 lip o e s a^ECTop naipx petxae.
22. A»£ ini AXKpap'b aAXNT>piî ecte c^oapTE cÎMiub, CE-f NTSMIIAT» ^NCb A£ MXATE Opî a C£-rp£mi, A^MeIj TpE-BXE Cb NE /JvNKpEAÎNJi’bM AS CVMb nplN OapE-KapE HEpKapE, AlliCTa C£-<|mE ^NHEnXNA AVKpapt AS 3K0C fN cxc, cavAEcnpfi CTXNra cnps Aptirra npEKXM 2758 CE-BEAS 4>N EKCEMIIAX A1N npOTlBb . Ani ^NISIIEM 3ogg A£Aa roaonb MiiAop KapE at> 6, mi (J>una in> Aa 469 cxmtj ecte 7, 7—6=1 aparb kt> a <|>oct 1 as 1029 jj’mxT Aa KOAONa cxteaop , KapE npiw xpiwapt a 7555 TpSBrâ Cb A’fe l3 Aap a^Bcrb KOAONb ATi NX- I23o
NYMEPfi fNTPEţff	25
iuaî 11; *3 — 11 av 2 ecte aBst be m giNVT AEAa SEnÎMÎ tnVA: Aa KOAON8 XHÎMUOp TptBVE Cb a^AbSI NSAl) AptriT AicpEpeNQb *
IIpoBa cKbAspi cs 4>a^£ Ravimină pbMbraijja kv wv-MbpJA ac cnbavr , mi TpEBve cb a(J)AbM m HVMbpvA ^£A uai Mape aîn beae aste »
23.	Am nvrfe cb aAEBEpÎM npoivirnrÂvitti |MM»Agipt Ae’a bom j.Mn'bpQÎ npin vnVa aîn <])bKbTopî; Kb*ri r*^ tva TptBxg cî> cf>i£ bea aA aAî: Aap npoBa noate ini Mai MVAT Ă6 K*T ATKpap'fe CI» CE-rpSmaCKb , A* *»P* Tp’lBV*
a ne 4>cp>. IlmM fNKb cb crîmbbm fiirpt chi« m $b-
tebTOpî ( 11 ) ; AcEMENi tim» Cb fMiibpftiai ne SNVA ■AÎN ipbKbTOpî npÎN VN*A AlN 4EJ EKCaKgk aî Cbî .fMîlbp-glTOpî, Cî> fMMVAJpM ilE BEA 8A BAT lipit» TOT BBEAUUI NV-Mbp mi Cb ^NBEIIEM AE BA AoIaI} AVKpap'fc 4 .
ITpoBa fMnbpgipî t£-<J>aB£ ţMMVAg'mA hs rat npiri ^MiibpgiTop, mi aAboiANA ataoî pbMbtniga, TptBs» cb a4>AbM iu ^MrrbpgiryA (18)1
fe. OapE“Eap£ |n c juipî a a £ N v m * p i * o p
24.	i° : Cb Atcnbpiiiiw VN nvMbp fhÂobnbpgî aîn kapE vwa cb KoHpiN3b vnîm'iae ; aAÎivb 474 = 4-70 -f- 4 cav 47 X io + 4; naprfe aîn tssk tot A’avna ecte ae hbpgÎT npÎN 2. lapAEtcTE mi b'1) A’âAoa NVMbpvA ecte AEfMMVAgb aviaoi>* Ama Aap NVMaiNVMbpVA kaps
4 . ..	... .
26	APITMETIK1»
c e-t e p m i n î> 3 t» r* o,2,4,6,ca? 8, noait ci» aîii> ţNcmipI ar a 4>i kicob 5.
2°. 3>*cni>pisiNA NmhpvA -j>N aot» ni>pi|,î aîn Kape «i'B AYm» vpivn» ci» 4*i£ AÎn z , 3,... jji^pe, beaem acEMtwi K<b,KaCTt<J>iEYNN?M'bp A£fMMYAIjiT AY1 4, Tpcsve Ka KiST'bQiM'6 Ht CE-apaTT» npÎN MEA# AOi»Qi$pcaAe av.Î aîn ApinTa, ci»<|>i£ a£ iM“ ntpiiiT-b npÎN 4. Qeae Tpei Ain vpMT» cakivm
AE-^MYAJţiT AY1 8 A«Ka NVM1>pVA Ba 4» i A£-
^MiitpyiT npin 8 mu a.
3°: NvMaî NmbpvA us c£-TEpMiN'i>3T> no, caî 5. noaxE <J»i AS ^um>pQijT npin 5.
4°. ^MirbpuiriA io npin g, piarmniija ecte i ; ace-hen'Ij iui>a 100, iooo...; aeyeias ypMÎteT» kt»ab 20,
200,2000,... pT>Mi>inijja TpEExs cT»4»i£ fNAoIn» ca~ =*; a»3o, 3oo, 3ooo,... cT»^>ie 3, nm. A£,“ opî vtks-
TbljiME CE-nOaTE AECITbpui VNÎMÎ , SEUiMl II1UA . npE-kym 8755 fN 8000 + 700 + 5o + 3, mi ^MrrbpjjiNA’o npiN 9, p'bM'biilijjEAE 8 + 7 + 5 + 3 $aK • Ama p-KM-hinîjia AVI 8 y 3 ECTE TOT auei KY a AYT 2JL cay 5 .
A>£YNAE KpMÎSl» K'bp’bMtmijja YNY1 MYM1>P fMnl»p-jjit npÎN g ce- a^>AT> aebom aAYNa Toan jji<|>p£A£ avi Ka Kanpe ruipe cuhiae ynuiÎ, miA*BOM cK'bA'b ne 9 a£ kxte opî ce-Ba îmi.
Opî UE NYMT»p a KTtpYl CYMa Jii(f>pEAOp ECTE A£*fMYA«
ftÎT ayj 9, ecte mi A£-fMm>pjîiT npiri 9.
NTTMEPE ♦NTPEţII	2T
5°. ^eani ce-noare beaIî kt> aqccrE aot> nponpifi-Ţbjp ae noatE anii mi NVMbpxA 3 »
25 . Teopia p’bM’biuij^ÎAOp ne aparb o Btraps ae c%> ^joapTE Kvpioacb. Cb ^.MnbpgiM n£ io npÎNTp’vN ny-
io2
»ibp a3t npsKVM npiN 7 ; pbMbmiya ecte 3; a a vî--
7
ecte Aap 33 (Be3. NOTa n°. a3), ca?g—7 —a: np£-103	10*
kxm mi a ayi-----ecte 2 X 3 ai? 6; a axi —■—- Ba <l»i
7	7
6X3= 18 cairNXMat 18 •*—i4 = 4; mi ama Maî'^NKO-ao. Bsaem a»P kt» ae bom j>Mnbpui npiN 7 NXMEpÎAE 1,10, io2 , io3 ... pbMbmijiÎAE Bop <|>i 1 3 2 6 4 uii 5; Axnb aqscrli nspioAiHEipE atjjAhM Ktpbmî ne aiECTE pbMbmijje, Kape xpM’feab aîn ?eae ae cxc , mi aîn aq^ii Kb pbMbiui-JJIAE cfiNT Mai Mmî AE K*T 7 .
Opî ie NXMbp CE-noaTE Aîcnbpui npEKVM i3 527 54a, fN 2 + 4o + 5oo + 70.00 -f pbMb-miuiAE aHECTop NVMeps -jvMnbpym npiN 7 i3 627 54a ypM"63b cb <J)it tot qtAE Maî aecxc p.E- 5i 546 a3i nETÎTE AE 2 op! , AE 4 opi , AE5opi,....	1.2 =	2
CKpiM Aap XtcrtpE Ap’SnTa crips cnwra 3.4 = 12 Jji(J>pEAe 13264 5 l32..«CVB {ji^tpEAE 2.5= 10 NVMbpsAKi npon*c; ^mmva^m nE xpMb 6.7 = 42 ne cpiE - KapE npiN qt ae cvcya ei ; craa mqA: io5 a npOAXRTXpiAnp Ba <pi pbMbm'ma	io5
fMiibpuipi, cav aqlicTb pbMbiuij£b
28	.	APITMETTKT)
Ba<J>i tot a'it'fe KvaAYÎ IM cava,; NVMtpyA jap HtA, *av x3 5a7 54a ecte A6*fftin'bp{jît npi« 7 .
AviTb aSECT MUKAOK nVTEM AYKpa iui K* opî aaps 8AT
^MmjpyiTop. Cnp. n. a ujî 5 fiunbpjjECK ne 10, nil p^bMiuiuiAE atvNHi aAE avi io, îoo, ... fMnbpjjm npi» a ini 5 cknt nyax» : Kaps ne aAiffiE xaipiuu pţivAiAS ueae ^e cvc (10, 3°.) aebom ,j,Mnp]ji npE 10 npiN g, pbMb-mijia ecte x; ÂetÎ L2£,	a?? acEMENÎi pUMb-
miyE 1: ap <J>i TpeBviT Aap ace-cupi 111... cxb (jicjipE-ae ^MnipnrrYAVÎ; ae ynae aÎN nov vpMÎi3b mÎîkaokva mea apbfar yai circ ( 4° ).
Ct> ben'im xap> Aa ^NT^MtiAapţ vn.j.e ae£M iMnipr^i* Top ns 7 . «ai ^n ApK aş a Ava 6 nefrrpv piMtuiya mipuipi a« xqoo npitf 7, tixtem cokoţx kt> ecte—1; 9 ţo1? xo4^
piiMimitjiAE avi-----:,----: csnt —r 5
7	7
iui—r2} nvţEM Aap sume *n> pT>aq»nijjiA£ x3 597 54a 1 3 iui a ecy tot aiEAii vwa aviii? 8atb , 3ţa3x a3i
.	v	-	----------y
Aap TpiBTC pXNAVpi p*NAVpl Cb aAVNUM	7	3
iui cx» cutjaem npOAVKTvpiAE. AvKpapli	6	13
ascvc CE-poaTE <f>aH£ mi Avniţ kym ^n»	io	io
npoTÎBX» ce-beae , vnae ŢpŢjcvpa apaTb	3a	3
npOAVKtVpJAE HEAE AŞ CKIţSVT, oii 3o-r-a3	3
a? O ECTE pbMbUlilia ME CE-HEpE .	3o
•^MntpjiiNA nţ io npiN ii piMbinijia ecte— i, 7 -MaT> 1 ,... AEfU X IUI — 1 E'A5JŞT pWbmijiiAE CVKCECÎBE pe aBEM Aa .^Mrrbpuip'b avi î io ioo...npiN n . ;Beaem
A >p KT> AE BOM aAVNa ToâtE Jjî<J>p£A£ YNE1 TpfllŢE (jlbpb
NTfMEPE f^TPElJI	29
AE coh, axim NYMtp wt, mi ne ypMt m to&te a*E «jeaîi ky couv, iui cYMa hî AYnt ypwt o bom cko3te aîn m1> aîn t£w, ptMtuijja Ba tot assi ky a j,Mntpijipi ny-MtpYAVl npÎN ii .
cjjÎE 732 g3i; 4>Hna Kt 1 +4 + 3=i3, 3 + 2 + 7=12; 8BEM ptMtniijJt 1 Aa NYMtpYA Z£ft4â-i. aCEMEN^b 42g 180 Aio + i + 3=sî, 8 + 9+ 'i-= 21; ani 21 aîn 3 ny ce-noaT£ cko8te , jap ynîna np£ 2X11 ky 3, aatM 25 ; a5 — 21 cay 4 sere ptMtmiya qepyrt. 636i3ecte m-
fMMYAUÎT AH 11, IIENTpY Kt l5<-----4pr Ilj	ptMt-
Ulijja ECTE NYAt,
26.	KxNA fMntpijÎM npÎN YN NYMtp <f)tpt COJJ? 7 . ptMtmÎQa nv noaTE <|u ae kst i , 3 cav 5; Aap kana e-
CTE 3 NYMtpYA ECTE AE-fMMYAJjiT AYl 3 $ Qlî fNKt pt-
MtUlilja 5 ECTE A’onOTpÎBt AYl---1 , AEHÎ Opî ME NYMtp
«IE NY ECTE A£-fMntpjjÎT npÎN 2 , MH1 npÎN 3, TpfBYE KY I <:t alBt AEOCEEÎpE AE aATYA «ie ECTE AE ^MMYAgÎT AYl 6 .
27.	Ka ct AEcntpiiÎM yn NYMtp AaT ie ny ecte aîk TA5» fN aî AYl (jîtKtTOpî, ^A fMntpJilM Maî fNTSUY npÎN 3 A’aTAT'fe opî ^N p.KXA, AE K£TE Opî C£-Ba II YtÎ) . Ct IIY-NEM K1j ECTE AE 3 opî AS ^Mntptj’lT, aTYNlî aVECT NYMtp Ba c£i npOAYKTYA IAY1 3 x 2 X 3 CaV 23 , npÎN K*“ XYA HE*A 3BEM • IIe YpMt HEpKtM ^Mlltpljip’i) aqECTYl
KjSt npiw 3; ct iiynem îapt îkt* aiicTd c£-<J>a<iE AE 2 opî; aiECT KIKT Ba 4>j npOAYKTYA AVI 3 3 npÎN-Tp’yN NOY K/KT, IIENTpY K8p£ NYMtpYA HfA npO* UYC ECTE npOAYKTYA aieCTYl AÎN YpMt K/KT, IipÎN 23 X 33 . Uli auio HEpKtM T0JJ1 NYMEpi HEI AÎN TSW 5,
30	APITMETIK'b
7,11,13 ... ini fNTp'anecT nin nxmt>pa &&1 Ba <|>i A£cm>p
iJlT fN H£Î AÎN TXB aî Cil (jjlK'bTOpî 8 .
<ţ>is cnp. n. 36o, f a f MnipjjiM npiw a ; ne xpMi kxtxa 180 npiN a; mi fN ccjj>£punT g0 npiN a; mi 4>iÎNA kt> 45 nu ce - pntbppqie npiN 2 , nepKiiM npÎN 3, ne xp-mt» ne kxtva i5 f a fMnipjjiM lap npiN 3, mi aBEM ne kvmi-pvA axntxix 5: ani AVKpap'fe fN-«tfei mi aBEM 36o=a*. 32. 5.
36o	220	a
180	2 io5	3
90	a 35	5
45	3 7	7
i5	3	
5	5	
CoKOT'feAa antcTa Mai oBinNxfa ce-
aina3T> A^ni kvm fN npoTiBl ce-beae ntwrpx Ka Mat bî-
Nt ct» ce AeacxAWe ^tKTjTOpi. A<|>at>m aceMEidi mi ne aio = a. 3. 5.7 .
AAtc-fe opt aBEM TpEBXiNjjt a a^)Aa ne tohi f Mirbpjji-
TOpi XNXl NXMlp AaT. ^A AECrrbpjpM Aap fNrsâr fN <J)i>KT>TOpi Axî bei cÎMnAÎ, ne xpMi fi fMMXAjjÎM kjktc a, 2, KSTe 3,3,... mi ^Ijkxpia ToaTe eombînipiAE bsae nxTiNnoace, cjsntem fNKpeAiNjjaiji kt> n’sm AtcaT nibi XN$T>KT>Top (an'fecTa ce-BaapiiTa a»n° 33): AXKpapfr ce-^ane atoij kxm vpM'Ii3i». tj3iiNA ki 36o = a3. 52. 5,
^aneM npoAXKTXA ( î-f 2+ 2®-f a3 ) X C 1+3+ 32 ).
Axm aniicTa fMMXAjjÎM acEMENÎj ne <J>ie Kaps aîn Ttp-menî npiN î + 5 , mi a bem ne tojjÎ ^Mnipniropi nspxyî sape c&nt.
i,	2, 3, 4, 5, 6, 8, g, io, 12, i5, 18, 20, 24,
3o, 36, 4o, 45, 60, 72, go, 120, 180, 36o,
.'.I’NTpX 210 aBEM ( 1 + 2 ) ( I + 5)£l+5)(l4-7))
/
NXMEPE ^NTPEţlT	3i
aeyna£ *»	®7» 10»	21 > 3o, 35,
4a, yOj io5, 5210,
28. Ce j.NTasMnAt yNEopî a CE-<f>au£ 4>Min>pjjip'b npin Aeocebîtsae WYMepe aîn txw 2, 3, 5, 7, c[>T>pi» ct> a-4>ai>m nt mu! ynya Kape ct» fMrn>pafccKi» m ctBsp-
1UÎT. &BNA KY YEpKap'b BEMM n£N> K-KNA n£ NYMlp ci»'a fMntpuiM npin pi>A:b«iNa ca m>Tparh, ny «^aie TpEByisB'b a MEpţtt Mai f wkoao , iui autcy Nxiwhp NErpE-niiT ecte aîn t-sht, kmî (J>iiNA ki> opî us k«tihîm6 ecte npoAVKTYA p'bA’b'iini caA£ ntTpaTt npiw sa ^ncyiuÎ, ae
Ba KptipE WYA a ÎN ^TOtiTOpi UEA 3A3AT TpEByE CI» cKaaij, sa upoAYKTVA Cb iaci» tot NyMi>pyA a ea npo* iiyc, ksna A»p ynnymbp ape ;yn ^MiTbpjjiTOp Mai Mape ask*t piAbuiita ca, TpEsve ci»aisi» iui batea
Mai Miaif.
Cnpe niAAt, 127 ecte ynnymt>p Aiura# mNTpy kt»
NY CE-|Mnl>puiipE nplN Nlll YNYA A1U NYMEpÎAE 2, 3,... nSNb Aa 11 mÎK'by^' 127 ECTE j>NTp£ 11 IUI 12 } aCE-men!> 477 noaTE ci» 4>îe ae 2 opî ^MnipTir npÎN 3, mi a»EM 477 = 32. 53; Aap 53 beaem kt» ny cE-ţMirbpgE-qis npÎN 2,3, 5, nmî 7, ăe ynas ypMtâi» 53 ecte ny« Mi»p aîn tmw, mi 477 nv c£-noaT£ AECiTbpui Mai ^nkoao .
Acvnpa nponpifirbijiAop NYMSpiAop c£»noaTE uinEBa axvTOpi aîn umpli <|>pYMoac£Aop MEwopii a ae avi E y-AEp,AarpaN*aîn koaekjjuae TypiNYAVi, Esp-aînyayÎ, napicVATÎ, mi IlETpECBypryAyî, aîn Ttopia ny-
MEpiAOp Alt AES^NApy, UEpHEThpiAE apiTMETllE 8AE
Ayî Tayce ( TpaA»c£ acIIoyaast AtAicA*).
32
APITMETIKT)
KAII II
I1ENTW JNXMEPE (pP&^EPOAGE

i. NaTxpa mi dRiMBapt <|)p£NţtepiAop
20 . Ae bom ^Mnip^l vrim^ fN nipaî A’oriofpiBT> $ mi bom Ava YNa cal Mai mxate AiuTp’aitcrt m>pij,t, aTTw-mi ai1> KXTbjjiMe o nvmIm (^pjKNţţEpc, mi c’apan» np'm Aot> wxMEpe, aîn KapE ynya me ce-2iiMe NxiaiTop, a part k£te m>pnî ecte yNiM’fe ţMithpgirb} mea aA BAT tl£ KapE ^A NYMÎM N X M t p 1>T O p , aparb KST* AiNTp’aqECTE ntpjii ce-tal. 3îkxna mîhmi aiuanTfe, fNj|E-ae^iem KT» ynîmI} ecte ^.Mni>puiTb fu 7 irbptjî A’onoipi-bi> , mi ki> aîn eae c’al AYaT 5 j KapE cs-cKpu ama 4 ; 5 ECTE NYMtptTOpYA mi 7 N»MÎTOpYA i £ , J , -j j I , CE-3ÎK O KSMliTaTE, Cal YN8 a*Oa ) cal 1 AÎN 2 , AOV a Tptij cal a ai» 3, 3 c<J)tpTypî, cal 3 anaTpa, cal 3 Am 4, 5 a orna, cal 5 aîn 8.
30 . Ka ctj ţMMYAjţiu ns f npiw 7 $ ipcBYE Kd <f»ic KapE a 7-a ci> CE-ia ac 7 opî, mi «piÎNA Kb <J>ic - KapE npOAVME YrTlM'fe , aBEM 4X7 = 5: AEVNAE YpM'fea'b KTi OpiME (pp^NţlEpE fMMXA Jj’lN A*CE npiN N Y M î* I O p V A CTjI, ATj nil NYM’bp'bTOp. ^NTp£BYiNJJT)M C6-i
NXMEPE (pP/ftNI,IEPOACE	33
mnya fMnipuipi mi a a <|>pENţi£pî, neNrpY kt» hîisvi a mânu (JiiiNA K*TV* ayî 5 , fMnbpuit npiN 7,
4>p*NţUp'& NY ECTE £ATa, ' &EKX.T KETYA fMm>pjjipi wyMixopYAYi ctî npiN nymî-rop (5).
Ketya avi 47 npiN 7 sere 6 -f f, nsNTpr kt> ^mm^a-
UÎNAVCE npiw 7 at» 4a + 5 = 57 . Auia Aap A»«a yryî
ket j-NTpgr aA yneî ^Mntpijipi aAT>orb« o tfipENi'iEpE,
Kape AS NYM'bp'bTOp CT» aîfib nt p'bMTbUlili'b oii NyMÎTOp
ne -j.Mrrbpiji'ropyA, aTTYN’ri aBEM ne ketya EKcaKf
(N.rpEiniT): 1M?-| 112- at> ket 864o, ini pbMbmijji
3u86 ; Aţii ketya ekchkt ecte 864o + îiM.
^ * «*60
As YNAE YpM^3T> 1° . El» ASE 8 NYM’lTOpXA , mi NYM"b-
pi»TopyA Bop <])i A’onoTpÎBi», (J>psNiIiep'fe npEUYEqiE o*-
rime, KapE c’apan» aÎn ^ncyuiÎ Ae^iNijjia cî;	.
2°. AaKa WYMTjp-bTOpYA KOBACpmaipE nE NVMÎTOp , ^pXNtyEpT) ECTE Mai MapE AEKET INiili UlioNYMÎM JN Y -M'b p <ţ)pENţtepoc, Ka CI» OAEOcisiM A1N ’ieae abate (JjpENJ.lEpi Kaps CENT <i. AÎn ipâNca CKOarîM ne iei j.NTpeţ[î ^Mni»pjiiNA ns NtMibpvro-pYA npiNNYMiTop; 3y îs a 'iiy'i'h~ 3-Z caî 7 mi j-, TIE'iTpY Kl» ^)pENl,llpt KOnpilVA* atElli YNJM1 j AS KXU opî 5 ce nonpiNAt ^NTpENca 4
AcEMEN'L ECTE AECNE a CE-aAYHE NYMEpî fNTpEţll |N
^pENţupî; a ai kt» Ka cb cE-({iaKb 7 |N ae a «lipriTi,
5’

34	APITMETUvb
myajjîm ne 7 npia 5, iui bbem i*± , a«Î 7 +1 =	.
31. Kxna ce-Mipcipe NVMipiTopvA nvHai, $pxN* y£pi Kpsţpc, iiEmpY kt> ce-my Mai myate nbpjp iui Mb-piMi AOp p-bMXME tot aiE'i . Tot npÎNTp’aiECT kybxnt AÎn nporÎBb, Aaxa Kpsipe mrBiitopvA «Jupi» a ci-ckîmsa NYMbpbTOpYA,	^>p£Nţ!£p'b TpEBYE Cb CE-MiKUIOp£3E .
llpt AECNE Aap CE-.ţNJl£A£ţtE £N YNEAE ^NT^MnA>pî KapE <J>p*NţUpE AÎNAOli ECTE Mai Mape; r>T>l>T> t>4 •
^.iNTp’aHiCTÎ ecte npi f,MBEAepaT kt> noaTE a CE-Mb-pl 8M£NAOÎ TEpMENÎ aYNEl <|>p.XNţI£pî, Uli npEQYA El Cb
my ce-ckîmbe , mi ian> kym . (J)ie -f; ac bom f naoî ne my-MÎTopYA 7, ^ie-Kape napre îs aparb aiicn» tfipjKN-ţcepE ecte ţMn’bpgirb fN aot» , mi sa cb aBE« tot aii mpiME apbTaTb fN a i4-aA TpEBYE ci> ayi>m aot» in>p-iP fN AOKYA YNUa; 4 f N AOKTA AYX 2; fN C^piUlT IO fNAOKYA AYl5; f£=4* ♦wTptÎNA HE 7 nYTEM BEA^ acEMENi KT» TpEBYE cb fNrpEÎM mine 5;... At'îi nns* pi (JipSNptpi NY CE-CKiMBb A« BOM f M M Y A JJ i car BOM f Mnbpyi n£ aM^NAOÎ tepMenI npin ŢOT a 1EAS1Q NYMbp,
2. PeAYHEpE AaaiEAanl NYMiTOp
32 , Ka Cb KYNOaijJEM 3KYM KapE Al» AOb «fipXNJJEp» ECTE Maî MapE, ECTE AECTYA a A E p £ A V *1 £ TOT A a 3 4 £ A NYMÎTOp MM Y A JJ i N A 8MA5NA01 T £p M IN i YN i a npiN NYMÎTOpYA IfiAaATC mi AÎN npOTÎBb. AliCTb AYKpapS NY noaTE CKiMfia npEQYA «JipANţlEpi-
wr
t
NXMEPE $PANI,IEPOACE	35
zop , iui <£ie Kape ape neNTpY NYMiTop ne npoAYKT*A
3	5
' KTMÎTopÎAOp a aMXiwoî; ama — ini — cknt tot A’omr-
4	7
3.7	5.4
repe kt---mi----ca* f* mi|${ ae*na« vpM^sTb k>
4-7	7*4

J
I !
i !
3\J
T>T*
Tot a’iecT ktbxnt ne noaTE aptTa kvm mi k.sna cjint Maî SISTAT A£ KXT AOT> ^>p£Nţ[£pî CT> A£ 8ATHEM Aa TN NV-MÎTOp AE KOMTN , Kape eCTe npOAYKTYA TTTTAOp NYMITO-p’lAop , a Am?» fMMTAyÎM te p m i n i ^ifi-Kipia \npÎN np O A T KT Y A 1EAO p AaAJJl NVMiTOpî. <J)ie J-, 4 mi 4; ama ^mmyajiîm aMXNAOÎ TepaiENi <|)p.XN-ţtepi £ npÎN 4X7» ca* ; ai 4 nP'N 3X4 cax 13; fN c«|)^puiiT aî 4 npÎN 3X7 a* 31 > miaBEM J-® ££ mi ll . AE TNAE TpM'b31» K1> £ < 4 < I •
A*m» anccT mîxaok aAYK^NA ^pzNţcpiAE Aa a»ieAaiii NTMÎTOp , noaTE «lÎNEBa CI» KTNOaCK’b mi Ml»piM£AC pEAa-tîbe aAi Aop, AYKpy cape NT ape n'iiî o rperraTE.
33. (pic aoi> ^pxNijEpî tt mi 44» A^ni» t« ce- Bop
BAYHE TOT A« aHEA NYMlTOp , IlOaTC TlNEBa XX l£Ka AaKa c«NT A’onoTpiai», caYNY, AaKa npOAYKTYpiAE pnKpsri
«tiur, 7 X 55 , 11 X 35, Kape cxnt^naok AENTMipt-Topt Bop <£i fNTps cine A’onoTpÎBi». ashÎ <|>iiNA aoi» npoATKTtfpi A’onoTpÎBi» 35 X 11 = 7 X 55, iixtem ci» <JmtM aoi» <|>p£Nţi£pî A’onoTMÎBi» 44 = r7r *
Ci ayih aoi 4)p*wVfpi ’onoTpiBi, aAita» T7f mi-
36	APITMETIKTi
IU ama awwHÎ 35Xn-—7X55; CKbsjRiu aîn aMXNAOb m>pHUE’7 X 11, ®b£m (35—7)Xn=(55—u)X7 i 3 35—7
* cay||=T?r. Ama Aap ’<|)i în a AOb 55—xi
$p*Nţ[Epî a’onotpibt», aqs-6 ie CE-$opM'&-si> aîn Ai^EpeNjja (cav cvMa) NXMbpbTO-piAOp mi NTfMlTOpiAOp ECTE A’onoTpisb KX EAE .
Cb nXNEM Kb t7x ECTE A£-N£pEAXC, &AlKb Kb *0 $pXM,I£pE A OnOTpÎBT» £1 NX c£-noaT£ apbra npÎN NXME-p£ Mai Mm. Ae bo** <f>aiE tot aM’Scrb AXKpape mi Aa 4 r COKOTÎNAO = TŢ , aBEM T7T = = 4	. Cb xp-
MbM KX COKOT^Aa AE CE-T10aT£ BXNb KXNA n£ NXMbpb-ÎOpVA CTj’a 3AXHEM Cb CplE <7 ; aTTNMl ini NVMlTOpXA Ba §>i <11, n£NTpx Kb(3i) (eihÎtxa £ ecte =T7r; bom «B'b Aap aTXtm <J>pjKfnIi£p'l; £ tot ae xn npEjj kx T7r mi apbTarb npÎN Mai Mm ŢEpMÎNi, Kape ecte 4>tmpoTiBa inOTEBXAXl. AlliCTb CKbAEpE Aap CXKCEClBb TpÎBXE Cb aAXKb $pxiq[Ep1» st nponxcb Ka TEpivitm ei cb asxN-rb 7 ffi 11, KapE cxnt ae ^MXAjjiy,î axî 7 mi 11. A* XNAE XpMisb Kb AaKa Al» A O b <|> pJRNţlEpî a’o-IlOTpBb XNa Ba <f»i AE NEpEAVC, T E p M E N î ABATE TpEBXE Cb $1* fi,g	MX A&1Q 1 T Ep M ENÎ :
A O p £1.
AÎNTp’anECT'S XpM’ii3b 1°. Kb AaBa XN IipOAVKT 35Xll ECTE AE-^MnbpaÎT npiNTp’xN NXMbp A1N TAIV KXM aM SIHE
NţTMEPE (pPANrjEPOACE	37
npiw 7 > TptBxE cb <J»ie iea nyjjifr mi vnya a‘in cJ>1iijt>to p
55 X* i
AS-'PirrbpijiT npiN TpxNCYAţ; Kt'iî-■ = 55, at>
7
35	7	7
55Xn=55X7 mi — = — * A£HÎ Aasa — ecte as
55	11	n
, rfEpeAvc, 35 mi 55 csnt AE-fMMVAjjirE avi 7 iui 11 .
2°. IIpOAYKTYA a AOIj NVMEpE AINTAUV, n« noaTE CT> CE ^MIT'bpgtcK'b np'lNip’aATE NVMEpE A£ K<KT np'lN EAE , npiN ymME , mi npiN ea ^ncyuiî .
3° . Opî «IE NVMTjp NYMQÎ ^NTp’XN <J)£A C£-nOaT£ KOM* I1YNE AE 4>bKbTOpl ClMnAi £uE31N° 37)
4° . 4,a*a yN ^Mmjpri'iTop ky aw si«n i4 , ny b» <J)i
A'lN TXHf, TpEEXE Ka YNVA A1N (JrbKbTOp'l Af-^MMYAJiiTYAyî avi i4 ci» <f>i£ AE-fMiVbpJi'iT npiN 2 mi mea a/aAi npiN 7, cay Ka a’iEcr (J)T>KiTop ci cfiit AE-^Mn bpyiT npiN i4 • Ama 8 X 35 mi 70 X i5 cxnt aE'^mmxajjîte avi i4; 8 ecte aA ayi 3 , 35 aA ayi 7 , mi 70 ua avi 14 .
5°. Aaaa 7 mi 11 ny ax (ţi'bK'bTopî komynî oaiki» cxnt
A1NTXK ^NTpE EAE , AOT> OapE KapE llVTEpl 3AE AVI 7 mi 11, npEKYM 73 Uliii4 CXNT aCEMENi» fNTpE EAE ĂXN-
txw, iiENpy kt> A£ ap (pi asvT yn fMntpyiTop komyn ap <J)i <|)oct acEMENi mi aA avi 7 mi aA avi 11 .
34. AvKpapli pEAvifpi a Mai mvatop <f)pxNiIt£pî Aa VN NVMlTOp A£ KOMVN Cb !IpECKVpT'fc3li fipL MYAT KXNA
28	APITMETIKT)
«*181)11 NVMÎTOpi NV BOp (fii fNTpt CINE A&NTX1V; <Jh£ CIipE IIIAA b 9	.	,	•	•	•	«	•	. i * î 1' î "6" 1 i' S
Cb 1IVNEM Kb KVNOaipEM NVMbpYA 24 Ka-p£ ECTE A£ ■J'MU'bpjJlT np'lN TOfâl NXMlŢOpi;
({ibKMNA «SECTE ^Mnbpuipi , BOH aB^ AE
KXTypî nt.	................,ia 8 6 4 3 s
mi f MMTAijiNA ri£ aMMNAOÎ TEpMEwi aî 4>it“
Kbpia (ţ)p&NţIEpî npÎN KOpECnVNSbTOpYA
KXTţ «BEM .	.	■•••••	'
♦n aorta avi a4 iistem fNTpEşviwBa ns 72, 48... A»p
EMaî BINE Cb aAt^IEM n$ 24 KapE ECTE MEA Mai mIk AE fM-ribpiiiT npiN tobÎ NYMiTopi.
Pm£ne «kvm cb ijiîm a a^Aa ns NVMbpvA 24; ecte
B£AEp«T Rb £ AECTVA Cb a(|>AbM UpE HEA Mal MÎK NV-Mbp AE^MnbpuÎT npiN 12 iui 8, <])bpb «KbVTa Aa *ni A8AB1 NUMlTOpl 9, 5, 4, 1111 6 KapE fMnbpJJECK npE 12; BbSl OplSENYMbp (J/llNA A£ fNnbpjpT npiN 12, Ba <|>i
mi npiN 9, 3, 4 mi 6. Acemen-!» wtem iivne ţN aokya av1 12 , 11b 3 , AbCANA ns ^'bKtTOP’fA 4 H£ CE a(j)Ab 8 ) NY pbM&NE aKVM 8AT ae k#t a a$Aa ns MEA Mai MiK A£-^MnbpBÎT npiN 3 uii8 KapE ecte 3X8 cav 24 . Ka cb
« <|) A b M 11 E HI A Mai MÎK NVMbp A£-fMflbp)jiT npiN OapE KapE KMTbBÎMi ABTE, KbVTM nc 4>bKbTOpi AOp SElClMllAi £27) n£ VpMb AV-*na xiE.NTpv <J}i£-KapE aîn u nt it Nai ap-A i K «Tb HVTEpE, BOM ^aît IlpOAVKTVA AOp KapE ECTE NVMbpYA SEpVT.
IN8MEPE (J)PANI,IEPOACii	39
âcemen'6 mintNTpx 3, 3, 5, io, i5, 8, 14, 13, mi 6, NYKbvrbM aeKiKT Aa io, i5, 8, Hii ia, ca? 3.5,3.5,3*. iui a3.3; aeynae ne ece 3.5.2* ca? 120 nsNTpy hea aiaî «ÎN NYMbp AE fMIlbpyÎT npÎN K*TluiMÎAE IipOIIVCE .
3. PfiAVMEpE Aa li MaiClMbAb ciiEpci E.
35. CaîNT OMYAJjÎME AE <J>p*NţIEpî Kape a? TOT H'IEA npsjj, ae lui CE-apbr npN aeocebîte NYMEpE, mi r’piiNA Rb Ka cb ct-KTNoacKb aAEBbpaTa Mbpi.ME a ynei ^repî, ecte Mai aecne rai na ci-apaTb npÎN Mat MÎ'rî nt-
NYMEpE, AE a'lE’fi O pEAYHEM Aa h'B Mai CÎMIlAb a U ClipE-
cis. IIvrEM Aap «lEpKa fMribpjiipi» aM«NAvpop TspEMt-NÎAOp npÎN NVMEpÎAE 2,3, 5...; Clip. Iii ^MIlbpjjiNA IU |-[£ CyCimiKOC npÎN NYMbpYA 5, «BEM ^3, 11F, ypMb npÎN 3, ce-<|>aHE fN c(|)xpmiT ripÎN 7 ne Ab I^irŞr •
Aap anliCTb AVKpapE ny iiobte (J)i Mai myat ae kst na O^lEpKapE; mi Mai 8,KpTOC KJ1NA ^p.KNţIEp1> ECTE AE ne-p£A*C, NT 11YIEM Cb OKYNOaipEM, AE K1KT AVnb MYATE fN-•lEpKbpî mi OCTEN’lTOapE . Maî KY pNACCrvipE Aap ECTE Cb KbYTbM fNAaxb n£ ’IEA Maî MapE NYMbp KapE IlOSTE Cb IMnbpyţcSb aM£NAOÎ TEpME.Nl ^jp^NţlEpi , K"£'lî £ AC”
ctya aiftaic a<iicTb {.NAoi-rb ^Mnbp{jip£, mi aa» cnpceia ii uaî ciunAb me cs-iEps.
(J)Îe nponYCE AOb KXTbHÎMi aAÎKb 2g4 mi gi. Aana gi fMnbpjJEipE npE 3g4, ECTE j.MBEAEpaT Kb gi ECTE NY— MbpYA MEA 'lEpYTÎ (JmEM Allp a’l’IiCTb fMlIbpyipE. AaP
40	APITMETIKl)
a<|)A"bM pbMbiuijja 21 iui rotea 3: ktj'ii.................
ay4 —gi X 5 + 21 . A£'JÎ £CT£ 4-MBEAEpaT Kb opî qfi N»M'li|) ua Ij)i ^Mllipuirop EKC8KT Ad AOb NXMEpE gi Bl i 21, TpiliXE aC£M£Nii Cb j.MlI'bpJi'îiCKTi Illi nS BA Tpti aT)
ugi; ktj'ii fMnijpgiNA Toarb EKsaji'ia npin 7 ubem ... ag4 g 1 X 5	21
— =----------------1---; Ama *ap napx^ a Aoa ecte
7	7	7
ag4
KVMbp f NTptl', Xt *NA6 TpEBXE CT> <£U Uli —1—- •CtMEM’S .
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si	giX3
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7
llxTEM COKOîi A'NTp’a'JECT'Ij Kl> Opî *IE fMnbpjliTOp KOM Vtt HA AX1 2g4 Uli 91, TpifiXE Cb ^MTVbpuIlCK'b nE 21
uiigi, iui aîn npoTiBt: a£ti ai iui gt , ax*tot ue asc-laiuî fMmjpyrropi komxnÎ kx 2g4 iui gi iui nx iie a/yi; uii iiENTpx aqbcTb, tea Mai Maps ^MnbpuiTOp komxn « c£-qEpE, ecte auEAa aA axi gi iui 21 .
’ÎEpEp'fe aKXM ECTE MaiClMIIAb, IIENTpX Kb21 ECT^ < 2g4 , uli Kb NX pbMJKNE Mai MXAT ae kot a ac|>Aa nE HEAMalMapE KOMXN ^MIlbpjilTOp fNTp* 21 Ulîgi. Yp-m*na ama, beaem Kb3i ecte auECTa, Aaub 21 fMnapTE HE91, cax Maî bine Kb ecte A’onoTpiab kx aqEAa Kap
NTTMEPE CpPifrNţlEPOACE '	41
fcn» /j>NTp£ 21 mi -jvNTpe p’bMimiaa 7 a ^Mirbpijipi i*î gi npiw 21 , mi ama ypMbai na ni kjsna a<J)A'bM yn fM-nbpaÎTop tKcaKT, mape Ba <J>i NYMbpYA •npyr. A<J>at»m BM1 7, HlHl 21 £CT£ AE-fMII'bpjjir npiN 7; ama kb ct qa^iem <|p;r>N- 2q't f 91 f 21 ( 7 ţiepi -f,9^ Aa qî Mai cÎMriATi a eî e- \ 3 j 4 I 3 cupscie, ^Mnipaisi ne aai^NAOÎ Tep-Mtrsi npiN 7, mi bbem -*-9- •
,1,™ Kice-a^uiM neg ea aiaî aiaps komyn
^.MlTbpîiiTOp -J\ N T p £ IOI NXMtp E j ^Mnip^ÎM
ne h e a Mă î Mape npiN mea sa uit; (|i a q e m ns ■ypani. nepiianjmiija ^Mn^pijiTop mine^M-n-bpyiropyA -jvaimj.pţjiT; HiiypMiM ^NTp’a-^ECTKÎn, nsKi KANi bom noi YN^Mmpjii-Top ekcakt. Mai OEi'nraT pTjaitmiija ce-cKpie cnps AptiiTa pMn’bpuh'opyAYÎ, Ka Aa-pMn’bpuip'fe ypMtToa-pE Cfc aiB"b AOKVA «1£A KYBIN'IOC, A'Xn'h KYBl CE-BEAS EKceMnAy hea ae cyc
mi /(vN hea ypMiTop ,	2g6i	799	564	235	94	47
YNAe 47 ecte mA aial		3	1	2	2	2
aiape mi komyn -fM-	63	*7	12	5	a	1
ribpjiirop Aa aai^N-
AOÎ TEpaieNÎ (Jipa.M/epi	Kape CE-p£AYH£ /a -J-J-.
36 . Xpailiat aîn meae 3ic£ Kt:
1°. Kaci>ar{MbM neTOii,î ^MnipaiTopi ae komvn ^n-Tps aoTj Nvaiipe, EAtCTyA a a<|>Aa ne tojji cfiiKiiTOpi
6
42
APITMETIK'b (27) a* veaxi Mai Mape aA Aop komxn ^MrrbpijiTon. Ama aA avi i5o aii 90, cjiiiNA 3o hbem ne 1 , 2, 3 , 5 , 6, 10, i5 , mi 3o , ^)‘bKijTopî aî axÎ 00, cax ciNrxpî ^mip-jjiiopî aî axÎ i5o mi go.
2° . Zic£pT>M Kt Tper.y£ cb xp\ibM kx AXKpapfe n*Nb KXNA BOM a^)Aa VN ^MUbpjjiTOp EKC3KT • BEAEM A3p Kb pbMblllij^iA£ MiKIIlOp&WCE iţ)bpb /f.VIETapE , TpEBXE Cb aaîXNipEM hea nxjjiN Aa xnîme, Kaps ecte ,j*MiibpjjiT<>p tx-TXAOp NXMEpiAOp. Ama 21 mi 5o ax xNÎjrb iiENTpv HEA Mat MapE ^MnbpjJITOp KOMXN ; mi TEpjlf.Nl Cjlp.YvN-iptEpi Ş-Ij (Jiiira aIntaux p.NTpt c'ine, xpv'bab Kb aalicrb ^jpXNIJfpe ECTE AE-NEpEA*C . EcT£ TpiCT Kb NX nXTEJl Cb NE fNKpEAiNJlbM AEClipE aitiCTb AXKpapE, AE KfKT A*nb «IE BOM ^NTpEBXÎNUa TOaTE MI/KAOa'IEAE AE COKOT'I>Ab £ to) .
3° . CIeA Maî MapE KOMXN fMnbpjjiTOp a AOb NXMEpE , Tp£Bxi.NA Cb ^MllbpIjfjC.Kb Tl£ (|>if.*KapE pbMblIiilJb , Aa-Ka -£N KXpCXA AXKpbp'l a(ţ)AbM UE XN NXMbp AiNT,KlX , Kape ny noaTE ^Mnbpjji EitcanT pbMbiuiya 4E npEME-A£, ECTE tţlbpb f(|)OAOC CbXpjlkM Mal NaixTE KV COKOtE-Aa , KapE NErpEmirr KV»NiM"fe TpEBXE Cb CE-T£pMiNE3£ .
4°. CpiiflA Kb |N ekcemiiax ae Maî NnÎNTE, 47 ^Jinbp-jjeijie ny NXMaî n£ 2g6i mi 799, ii mine 564, 255, mi g4, KtxibM ae k*te opî CE-KonpiNAE 47 ^Ncfiis-HapE AiNTp’aiECTE NXMEpE . Ecte -J\NB£AEpaT Kb O A^Tb ^N AE 2 opî ^n 4g : iixneji 2 mi t cxut a)4 mi 47 . Abeji 255 = 2Xgi + 47, aebÎ 2p/’ = 2X 2 + 1 =5, ne aa-
p£ |A nXNEM CXBT 255; aCEMENij KaCE'fjjAbM K/KTXA AX 1
564 npÎN 47, ^MMX/ijiM ne 5,ne Kapt ^Aac])/iapbM ripin
NXMEPE CpP/RNţTEPO A CE	43
2	Kape eote A’acYnpa mt aAtorbM ns 2 , Kapt ecte ae-cnpe Aptim ay î 5; 2X5 + 2 = 12, riEKapE ’a iiynem CVET 564, -jvN C(|),KpuiiT aBEM 12 X 1 + 5=l7, . . . 17 X 5 -f 12 = 63j. Aula NYMfpiAE 63, 17, 12, ... CiS» KXTxpÎAE ayi 2961,799... ţMirbpgrrs npiN 47 .
Bea£m| Kb KY aiECT MiatAOK nYTEM atjlAa npEJJXA -|J- , +n nli Mal cImuat» tcnpf c!e a-/g9fi9r, mi Kb ^nktj ecte Mai CKYpT a AYKpa ^NTp’aiECT KÎn EKCEMTIAXA aMECTa , AS K/Kr apMiibpjji bmainaoi TEpMENi npi.Y 47 . IIynem am AOb AYKptpî aCEMtbli	Uli	K8P£ C£'P£**K Aa
3	TT1I 3 2
*r UJi -r. -r •
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IIYTEM '•JiNK'b Cb4iE AEUplNAEM a KYNOaipE Kb <J>pXNţI£-
pîi IS-3-2IT £CT£ NEpSAVC Kb TsVs — iT’
™3 8Î-6 2 =ff •
5°. Ka cb ac|)AbM ns iea Maî Maps komyn ^MnbpjjÎTop «JvNTpE TpEl NYMFpE 100, pO, 4o, KbYTbM AÎiV T/HlX UE aA AYI l5o Uli 90 KapE ECTE 5o, UE YpMb I1E 8A AYI 5o mi 4o, KapE tCTE 10. IIpiN Mi'/KAOKYA auECTa iiytem a<|) Aa rie T0J|1 ^LMllbpiiiTOpi a opl KAITE NYMEpE N+CE-BOp Aa .
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37. Niuiu nyecte amu ae-aecne a£ k.kta aAYNa mia c,Kb-
aT) (jjpXNJ+Spi KapE aî TOT YN HYMirOp , UAÎKb aAVNbM
mi cubAEM iNY.Maî nym iij b mp!. Ama r’2 + ţ-2 ~ nţ- cax
7 . 2 f
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7 4.34.1 ____ 4 -- 7
1 2	1"2 - 12
44	APITMETIKTd
Iap Aaua cJ)pxM,ifpiAe nv ax tot vn NYMÎTOp, aTSNaî as <|m£M CbaÎB-b (52); auia | + -7=!I +-?s=:'2s—1 + il • AcemenK | +-? +-J C£ pW* K Aa s ® + 2" + SI = 2 + li .
fu cc^.Kpmir riENTpv 4 + 5 +4 + /u + iV +-g—s—iV
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60 + 80 + 72 + 84 + 56 + too-45-3o-5o 5yj	29
.	==	—2 + —
120	120	40
K-KNA ^pXOTjIEp'lAE H£ CE-nporiŢfN C&NT ^NCOTiÎtE KY NYMEpE ^NTpEI,I), AVKpljM ^EOCIBIT aCYnpa AOp . AaÎKTj Ka Ci VMM nE 5 4-4 KY 5 +-a, VMM ri£ 4 KY | llli aBEM -* hvnem ■] , iui u,is£M 1, ne Kaps o aAtortu ayÎ 3 mi 5 : mi a bem 9 + * ■
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MTj TpEBVE Cb aAl>On>M 1 A'l NYMbpXA MEA AE CK1>3XT ;
A£‘rî 3iuEM 3 — 2=,i 5 i+l ecte pTaMimijiu uspErb.
5	. + m m x a jj i p 6 mi f Mnipjj itp.e .
38 . Ka ct pMMVAuÎM ns | npiN 5, Tpfeve Ka ae 5 opt
0/b HAbOI'bM IIE 4 ; 4 MMV/ U i,M A^p UE NvM'bpbTOpVA 5 upii\ 3 , mi uuim 'î . AmaAapKa ci | m m x a ij,i M o (J> p X N i,t £ () £ 11 p 1 a T p’x N NVMip N T p E T, ^ M M V 1-U,ÎM N KM b JCb'ru p S A !i p î N TpANCVA. llxTEM H-actMEK'fe CU p ai] IjikiJI Jlfc NX.UITOpXA lipiri BXMbpXA MEA
NXMEPE (pPANlJEPQACE	45
^NTpsr Ba cţi 'vn AE-.pviyAjjiT aA avi ; neNTpv kt» . . .
3X2
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4
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3
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46	APITMETIKT)
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qfe AÎN T/K1X, li Maî BXpTOC Kb ECTE O citVTXpB ^NTlNAEpe KapE ceab aqEipia; riENTpv KB KOMrrbp^NA npoAXETXplAE 4 X -1 - mi 4 X 4’ npfe AECiVE KXNOaiJIEM KB MlîKAOKXA AXIÎpBpi ECTE TOT a4EAa . Ama IIENTpy -LS X — > TpE-bxe a ^MXAj{i ri£ 1 ® npicv 5, aaoî npÎN | , KapE ab» . . •
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NKMEPE CpP/YrNI,IEPOA CE	47
aw pXTpiuxc NXMai xn Kin Kaps ne aparb isiqiE mi-ac/oaHE acEMEN’t ini KXBiiNMoacE Aa tobte	iiAtpi ae .
^.ÎNTpVlECT'fe XpM't3b 1° . Kb Ka Cb ^MMVAIjiM AOb (JtpMNţlEpl, TpEBXE a ^Mllbpîii JipOAXKTXA NVMV pbTOpiAOp npÎNT p’a A NXMÎTOpiAOp.
2°. IIpOAXKTXA ECTE Mai MlK AE K.KT Opt KapE (|)bKb-TOP A8Ka £1 BOp <J>1 Mai Ml41 AE K/KT XNlM'fe .
3°. lJxTEM Cb CKÎM15T.M pXNA^A CpbKbTOpUOp Ka ffll Aa MEI f NTpEJjî £ 11 ); | AE 4 C-XNT AE XN IipEIJ KX •* A£ S. .
4°. I\a cb aBM he ] ae * ae-£ ae 4 a ynîmî TpciiYE cb nps-
2.5.5.4
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5.4.6.5
41. KxNA aiSEM NXMEpE .ţiNTpt ţii pMnpEXNaTf. KX (|) pXN i,iEpî, aehaxmem >jn NXMEps «jipsuvţtEpoacE (5o 2°); aina.
q ? V - i — H V ” — 6 3 s —	17.
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45 $ 17 î-
45 -l X17 î—^ X-s33 =■— l °=So8 -l.
A,ap AEMXATf cpl ECTE MOI aICNE aAXKpa OCEE'iT MXAjjipT) (})i£-Kbpia nbpn,î mi nExpxib a aAVNa. IlENTpx 5 ] X 8 ■JvMMxajjîm jiaî pNT^ix 5 npiw 8, mi aBEM 4, aimi 5 -] X 8 = 24 + 2=26. AcEMEN'b uii
IlENTpx EKCEM17AX MECE-BEAE fNIipOTi-Bb , XNAE AXHb ME BOM (|>aME TipOAX-
KTXA •jNTpETjUAOp 45 X 17 » miaA c|)pA;NT,TEpilOp | X 3?, Mai pMMXAIpM j,NKb <|>i£ - TîapE ^NTpEr HpÎN cflpAlN-Ijupt ME ECTE «fiNCOJjflTb KX MEA aA 3AT CpbKbTOp .
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3 • 7
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6. (JîpXNl^Epi Z £ H î M a A £ .
43.	I pESTaT'fe KapE aAAYIE KYC1NE AVKpapE aMJK N A-oi TEpMEisi ai ([ipALisycpiAop nebaiit npiuiNb Kawaîwa-
KTE Cb XOTbp.bM 11E NVMÎTOpyA mi Cb*A CXBT-^tSIlEAU.lf.Jl AXKpX 4E NE 3AX4E ^NaiNTE AOl»	4£ AlClIOl-iiIjll

NYMEPE (JjP/^NIJLE P O A CE	49
A1K1» ^)p*NţI£piAE 3£MÎMaA£ Uli NVMEpî AE KOMITAET1TE ; Aap uii *Na mi aAia csnt o.snmrce Aa persr/iA£ meae AaTE ae waî NaiNTE , Kaps a*ii cs-Bop apTjVa Mai ks AECA*mip£ Cl> j-NHEIIEM Ma] ^NT/EE¥ AEAa ^pjKNţtEp'lAE 3£ui\ia/E .
Am BTj33T (+Ţ) K"b O IJI4)P"b npEIJYEipE AE3EHE Opî Mai nxii'iN ae K/Kt AaKa ap cpi atfrr aokha mea A*a CTXNra ei ; A£ bom ypMa Aap ciipE AptriTa. tot ky au"fc -pvmoipE, api»-TiKNA TpliiîTa aMECTopa ripmTp’o BipryATj, beaem kt» iji-(£>pa ni aîn t;rb Avrii) urmii ecte aîn 3eme ; 3* 3 aparb 3 ^NTpEţii tui m'1î ae a aoia^ Ba <J)i Airn-p’ocxrb; . . . 42,05=1:2	h1> AEaTptiAi Ba <j)î AiNTp’OMÎE . * . i
o,4o5 =*,£&> m4A:
VJIapi* Aap Kaps vpMi>3ij Avm» BipriTATj ecte NVMipT»--ÎOpXA mi NX E ae TpÎBtfiNJJT» a CE-CKpi NKBliTOpXA, KapE TOT A’auNa ecte i ypMaTij AEaTST'fe nvae k,kte 3£HÎMaA£ cair iji-<|ipE caint Avnii BipruA~bj Ecte Aap np'i aecne ae a a-pTiTa O cf)p/BNJ,I£p£ 3EMÎMaATj:	8,700201 =8 + 700201
ĂÎNTp’xiN wiAioN ; 354,oo63=354+ 63 AiN seme mii ;.......
.X.iNnpOTÎB'b saci CKpiM 0 (|)pXNJ,IEp£ 3EMÎMaATj CKpiM ns NXMTjpTjTopxA abt, mi ne xrpM-b ixnem BiprxAa ac(|)£A Ka aTiKT'fe U,i<J>p£ 3£4iiMaA£ C"b alETj, K1KTE NVAE BOp (|)i W-MiTOpUA ME’a CXBT.jvNIJEAEjgLEM . 3 A™ 3EHE Mlî C£-CKpix...
o, ooo3; o Mis /jvisTpEjjî mi 4 ain o cxti> = iooo,o4; i3 Mii Aiw o cxnb ae MiAioaNE = o,oooi3ooo ;......
44. +KCEMN1M ^NTAiB , KT> MXT/KNA BipWAa CTipE Ap'fe-
7
50	•	APITMETItîl)
ma ca? cnp£ CTXNra KynTpl3rrrb, NYMT>pvA ce-^mmya{je-Tps cav cf-pMrrbipipE npjN io, Kv^otupiN 100, KVTptî npit» 1000 uiia : neNTpv kt* (J)i6-Kap6 ijicjip'b apun» VNNVMTjp, KapE fNCVIUl ECT8 fMMYAy'lT Ca? ^,Mnip(jil
npÎN io, 100, iooo,.... ama 342,53 ecte ae 3Ei£ opî
34, 253; ae îoo ae Opî 3,4253; ae iooo ae opî o,34d53
miA....
f 2°. IIvTSM (|) Tj p Tj aCKlMBa nVTEpi VNEÎ ^jp^Ni^EpiJaEMÎMaAE anvNE cav a c k o a t e y n a
cav Maî mvate NVAEcnpEAp'fenTa;..................
0,3 = 0,30 = 0,300 =.....IJENTpV K"b pMMVAJjÎM aTTVN-
11 E YlXNAOl TEpMENÎ (JjpAîNJjEpi nplN 10, ÎOO, IOOO;. .. iui Kl.11 f N AOK VA AVI ;0. CKplM ^ + 1 OH + TTO) + • • ••
3°.	^pASNtyEpl 3E11M8 AE KapE aV TOT 81EA NVMl.p
AE iii^ps av tot aiEA NVMirop; n£NTpv kt. kxna Ba aeocebît , ce-bavie a (J>i tot aiEAa KOMnAÎNÎNA np'm nv-
AE NVMT>pVA AE3£liMa*fe.
4°. Mt>P*IM% VNE1 (^p^NI.lEpţ 3E11M3AE NV CT1 piNY-MbpyA yi^pEAOp npÎN K«p£ CE-apaTb, 11 pN fipEIJVA yi-<jîpi KapE vpMli3T. A*m» BÎprvAT». Ama o,7>-o,5432i; o,ooi> 0,00078 ; o,687> 0,6793.
Cu BEUM OKVM ait1> IE NE UpaTl pErVAlAE I^ENEpaAE ( 07 mi 42 ).
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rp’ubOAuM. BEpiiKaAL , ae aAV.VbM asut. pirvAT. mi
NYMEPE (J)Pi&NţJEPOACE
,51
cvmtj itxnem BiprxAa tot pN ai'b Tp1>-im>; ekcemoax aîn npoTÎBi» ecte aectxa 4852,791 c"bN£<J)aK-b a^Nji£/,ej,iE aH’fecn» pirxAb, 4,oo745 ani beaem kt» (ppiKNijtpiAE casnt peaxce 2,7 TOT Aa BEA NXMlTOp UENTpX KT» NXME-	0,o4g
pipiAE 3£BlMaA£ A£ f.NKiimM KOMHAUiiTE 4859,54ţ45 npiN nxae .
CKbAEpT) CE- (paBE lap AXnb aBECT Ml/KAOK ; CK'bAEM AXLlb pETXAb, mriTpX KapE KlTb K2BTE Ba EKCEMIIAXpi .
57,02
48,i
4,8274
2,0139
6,oo435
0,17
3,842 1,oo4554
8,92	2,8135	5,83435	*2,837446
46 . Ka Ct ^MMXAJJÎM AOb K&TbJjÎMl 3£B'lMaAE, llp£-Kx.M 43,7	<Î,‘NA Kb cxnt A’onoxpiBT» kx M*. mi
^§0-, KbXTbM UE 437 X 391 Aap aBECT lipOAXKT KA NX-MbpbTOpÎAOp «xpEBXE a C£-j>Mnbpui npiNTp’aA NTfftli— TOpÎAOp 1000, A£B1 BEAEM KbKaCT»a<|>AbM n£ npOAXKTXA a AOb N X M E p E 3 £ B i M a A E, f MX A JJi M aMANAOb RSTiaiMlAE nponXCE cflbp’ a KbX-Ta Aa BÎprxAb; AEctibpiiipM ri£ xpMb ripÎN-Tp’oBÎprxAb arait y i cp p £ îEBÎMaAE, kxt-
NXAE UXaBXT aM AN A oi (pbKbTOpi; npOAVKE T X A ECTE a B 1 C T a : - 170,867. 1 arb UliaATE £ K,-> cuuus pi Q°).
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52
2,4542
o,oo53 7 3,(326 122 710 0,013o 0726
APlTMETUvb
4,i 2 7 4 37 i48
21,32 0,1001 o3 63 96
2l52
2 132
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0,00028
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-----cKpiM -----mi ^MUbpjjiM ne 8445 npiN 32.20;
5,22	5,220
8,445 4oi
kxtva ecte 2 mi p'bM'tiuijja 2000 ama---------=2--------;
3,22	644
4q,i	4q,ioo	4qioo	8g52
aCEMEN’fe — - = ----------------------= 2--------:CI0>*
20,074	20,074	20074	20074-
Anton» pervAT, ct-^aHE: Mai cÎMnAi» k*na fMnipjji-TOpVA N’apE 11,1 (jjp£ 3E^ÎMaAE, ^MfTbpjţÎM' /JiNTpEljli Ulî
6-g345
^>pfiNI,lEpiA£ fNllupTE ; aiija ------= 253ll5. AaKa
fMn bpuÎTVA ap£ war imitate ui(|jp3 3t>iiMaA£ ae k*t înjpyiropxA, ae cKoarsM ain NVM'bpyA iea AWTb xpwb kv MXTap'b uipivAi ar anii rpiriTE cnp£ Ap^nia aMANAV-popa, Kapt NEaAS'iE aa nţ Mai a^ esc AXKpape . . . • 8,115	8 u ,5	200,5
----------------= 2 + ——
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NTTMEPE <J) P/RN],IEPO A CE	5 3
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mxate iji<J>p£: ama kxna bom cokotJ rrE<>,4 -p aokxa axi c ,43, aBEMj-^ rpEmaAi); npEKXM mi o.o4 Axart iien-Tpx o,o43 at> Mai nxijiN AaeCλ opî c e- p tx; m n at,
Ka CT, AXOM 2 CaX 3 3£HÎMaA£ mi CT» AT»CT»M n£ MEAE A3ATEJ kt,mi nx bbem TEMEps ae Mapl rpEmaAE: np'fe pap a bem TpEEXÎNIJT» Mai MXAT AE KMT 6 lji<J>p£ 3£liMaA£ p AXKpTi-piAE ME AE (JiaMEM .
A,aKa EmiTVA xnei AXKpi,pî ecte 4,857123, jtxtem a-hî Axa 4,8 cax 4,83 cax 4,837... AtxnmÎ npcijXA ecte anponiaT Maî iTxiiÎN kx ţ1^ kx kx	NXMaî, Ka
C"b MlKIIIOpTiM rpEUiaAa KXT CE-Ba nx/t, nXNEM OXN1-MEMaiMXAT Aa M ’fe AX ITT, XpMT, AiN Iji(|>pEAE«l£ aMJjiNXT, KSNA XpMtTOapi KOB^pmEipE nc
4. Ani Aap axt,m, 4,84 minx 4,83 AiNnpiiiNa axi 7
KapE ECTE AiNTp’OMlE.
49. A£ MXATE Opî CE-pTASMUAl, Ka EmiTXA tXNEl AX-KpT»pî CT> (J)i£ O ^»p«Nţt£p£ AE NEpEAXC KOMnAETÎTT» aTXN-mî ne mxajjxmîmîm , kx o airponiEpE, aA Ki»pia rpaA crfa p pi riponxNEpi. Ama p aokxa axi £5^, ct,jix-NEM KT» C£-M£p£ O BATT» (JipXNţIEpE Maî ciiMUAT, , mi KapE Maî nxjjiN kx \ nx ecte A’onoTpiBi» kx A-RNca. Ae ap
4>i KXNOCKŢE AOT> «JtpaSNţlEpl | Uli ® , p’TpE KapE ‘li
54	APITMETllTb
nponxcb cb c|>ie KonpiNCb, mi naps aBSNA 8 Aa nxmî-
TOp C"b NX 31Bb Mal MVATb AEOCEElpE A£ K/RT KX0XNÎME lipÎN NXMbpbTOpi /.Op , ECTE fMBEAEpaT Kt aiECTE AOb ^p/KNţiEpî | mi | ap jiMiiAiNi mixNa mi aATa nponxNE-pli AaTT>, xtsa anpouiarb upÎN Aiiicb mi aAra npiN ko-B&puiips. Ka ct> ae a»|)AT>M ^MMVAgiM n£ -|UnpiN 8, npoAXKTXA y y tCT£ furpE 5 mi ^NTpe 6 -jvMnbpjjiNA iie 34x6 npiN 68o; A64i e^te pivrpE | rai | napE calnt (jjpXNIJEpiAE UEpVTfi:	IIEN rpX Kb Mal MXATb ASOCEfiipE.
nxap£ AS-elff aekxt kv^OO-
Cb saxiem autCTa -p 3£niMaA£. Cb nxNEM ktj boxm a ne anponia ae ţ- Mai nxy'iN !kx -2\; fMMXAyiM NX.ubpbTO-pxA 4 npiN io, kxtxa o^5 ecte npEijYA axi 4 anpo-niaT Mai nxyÎN kx ^	a» <|>i Boir ct> NEanponiEM
Mai nxyiN	aM <jri pvmxAjjiT 4 npiN îoo mxpMb
^Miibp^tM 4q.j npiN 7; 0,57 ap c[)i <J>oct EuiiTXA uece-KaXTb. A£ OBlJIEţ T p E E X £ CHAluriM 0 N X A b AS p b m b iu i jj a cj) i e-k b p i a pMnbpyipînxNb kana aoM aet.Aa i^st 0 iji<J>pb, KapE cb ie tot a£ Şhea p,*NA KxrpaAXA aripoiiifipi he c e- h e p e .
Auja aoEM 3,5 cai? 3,57 cax 3,571 cax3,57i4....
nfu-axpiAE axi y anponiaTE Maî nxyiN kx	,
-t 0'0 Q  . aCEMEN'fc	Ab 407 nENTpX KA1T ^N-
TpEL1 mi l4l ri£:NTpX pbMblllijJb; aAbOrbM ONXAb A3 i4i mi fMiibpjjiM i4io npiN 362 , mi bem kstva 5 mi pi>vibrară 3si, nE.vrpx Kb ViLZAT s — -1.17 3
4	4	362	'
Mai ÎIXLJIN KX . AAbOr*NA O NXAb Aa 021; KA-
txa 8 ua axi 3^*" Ab 107,08 iiENTpx up&y aupoiuax
NYMEPE CpPrfrNţlEPO iGE	55
Mai flXJilN KX YTJTJ miIA*
50- Kjkna Axm» flAtorapt oap£-KT>pria nxmt»p Ă£
NXAE NXBOM aBl> Nllî O pbMbmigT» , ^pAiKJ^tp'fe ECTE 4E CbBSpiIliT pEAXCh 3E1'MaAE ;	\ = ',5; 1 = 0,75;
| = o,625; ^ = o,65. Ecte aecns ct» KXNoaipeM ksn* noaTE cb isi cs-^NT^MnAf a<rî>CTa: ntNTpx kt> fsmbpyips NEIIXTSNA a CE-^)aHE AEKST iîm> he bom -jMMXAgi uenx-
M’bp'bTOpXA npÎN l't, ÎOO, 1 OO....TpEEXE Ka antcrb
nxTEpE a axi io ct> cJ)Îe ae fMm>pgirb npÎN NXMirop, Aebom ţNKinvi $pxN]pp'£ ae NEpsAic (53,4°. ): iui (J>una Kt aiTici b nvrfpE Nx noats ci> aiBb a/gi ^Mnbp-glTOpl AÎN TXBf AE KST 2, IUI 5, BEAEM KT» O ^pXNţCE-p£ AENEpEAXC NT C£-nOaT£ CKÎ*'Ba A £ CbBXp» iniT^N3£’liMaAE, AEK*T AaKa NXMÎTOpXA Ba f i npojUKTXA nxTEpiAop 2 mi 5 n x m a î, opî
BXM Ba <J)i aAMÎNTpEAi) NXMbpbTOpXA:	NXMbpXA A£ 3£-
nÎMaAE ecte aTXNiî nli Mai Mapt nxTf.ps a axÎ 2 mi 5 fN n MÎTop ( 12 ) . ^aicb Ba <£i 23.52 , bom ant Tptî gi-<|>pE BsniMaAE.
51 . ^NB-tcrb AaATT> jvNTSMnAapE NX noaTE O ^jpAiN-ţlEps ci ce apaTE ,j>n 3EmMaA£ a£k*t npiN anpocKÎMagiE. ,A,ap <J>iiNA kt> pT»MT>migi/iE ^MirbpgipiAop cxkcecîbe CiKNT NErpEffliT Mai Mm AE halt NXMÎTOpXA , NX ^NT*p3Î-EM CT» Mai a<J)AT»M fNKT» XNa AÎN EAE Kape Tpf.EXE Cb A"6 tot UE aiEAamî kait , mi anoi n£ antumi pbMbinigb iie KapE cfcaM a<|)AaT aTXN’rî, mi ama Mai px koao : cpiiNA kt» HEpioAlHEipE a^)AT»M IOT ll£ 8SEAE gîtJipE f.NTpX a-HEAami p-KNA .
56
APITMETIKT)
ITpsKVM .|.==l.J666 ... T3r = o, 27 27 527..........<
TVr = °»3'i2 342...» •£=0,571428 571428.. •• fN-Tp’aHECTE aeoceeîte £KCEMn/iypî nepio^VA ap£ KXTE OW-» ■Hj 1,2, 3, cair 6 Hi<J>ps, mi bate opî ns -pasiiE aek^t A«a» a 2-a , cav a 3-a Tplîm b AyiTb BÎprvAi».
A,E OmpE (J)iiNĂ K"b pT>MT>Iui[jiAE CSNT Maî Mm ĂE kxt jiMm>pjiiTOp-xA, ini ki nepio^yA CE-craTOptm'îjîî. ^NAaTij Ayn"b me a<|)A-bM *Na aîn piiMiiinijiAE HEnpEaEA, t p e-he ci ct-KoiiniE ie Mai ny^ÎNE jj'hJipe, je kjrt i*ni kste y n i m î RonpiNAE nv ni to p y At Acynpa anEcTyî oeîket BE31 lEpK'bpiAE aphwiEmE a-AEAyîTayc JN°. 5i2, yNAS bei îmis a^*a AEciyAE uii Nyot TEOperuî acynpa aHEipiî RiaTEpii.
52 - Ecte np't AECNE A£ a BEM ^NaifOl KX O ^p/BNI^EpS
3E<iiMaA'b rnsusi'b ah MjCH’bToap'fe ei : ama 0,75 cKpici>
CSE <|>OpMa -l-jjj CE-pEAX'IE Aa -3 , Aap KXNA <J>pXNJIIEp1j
3E4ÎM3AT3 ecte isyjuaî ariponiaTi>, npoBAEMa ap£ o MyA-JIIME A£ AECaEI'I pî . AaÎKI» 0,7.5 . . 0,706 ... 0,7.03 ... 0,7512 ■ . . juma: pEcnyNA Aa cjipxwjtEpî ae aoi TEp.vis-isî KapE pEAxe.E f n 3EiiMaA£ ay 75 nsNTpy «ieae aîn t^k fticfipE.
IxIKNA «JlpiBXI.Ifp’fe 3E'jÎMaA’b ECTE nEpiOAlKIi , TpiByE CI BTirTiRl cijMa AaAOB /J.NT/BMTTbpj .
4°. A,ah,a nEpioAVA ^n'ieue .jounTi» at» nt BipryATj, npEKyai rieNTpy 0,6666 .... 0,27 27 27. akcemrbm
Kl>	ae irV îrlir • * • P£AXC£ 4.N 3EMif\iaAE A3V
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jyiTMEPP <£>Pi&NlJEPOACE	57
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1°. ’îfpiÎM’fe ATM/lMl CE-NXMf.ip6 M ET p V, Kap£ ECTE YNtf AiN 3E1E MiAioaNg a apRTAsî ain MspuiaNyA IlapicyAYl i 1* ci-^ntIna* Ăî/a hoa nsprt> Aâ EKyaTop.
2.	Yn mbTpa? a Kipia /aTyp'h ecte ae 3ehe METpvp» Kapi ECTE yNIM'fe (J>T>JjaA61 miCe-N»MEitfe Âp>?.
3.	I'pEOTăT'fe nm kyey As ain» a K’bp-m AaTypb ect& © a curb napTE aîn met^y ect£ tnimI rpEOTbj^Aop, mi ce-HyM£ţ£ rpăMfify (13).
4°. Kybwa aA tfbpyKt AaTSpT> ecte a ăE^fe napTE aîs* METpt, ECTE TfilME &t Tpyn 1111 CE-NYM£Ip£ AlTpy. Ge-» fNTp£B«iNji'fe3i» ^nki» mi Gitp y , sape ecte ynmetPy> K1B .
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A.apa'iECTE MtcVpî cxrif ^nyreaE ^NTXMnAÎpî npii Miai carnp'fe Mapî, nENTpy kt» j.NTpiEyiNjjap'B Aop n® îloaTE ayi* Aa NYMEpE npfi Riapî caî npT) mîii : mi iien-» tpy aq^cta ae cokotim CYET^MnbpjjiTE ^NTp’aATE ymmÎ, ă s,îkt> iMnipyiw nt <J>i£-Kap£	3eqe m>pjj,t mi ae nymîm
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<J)i£-Kaps a 3tq1> napTE CE-^MnapTE Ktp ^'n sehe ji-bpjj,î
flm: ae vna.eBlîi'si^EpÎAE ^enti'me-tpy,^entîm... Mi^ 4 a i uet pKapg im TpiByiNjih ae mhi o ASCAvaiipE^
NYMEPE (pP/RNţLEPOACE	*9
AcemenIî AÎNgpiE METpypî c’s^Tjkvt oxiume, nt K*-jpEOHyMiM? DeuaMETpx: DsBaAÎTTpy apEjţygiţic 3£i£ AÎTpypt uma: ocvţTj as METpvpi <J>aK vnEetomi-t p ?> o cyrb as Arrpypî vn J£ k t o a ît p?, o cxrb as rp*_ ME XN EKTOrpaMV...Kap£ ECTE rpEOTHT'ţ AE4 BTKT»* ||î A£ 5 ţjjpaNiij o mie ae METpypî <|>aK xn K i a o m s -Tpx; OMiEAsTpaME xn KiAorpaM?..,. sehemu as METpVpî IjpEjJTfECS XN MîpiaMETpV; 3EHE Mii AS TpaME
«NMipiarpaMM?.... as ani beaem ki> 4o54, 55a me-Ţpvpî npEgVECj; 4 KÎAOMETpxpî, 5 AtKaMSTpxpi, 4 mc-
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pî , Aap s Mai eîne a ce-3£>ie *4o54 as METpxpî uii ; ca? 4o5 ASKaMâTpxpî, ini ţVîtto ui’Ja;
ApXA ECTE XN ASKaMETpy UVrpaT ca? Q CVTb AC METXpî ţiijTpaTe; Arrpy ecte xn ae^Îmetp? kve ; CxEpxA ecte xn Metqx kxb; rpaMTA ecte rpEcrratfe xnxi HENTiMETpy kxb as aut> CTpEKypaTi’npipţ ii Maî Mape ascims .
AitcTa ecte cicTEMa rpEOTbjiiAOp ini a Micxpip'uop; NVMipÎAE NVM'bp’bpi CXNT 5l Ap?, TpaMX, AlTpX, CTEp?, <J)paNK ; mi AE-fMMXAjjiTEAE AQp api>TaTE npÎN aAbon>-piAE ASKa, 3£'ie; ekto, ocxrh; ni a o, omîe; Mipia 3£he Miî; ns ypwb cyn-AE-fMUbpjiiTEAE, ttapE cs-apiT ppÎN AS^i, 3£HS; lENTi, o cxti»; Mi ai, omîe.
Pap ce-^ntxmiiatj ct> aBEM TpEExijjTi as ToaTE xnîmîac KapE NEAa? anecTE aAXNbpi; A«p aNa^opia AEaxorbpxr. Kpoip’fc Aop , ci.MnAa mi Mapfc îaee, Kape a ni>ckyt
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'	<J)iaoco^jeck Kape a npecTar acvnpa aneşiţ
«JpxMoace aiJjA'bpî ecte BpEANÎK ae b'Bkxa NOCTpv; oa-MENi hei Mai BECŢiyî ay ascmŢ a^ anicia; ^NTp^Nca KX-«oaipsM ijemyA a*î AariAac, Aarpa*,' Monk, ^e-AaMBpy, A£*aNApy, Mekhn , Ae^sEp-ţliNo , iIiha : ... Ne-j.MBT>H'bTxpa ini kpEAÎNga, AEtnapTb ciNrypE ihy Mai nox ci» TbrbAyiacKii npiiMip’6. anscii? MinyNaTS a(f>Ai>pi.
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1	= 8 = 80 2= 8oo î = 24 raz i44o = 864oo Aîb. Map. ITiî. Dpa>f (^Kpv. Ipt. y\ÎB. CpAjii. AiNaP‘ j 3= 2 3= 16 = I28=584=:g4i6 î = 20 arz 2o4 1= 8= 64 =192=4608	1 —
1 ~	8=3 34=3 576I
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^OKa.AiTpş.Âpaw^pî. Aeî. Opjjt. JŢap*. Ale. Baitf, 1 = 4= 4oo	1 ==. 4 =? 4o =; 80 = 12a
x = 100	’	1 r= 10 =SZ 20 = 3o
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CVA j>A CBp'lM SOC CYET pSNAYA ÎEAOp aAYIWE CaX CH>l»-v 3VTE «
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i£7 0px 25 ApaMypî=i75 ApM:
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AaKa fMn’bpjiiTnpyA ny Ba <J>i komtxaetît , \aTVN4i av-Kp"bM napTE acvnpa (flituri Kbpvia (f)tA ă£ vnîmi sae -jvMnbpjjmAVi , ^NHEiixtvA A£Aa Maî Maps . Ama ua cb ^MiibpjpM a34 raABENi i5 aeÎ mi 7 npA: rrp'iN 4, AVbw anaTpa napTE AiN25i raA: Kaps ecte 58. AÎNripEVNb kv pbMbmijja 2 raABENi cav 63 aei; Kaps dAVNau,! kv i5 Atî Aaî 78 ah; anaTpa napTE aîn ei (fiaus jgAÎNiipEVN'b kv a pbMTuciga cay 80 npA; 80 + 7—87 npA, a Kbpvia a uaTpa napTE ecte 2 • | npA, kxtva Aap ecte 58 raA, 19
AH, raiai* npA. ^l5 A£Îf	
Xn AVKpbTOp	i5 aei.
42 AE31AE, a	i QOUU.
A.vaT ne AyKpyA	14
cbv l5l AEI l4	101-1
upAt mi 6 bani;	174
ku cb ipiu heIî	6
4£ a K&ipiraT ea	12
118 cfjiEipE KapE si	2
<$-M .Cbpu'lM 15 1	12
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2	aa«i npiNimibpvA aecTpaKT 4e. mi .puripOTiiîb beaem
<>A bpVNTVA ftOKOTtAU.
N1TMEPE <J)PiftNţIEPOACE	69
A,aKa |Mm>p{iÎTopxA sere KoynAtTir Ka ci» iivtem a*A coKOTi Ka accTpaKT ; Mai ^ntxix TpsEXE aA cjiavie cbkî pÎKb cf>p*Ni(i$pî, ini nENTpv a>i'fccTa ^MMXAjiiai mi ne irbpijiTyA mi ris ^MmjpaiTopyA npiw NYM'bpXA Kape apa-TT> AE K«T£ opî q£A Mai MÎK c{)EA ae xnîmi aA .prrbpijiTO-pXAXi CE-KonpiNAE hea Maî MapE' (Jea . AxKpap'fe a-ntcia nvBa ciuMBa kxtxa (21, 6°) mi <|)iiNA kt> (fnEqiE Kaps g[>ea ae vnîmi a fMmjpyiTopyAxî Ba npOAYHE xnImÎ ^NTpEl,!! , 3HECT fMmbpjiiTOp CE-Ba aAXIE ’ A3 NXMTjp ^N-TpEr. Ama 24 ctsnjk;km 5 iibame. mi 4 aejjste cav kxm-m>paT kx 554 ihabeni i3 c<|>aNijixi mi î aex, Kaps e-CTE npSJJXA (flitipE KTjpyia CTjKPOKMN ? (JiilNA KT> 4 AE-ţlETE CaX f AÎN naAMt CE-KOnpiNAE AE 20 opî ^Nrp’xN CT/RNJKXN, TpEEXE Ch p»MXAJjiM aMA5NA0b NXMEpiAE npO-nxcs npÎN 20. ^EpEpi aTxrm CE-Ba aAxiE ’Axrrb kxm xp-Mfot 851 ctxnsokni c’ax KyMfnjpaT kx 1 *099 tbabeni Ţ <|>aNu,ixî, mi j aîn c^aNg, Kaps ecte npEjjxA xnxi ctjsn-3cxn? ■^Mn'bpjiip'fe BaAa i3 iraAEtNÎ mi ||-®- AEaTpEia napTE aîn ccJjaNij,: aAiKt 33... napaAE.
Acemen'S Ka c-b pvnThpj;'M nE 806 aeÎ onapa: mi 2 naru npÎN 17 f, TpEBXE Cb j.MXAJiiM npÎN 3 miaBEM 24x8 AEÎ mi 2 napaAE a cE-pvnrbpiji npÎN 53. AaKa .pwm>pjjiTO-pxA Ba 4>if3 OKa 3 AÎTps mi 5o ApaMxpî, aTXNiî |.mmxa-yisi npÎN 8, ki>hÎ 5o ApaMxpî ecte o acxwbTaTE aîn AiTpi» KapE CE-KOnpiNAE AE 8 opî OKa . 1U4A .
a-a, f NixunAape. AaKa ^MntpyiTojpxA ecte|,m-
MXA(jiT , aTXMqî TpEBXE EA Cb <J)ÎE AE 8HE^mî NaTXpb KX
70	APITMETIKTjj
■j.MnbpjjlnrA, ini k&txa Ba <|>i aBCTpâKT. Ce noaTe a nx a-? b-! «JjpxNijupî aT/KT Aa |.Mn-bpyir kxt uiiAa^MntpjiiTop Axrrb KÎnvA hz aKXM ce-Ba apbxa. Cnpe niA^b na c'b fM-irbpijiM ne 3g4 aeî, x4 npA mi 2 saNÎ 4 npiN 5j aeî, io napA mi x ebn , ^uvaqîu ne aMXNAOb 'NXMepiAE a-mectIi npiN 4o X 3 X 2 cai? 24o nENipx Kb sxMbxati A£ saN ce-KonpÎNAe as 24o ^ţvNTp’xN aex . Ama ^ap sa TptBxi cb pMnbpji'iM ne 82349 npÎN 8912, Kape Ba *a
Q .2 3 4,1
y 8912 •
59. IIoaTE nÎNEBa c'b aj,YKb o tjipsNŞEpE px NXMbp
KOMnAET'lT A£ Ba ^Mffbpfii n£ NXMbpbTOpXA npÎN NXMÎTOp. Ama na cb 8bem | aîn aex pwnbpiiiM ne 5 aeî a^isb 200 npA. npÎN 8 mi a<J»AbM 25 npA. Aa 4 ain oaa pMnbp” Jl'm 5o OKa cax 20 AiTpe npiN 7 mi aBiM 2 AÎTpt 85 mi 4 •
A,itf npOTÎBb I<a Cb «J-NTOaplEM VN NXMbp KOMnAETiT fl.N ^psNifepe ae aoî TtpMENÎ, TpeBXE aV aAXHE-j>Ntpy bea Mai mîk aA cbx cjjEA ae xjnMi. AiiKb 2 AÎTpe 85 Ap : mi 4 npEjjxeijis kxt 285 ApM t mi 4 eax Z°£°. ae ApaMxpî, mi ţJfUNA Kb OK3Q apt 4oo ApaMxpî, pMnbpjpaţ npÎN 4oo mi aBEM | cav 4 aîn OKa.
ţîa cb npEijxiM pv napaAE mi BaNÎ ^pXNţCEp'S 0,715 AiNAex ^MMVAgiM npiN 4o miaBeM 28, 6 napA: aceMEisi PMMxajjîna mi ne 0,6 npiN 3, aBEM x,8 BaNÎ ama Aap •••• 0,71 5a. = 28 np : mi x,8 BaNÎ.
Yn NKMbp KOMIlAETiT C£-n0aT6 pEAXIE pV SE^iSiaAE j,N-XOpKXNA^’A Maî ^NTSiy |N ^)pSN],I£pe AE A°î TtpMENÎ .
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NYMEPE’ ^PANţlEPOACE
71
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1.	(J)opMapcb IlytiEpi/op.
60 . ^MMYAipNA WN-SMX>p5 npÎN £A j>NCXIXlî 1, 2, 5,... opî, atJiAtM nmpÎAE 2, 5, 4 ....
. . g . 27 .	81.	243 .. 729.	.2187..	656i . . ig683
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i,..81.729 656i.5go4g.53i44i.4782g6g.43o4672i.58742o489
IJiTpaTVA A Vi î ECTE	= KyBVA ECTE jVyî...
A£YIUE YpM'fea’b KT> IIXTEM <]j O p M a Opî HEflXTEpE aVNEl (JipXNÎJCEpî apAÎKXNA a M X N A O î TEp-Meni Aa a^IcTi nifTEps.
2. CnoaT Epi a pii atjhînîa op m>TpaTE.
61. n-bTpaTYA 'SNlfl NK^tbpV A£ AOT» JJ,î(J>pe, TipEKYM
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72	' APITMETIKT)
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Kpv me qgpE naTpx npoAXKTxpi ^NTîapn; i0 5Xă • ca$? nbTpaTKA yNiMiAop ; 2° 3oX5 ea? npoAvimA .staiMÎAO^ npÎN VNiMi; 3° fNK’b OAani 3o X 5 ; 4° 3oX3o ca? ni>-
TpaTÎTA 3£HiMÎA0p; A£iNA£	Kt ntTpaTYA YNY1 NY-
Mtp Ă£ĂOT> jji^>p£ £CT£ (^OpMatAiNmjTpaTYA3 6-HÎMÎAOp, AÎN npOAYRTYA AEAOt OpîaA3£»U-MiAopnpîn yn'iMi,mi4^NC<|>;KplIIiTAiN,ntTpaTYA y n i m i a o p, Auia 352=9oo+3oo + 25=i225 .
Ka Ct C£-pMMYAIjî)CKt 7 + 5 IIplN 7 + 5, f M Y A JJ i M Mai -pnYKix 7+5 npm 7 nEYpwt npÎN 5 , KapE ^ntsiy ne At 72 + 7 X 5, roi n£ xpwt 7 X 5 +52 . Ka ci> ^>a-•jem Aap iiijTpaTYA ayi 7+5 ny e aectya a ^MntTpa nf. 7 roi 5, ii Tp£BY£ |nkt> ct Mat aAiorbM mi n£ npoAYKTYA ayi 7 npiN 5 fNAoiT; roi ama aaEM 4g + 25 + 2X55 a? l4i=l22. A,6 VNAE YpMT)3t KT.miTpaT*A <J)iE-Kt-p Y ia N VMT) p K O M n X c !a i N A O t n t P li î, C. £-<J> o p-r.if>3t ain m>TpaT£AE <|>is-Ktpia an>ors»A mi llpOAYKTYA A O p JNA oiT. (BE31. 97, 1°.)
62. ITbTpaTEAS AYI 10, 100, ÎOOO, ... ECXNT IO , 10 OOO, 1 OOO OOO ... AS YNAE CEBEAE Kt TOaTE NYMEpi-AS AEAOt ui<|)p£ $iiNA j-NTpE IO Uli ÎOO, 3?IltTpaTYA
Aop |NTp£ îoo mi io ooo, aAiicb komiiyc as 3 a? 4 iji-+pe: KapE Ba ct 3iKt Kt opî he NYMtp ae Aot jiî<f>p£, ap£ nvrpaTYA ae 3 a? 4 m+ps. uiia: mi ae obijie rit -
T p a T X A a P £ II, i + p £ A £ P T> A T> Bl N i p N A O i T £, C a T fNAoiTe Mai nxjjiN »Na.
mrrEPi mr PT^muNi	73
NvMtp’/s as i ca* 2 Kicfjps ax piAT^iaiAE Aop rrbTpa..
t£ |N T3EAEAE AIN § l3 IUI 6o; Irip nENTpV ’lf.AE Ai\AT£ NX“ M£p£ TptEXE Cil AEOCÎbÎM AOb |NTAiMnAbpî .
i°. ,i,aKa NVM'bpxA nporrxe npEKXM 784 aps 3 cax 4, JjitJjpg , p'M'MiNa axÎ ape AOb; mi 784 ecte komiivc ain TlbTpaTXA .SEliMÎAOp , AlNTp’aA XNÎMiAOp Uli^ÎNnpOAV-
ktxa pAoir aA 3miMi<iop npiN vnImi. Xwi iTi a'in txix AÎNTp’aqECTE rrbpijî c£-(f>opM’fc3b ae bom aAbora AOb nvae irbTpaxxAXÎ u,icf>pi 3EinMiAop 06); ae vnae xpivitab Kb aq£Cr niTpaT pa^vNapE TptBSE cb ia Tp’fenra cxrÎMÎAOp. ^fcnbpyiNA heae AOb ji'uţ)p£ 84, 7 KonpiNAE nbTpaTVA Xji^)p> 3£MÎM)A0p q£ CE-COKOTECK Ka NÎipE CJMnAE XMM1 ? KOIipiNAE fNKb mi CXTIMIAE IipOAVCE HplN ^EAE A3ATE nbpjjî aAE nbTpaTVAxî.
AvbM pbAbHÎNa MEAX1 M31 MapE TlbTpaT 4 «IE CE-KO-npiNAE 7 » mi Î'Îna K-b 7 ecte tNTP£ nbTpaTEAC axi a ini 3 ecte tui PiWbpvA nponxc 784 fNTpE 202 mi 5o2, ama pbAbqÎNa ecte pTps 20 mi 3o imi aaeM 3 iiENTpv jjic|)pa 3E*iiMiAop.
Ckoqxna 4 aîn 7 pbMbmhja 3 ecte aqE’fe he aM jjînxt
NbCKXTb A1N nbTpaTXA XfiiiVliAOp mi AiN 3tqiMÎA£ fNAo'lTE
ţMMVAgm np'lN XNÎM1 ; AE>JÎ 384 ECTE KOMIWC AlNTp’a-
MECTE AOb nbpjp .
AhECT AXHb XpMb npOAVKT CE- <J)0pM'b3b piMXAyÎNA npiN xiviMÎ yicfipa SEqiMÎAop pAohb mi mrÎNA o nxat» cnp£ Ap^iiTa ; ama aAVNaps aHECT npoASRT ecte Tp'fcrm 3£qiMiAop, mi KonpÎNC fN 38, AEcnbpjjiNA yi-
10
74
APlTMETlltb
4>pa 4 a vsÎMÎAop: 58 KonpiNAE fNRb mi sEiiMiAE npo-A»ce npiN m>TpaT!f a XNiM'uop mi a^EAls'KapE cJ)3k ns 784 cb nx cjjiE xiŢ ribTpaT EKcaKT. A.aKa r_a4ECT£ 3ehîmÎ ap 4>i <ţ»OCT KXNOCRXTE, CROJIXNAXAE AiN 38, pbMbUlijja j>VI-nbpyirb npÎN 4 fNAoÎTa jii<£pb a 3£HiMÎA0p, ap <J)i AăT xmmîae. Cb-jvMiibpijiM Aap m> 58 npiN4, fMnbpjji-tya am‘i ecte Mat Maps ae kjrt auEAa KapE ap TpEiixi cVa
. ^NTpEB'fÎNIi'bM, IUI KXTifA HOaTE Cb <jm l^lip^ MapE Aap ECTE /ECNE CTj’a fNApUirbM .
TTeNTpy Kb, A»Kaj 'kstva JJ cax g NXMbp |N-Tpsr aparb fN4»UNjjb Xinîm'iae, nxiNA 9 a*nit> ^NAoi-tya 4 sa jjicJtpi smi.vnAop, 4g Ba cf>i 3E4iMiAE ^naoîte a-AtoraTE XNLviiAOp; mi 49X9 Ba <J)i ^naoîtva npoAXKt aA
3£>nMiAOp ţipiN VNÎM1, Mal MYAT m>-	7.8 4	28	
TpaTYA XPiiMiAOp ; AE41 49X9=441	3 8.4	49	48
K8pE £CT£ > 384 ; ae YNAE VpMfj3b	58 4	o	9
Kb 9 ECTE npT> MapE; MEpKbM Aap 8	0	1 38444	
TOt kx a4ECT nîjkaok ; mi 4>iiNA Kb	27.35	52	
48 X 8 = 584, KapE pETpac aîn	213 5 1	102	
p'bMbluiljb Ab o, BEAEM Kb 784'ECTE	2 0^4 1	2	
IlbTpaTXA EK^aRT HA AX1 28 . IIv-	3 1	204	
CEpbM aii ERCEMnAX COROTEAl, Iip£ KXM miaAXly/2755 KapE ecte 5a	1.2 1	1 T	
KX pbMbmijia 3i ; nero-pv Kb 5a	2.1	21	
eCTE pbA'b'jiNa 4EAX1 Maî M^pE nb-	2 1	1	
TpaT 4E CE-KOnpÎNAE fN 2735 . A-	0	21	
4>at»m ^nkt» mi my/xQi = u .
I1YTEPI IUI PUAUqiNI	75
2°. Kybxntva ecte tot ast/.a iui k*«a nvrparxA apt Mai MYAT A£ K.ST 4 H’u})p£ ; lIEiNTpV KT» aTXN«I] KY TOare kt> piAimiNa apt Mai myat a£ b<bt Aob Jiltjjpe, Aap uii a-Uia O UYTEM COKOTÎ KOMnYCi A£ 3t'liMl uii \i YN1M] ;	523
apt 52 3£qiM] iui 3 YMM1 .
Ama iiENTpv 270 529 a-	27.3 5.2 9	525	
CEMEPili BOM aBli nbTpaTVA	2 3.5	102	ioi3
3EqiMÎAOp, cokotîte Ka Niipi	2 0 4	2	3
ciMnAE ypumi, KonpiNC	3 1 2.9	2o4	3129
2735, mi BOM BEA-!» KTj pi»- 3129 ĂtniNa aqEAvî Mai Maptni»-	o
TpaT qt Gt-Konpi«At 2^35 at> 3£qÎM!A£. ekcemuay ae CYe a(|)Al>M pT>AT>q’lNb 52 iui pT>MT>inijiT> 3l iui KOBOpXNA 29 AiKNrb 3l aBEM, 5l2gntNTpY jvNAoiTVA nDOAVKT aA 3£-qÎMÎAop npÎN uimii Maî Myat niTpaivA YNiMÎAop; cko-jjxna u’ufipa 9 fMirbpHÎM nt 312 npÎN io4 Knpt ecte 3tqi* M'lAf. 52 |NAoiT£, UliaBEM VNIMIAE pijAbuitSU, cav YN NYMbp Mat Mapt.
cc^pmiT nvÎNA uekjktya 3 cnps Ap^UTa AVJ io4 Ui! /JvMMVAJJlNA 1043 npÎN 3, CK03TEM UpOAYKTYA 31 2Q Ai» p'bM'buiijib, mi auia a<J>AbM to> 523 ecte pi^AViiNa q£-pxrb.
/LjVni MÎafAOKVA aqECTa AVKpi>M acvnpa opt KTipvî ny-
MT>p aAÎKTj BEAEM KT> TpEEVE Cb’A AEdltpu'lM /{.NASCUbp-
jjipi At AOTj ui^pt -ţvNqEnxNA A£Aa Ap’brua, mi Ba pijMS-rdî wvMat ojj'HjjpTj -j,n Atcn'bpjjip'fe Avirb vpMT> Aaua ny« MipVA gî(J)pEAOp Ba (jj‘l (JxbpTj COJJ . (J)îe KapE AEcnup-jjipE at> o jji<f>pij ptAVi'tsi, AVBp£NA acYnpa <J>iiKbpia AYIIT» KYM sictp-hM .
APITMETIKT)
76
flvNtM avi
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CEMlIAX.Maî	2 J . 1	63	663
17XTEM pKb	1 8 9	3	5
Cb NE EKCEf-	2 2 0.8	>y9 >989	
cim uu acx-npa avtCTop xpwbToapE. y/ 7 283 291 \/04 000 000 y/ 3 179 4a i
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63. NxmÎm n xme ps I\ o m b c x p a b i a e cax P a j^î o n a-Jit Opl (s'lCe) aVEA^ KapE av O KOMVNb MbCXpb KX XNlM'Ii IIpEKXM ECTE TIENTpX Kb & 5-a IiapTE a XN1MÎ CE-KOIlplN-M fN 1 A£ 5 opî ini.AE 2 opî -p |. A»ap y/i1\/7 ■> • • . C*VT N Ep a îi io N a A £ CaXNESice, lipEBXM mi pbĂbr VÎNa <J)’lE Kbpxia NX.Ubp pTpEl’ Kapt NX IÎ08TE <Jâ ITbTpa-TXA EKCaKt 3A XNX1 NXMbp pTpET ; aAlKb y/7 R* noa-T£ AEi-bBXpUliT CbCE-apaTE llpÎNTp’xN NXRlbp (|)p*iNj1IE-poc, nENTpx Kb AaKa ce noaTE , cJjîe	, npAÎ-
kjrna AanbTpaT, a\i aB'b 7— ‘^-2. , Kapt ecte aiiAvpj., IlENTpX Kb c{)p*NIlIEp'fe A-6-â ECTE pNBEAEpaT AE-NEpEA&C
c])Îîna ini - î. £ 33 o°).
y/7 Ksae fNTpE 2 iui 3; A«p ecte aecne a beaIj k b y/7 koae acEMf.N'b mi prp£ 2 mi 2 ae *nae ypM&şb Kb 2 -| MiU MXAT C£-anpOlli£ AE y/7» AE K/KT 3. C£-IIOaT£ .JiNKb cb fii cE-nponxs aNEanpoiiia Af y/7 ®c$eax Ka AtocEu/pt
IIXTEPI IUI PTd^1)tIINI	77
ct> <J>îe MainvjiiN kx A, Kaps Ba cb 3ÎKb Kb CE-nepe aoii ^>pxNi,ifpî npbRVM Ai mi î± mi Kap£ cb aiBij’ 5 ntNTpy
NXMirOp , aKT>pOp NXMbpbTOpi KX XNa Cb BlEb AEOCE-EÎpE mi a Kbpop nbTpaTE KOnpÎNA ^NTpE EAE nE 7 . A-4&crb AE^irsiiiis CAxataipE a» napaAOKcxA aaECTa Ka ob ne anponiEM ae 7 kxt bom boî, kx ToaTE Kb a^crb pb-Ab^Nb NX C£-noaT£ a<J)Aa . Cb ^MMXAIjiM npÎN 5 (JpiKN-^ICpiAE HEpXTE mi NXMbpXA	-	Ba (J)i jvNTpE NX-
.MbpbTOpi NEKXNOCKOJJ1 ; Cb apAUtbM Aa nbTpaT, a5X7 cax 175 C£-Ba KOnpÎNAS ^NTpfi' nbTpaXEAE NXMbpbTOpi " AOp Kapg NErpEmiT Bop <£i NXMEpiAS ^.NTpEţii npiN KO-Bspmips, mi npiN Aincb aAXi y/175, (a«J)AbM i3 iui i4; Ai mi Ai c^nt Aap ^pfiNţrtpiAe HtpxTE.
AcEMEN’fe Ka Cb aBEM y/^3 ţ') Mal nXyiN KX^j- Tp£-EXE Cb fMMXAJi'lM n£ 3 \ lipi# nbTpaTXA AX1 11, KapE NE Ab 3 ţ X 121 cax 44g 4; n£ xpab cb cko3tem \/^4q % ^NNXMbp /jiNTpEr cax y/44g, mi aBEM qi; ae xnae ce-B£AE Kby/3 ^ CE-KOnpÎNAE fNTpE -2-| mi f ţ CaX 2 . &Z OBipe Kacb C0K03TEM pbA^UÎNa XNX1 NXMbp npiN anpoKciMayiE ^a ^ m m x a iji m npiN nb’ TpaiXA N XMbpXAXl AHT, pbAbHÎNa aMECTXl npOAXKT f N NXMbp ^NTpEr, B a (|> i NXMbpb-X Op X A HEpXT.
64. ^e Boia cb ne anponiEM np'rn aacXTOpxA 3EuÎMa-
AtAOp aAiKb Mai nXJj'lN KXylj, UITAI TpEBXE CbijAl-MXAJj'lM NXMbpXA KX IO2 , 1Q02 , , . . aAUtb Cb aAbOl’bM
17
78	APITMETIKTî
1	2, 4,... NYAE AaKa ECTE pN’TpEL1 , ca? Cb MVTbM BÎprvAa
I	jur 2, 4TpEim cnpE AplinTa-, Aaita KOiipiNAE iuÎ3£-
HlMaAE. CKOaTEM n£ YpMb pbAbl’lNa NYMbp jvNTpEl’ ini anoî nvNEM BiprvAa ynae ce-kybîne . Ama y/o,3 Mat nvttiN ky xiix C£-a(|)AT> myţxna BiprvAa ky 4 TptnTE mi <{>iiNA Kb y/3ooo = 54, aBEM y/o, 3=o,54.
Acemen1> y/5,7 Mai nxgiN ky		ECTE —	y/17000
cav 2,38. cb coKoriM ani			5oo
ţ/o2ilmiy/2. Ecte 4.N-	3.2 1.0 0	f *7»9	
BEAEpaT Kb Aa î-a AYKpaps	2 2.1	\ 27	349
fN AOK AE a HYNE a«l£AE *AOb	1 8 9	7	9
NYAE Aa 321 , IIYTEM Cb AE	3 2 0.0	11 89	3i4i
aAbOlTjM NYMat Aa pbMb-	3 1 4 1		
mi ga 3a ; bcemen!) ae bo-	5 9	uma:	
KIM AOb gitţipE 3E<liMaAE,	2	( i,4i42i.	
TpEcvia a iiyne naTpY nyae	10.0	{ 24	281
AYnb 3ni aAÎKb cbMat a-	4o.o	V 2824 28282	
AbOrbM ţNKb AOb NYAE UIl	11 90.0		
Aa pbMbmiga a Aoa 59. Be-	60 4o.o		
AEM Aap Kb ECTE Mai BINE Cb	3 83 60.0		
1IYNEM NYAEAE KMTE AOb	1 00	75 9	
AOb AvnB (|>iE ccapE pbMbinigb niKNb k*na bom ben! Aa anpoKCÎMagia he cE-HEpt.
65 . Ayrn> MiacAOKYA ky Kapt rE-i^anE nbrpaTYA ynei (JipXNţlEpî (6o)bEAEM KbpbAb<UNa YNEI (jipjKN-ţl £ P 1 C £-a <|> Ab AC BOM C K o a T 6 f N II a p T £ II ea
IIYTEPI IIII FbAMNI
79
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A1N TEpMENl XN IVbTpataT EKCaKT, A1N K3pE aAEţUM Maî bîne ne PiVMiTopxA , {neriTpx kt> apaTb NXMipxA nbpip-Aop ne ce-KonpÎNA 4>n xniMf.. ^MMXAjiÎM A»p a-MXNAOl T t p M £ N i cf> P X N ţi £ P i Iipi’N HXM1TO-pXAEl, Ulins XpMbCKOaTEM pijATiMlNa <|) i £
2 i y/ z \
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72	7
aKipxia a 7-a napTe ecte o,654=y/^ ^
// 5 \	x26	182
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A,£ OBIţIE KXNA COKOTÎM OKXrbJjÎME NEpajpONaAb , TOT A’axNa TpeBXE c*b cxBT-^yty Kt kxbipîteae cxnt cra-TopNÎ'UTE acxnpa npfjpiAXi anpcmiiaT ae a^cn» kxti» jj'ime; AXKp"bM Aap acxnpa antCTopa Ka mi kk NSMipiAE (jjpxMjepoace. Ama ,
1° Ain\E ftvjJEMţl! M H£ fKCEMr'’l>3,b 4 s/'J .
2°. 4 x \/7~Vl X 4=v/(42X7)=V/l12’ 5°. V^X V/3 = y/5X\/2=\/C2X3)=V/6V
80
APITMETIKT)
4°. Ilrnw ei ftosmyht aMJKNAOÎ TEpMENÎ ynei (JipSN-
ţKpî NEpayioNaAE tot npiN a'iEAau: NXMbp............
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66 . ObB/KpiIlÎM KY Mai MYAT£ .jvNCFMNbpt t 1° . Tot AaVNa TpEBSE CI BAY1EM NYMSpiAE ^NTp’alECf Klli Ka Aa COKOT'feAa CTpaj(I£pi CI NE A'6 f.NTpEţll .
2°. NtfMbpYA SE'llMaAEAOp YNV1 ITbTpaT TOT AavNa ECTfi KT coy iui |.NAOÎT AE K«BT Ba pbAb'UNÎ t TpEEYE Cb aAbO-rifti nyae ca? ci cKoaT‘M .SEiiMaae Ka a+berb AYKpape CI CE-^MHAÎN’fecK'b fN TOUTE j^NT^MJIA'bpiA£ .
5°. ^)îe KapE AEcnipaipE NfnvT-KNA Aa Mai myat a«
1'wVIT O Jjitjlpb , NT UT TEM ASIŞTI Mal MVAT ^KfiT 9 CI
nvNEM Aa pbAb'lÎNb .
4°. A,«NAVNiCE ribTpaTVA YNY1 NYMbp ITpEKYM aA AYl 18 KaChai|>AbM IIE aA VpMbTupVAyî 19, +ÎÎNA Kb . . . . 19=18 + 15 HbTpaTYA ECTE l82+2 X iH1) O » AEXWKpMiab Kb TpEEYE Cb UAbOIlM 57Aa32-J Ub-TpdTYA AS1 l8, IUL aBEM 36l = ig2, A.E OBUIE, K Si N A aBEM nbTpaTSTA JfNYl »»Mbp, ailiOrXNAVÎ 1 MaiMYAT ^naoÎtya ai aiECTsî NVMbp, a-BEM nbipaTXA NYMbbpYAYl YpMbTOp. ^p-»ife3b ae ai>« Kb <J>ie KapE AEcnbpa’ipE ny noaTE Cb A^ OpbMbUlilJb Mai MapE AF- K-KT ^NAOÎTYA pbAbHÎNl ai|)Aa-TE ; ntNTpy Kb aTVNBl TpERXE Cb Mal IIVNEM O YN1ME Mat myat Aa pbAbaÎNa aţţ>Aan.
TT'KTEPr im PbAMNT	81
5. EKCTpaKjjie	At^ÎNi KYBiqt.
67. Mat NaÎNTE As a cko8te pbAi'iJNa	Tpg-
BYE CbapbTbM MÎîKAOKYA KY KapE C£-(J>0pM^3T» KY-EYA, K3p£ £CT£ IîpOAYKTYA YNY1 NYMbp npÎN Tn»TpaTYA
ctjy . As bom cokotî maqECT NYMip AserrbpjjiT |N aot»
ITbpijî, HM Bt3*T (6l) KT> 11'hTpaTYA £CTE KOMflYC A1N mjTpaTYA q£Ait aîn txht, aÎw nijTpaTYA veaîi A’a aoi'a'B , 1111 AÎN npOAYKTYA AOp /fNAO'V." aAÎKh KYBYA ECT6 C1CTE-Ma aqfXTOp rptt K/KT'bJjiMl, Kap£ TpEBYE Cb CE-fMMYAJjl)-CKT» npÎN aMSNAOb nbpyÎAE NYM’bpYAYl AST . ^EHl |.M-MYAJjÎNAVAS Mai fNT*Hf Iip'lN 1% A1N T/KW , 8B£M .
1°. KYBYA ITbpgi qEÎAÎNTSK.
2°. IIpoAîKTYA m»TpaTVAYÎ heaîi A*a aoiaE npin lil A’iN TX1? .
5°. As 2 Opî npOAYKTYA ntTpaTYAYl HEAlî A<N TSlfr npÎN q-fe A’a Aoa.
Acemen^ fMMYAtiwA rn»TpaTYA mi ripi« a Aoa napTE a
NYMtpvAsî ast a<f>Abi\r.
1°. nbTpaTYA HAll^AlN TAHT ^MMYAJJIT npÎN râ A’a AOa
2°. Kybya qEAÎÎ A’a Aoa .
3°. As 2 opt npOAYKTYA* nbTpaTYAYÎ hea’u A’a ao» npÎN q’B a'in tauy .
Xnîna aqf.cTE ftiars irbpjii beaem kt» kybya a opî Ki>pm nvMlp a« aot» m>pgt ce komiiyne as narp*
11
82
APITMETlIvb
(b!3Î. K°. 97 2°.aAÎK-b 1°. aÎN KXEXA HEAU.AÎS T*», 2°. A e 3 o pl TI ’b T paTXA M £ A i î a i n txk' fiMVA^iî ripÎN ui a’b ao a , 5°. ae,5 opî n p o i y-kiia liMpatiAii ueaIÎ ae a aoî Ai npiN ni A i N TX11', 4°. ain k itb v a ueaîi A’aAoiAi.
r Aina (7 + 5) 3 = 73 + 3.72.5 + 5.5*.7 4- 5* ; av i33 = 545 + 735 + 525 + i25~i728.
xnae ypMTj3t kt> kxbya <|>is Kbpxia NVMbp KOMnyc AÎn3S'jzmi iuiaînxiumi C£-c{iopMÎ>3b ain kxexa 3 e u i-M IA Op, A E Tp £1 Opl IlbTpaTyA BEUlMiAOp fM-MyAjii-r-npiN XNi&n, ae Tpeî opî niTpauA x-N i M i A O p npiN3EniiMl, IUI fN C (|) Al piUlT AÎN rsesa vpii&iiAop.
63. ApbrbM ani Hiiiui Mai NaiNTS (62) ki>kxexa x-KXÎ NXMbp ap£ JjîtJipEAE pbAbsiNl pNTpElTE, Opî pNTpUTA nai nvjiiN 1 cax Mai nvain a .
PbAbnilSlAE NVMfpÎAOp < ÎOOO, (^UNA KT> nx a? Mai MXAT AEKXT Ojjicfip'b, AE X1XTEM a<|>Aa pN TUBAS A£Aa »P HtpnETapi HEAOp A3ATE MYMt'pE O BOM AECIIbpJji fN AOl» f NTiKMnAbpi .
l-a. 4,aKa pbAtu’ma nyaps Maîmxat aekst r\ot jji-4>p£> ksbxa TpEEXECbaÎBb 4, 5, cax 6; npeKXM ec^e ny-MbpXA 2ig52 . Ka Cb a^)AbM pbAbnÎNa TpEBXE Cb <tM-CEMNbM Kb KXBXA ’{36uiMÎAOp 4£ CE-MEp C£-(J)OpMi3b'
^.nkxeaina	3E'iiMÎAop mi nxinA Tpeî nxac cnpt
83
I1YTEPI IIII Fb,i,rbTIINI
ApIînTa (17)- A£cmipuiNA Aap heae Tpeî ATnb'*pMb jjicppE g52 a NYMbpxAYÎ nponvc, 21 KonpiNAE .kxbva jji(J»pi 3£TnMiAop cokoiîte Ka NiqiE cimmAE knîki ini fNKb ini mî'iae Kaps npOBÎN asab heagabate nbpgî. ^ea Mat MapE KXE HE CE-KOnpÎNAE -J-N 21 ECTE 8 , a KbpXia pbAb-llNb ECTE 2, EapE ECTE yic|>pa SEliMlAOp: BH1, nENTpV
Kb 2ig52 ecte > 203 cax 8ooo, iui < 3o3 cai 27000 , ' p'bA’b'liNa «IE CE-HEpE ECTE |NTpE 2Q3 Ull 3o3 .
Cb CKOaTEM 8 AÎN21, pbMiKNE i3g52 Kaps Konpiff-
&£ npE «IEAE ABATE TpEl nbpHI 3AE KyBYAVi: i.f.'ll IipOAXK-
TVA AC 3 opî aA nbTpaTVAXl 3£liMiAOp ’npÎN XNÎMI CE-«|>OpMl53’b ^MMXAgÎNA nE 4 ^NTpELT C3Y 12 lipÎN XNÎmT , uii nxiNA fNKi» mi aotj nxae cnps Ap'frriTa: auia cb as-cnbpjjÎM i£A£ aot» jjicJipt Axnb vpMb 52 , i3g Ba ko-npÎNAE a£ 12 opî xpisiiAE, uiî cxtîmiae npOAYCE npiN MEAE A3ATE nbpjjl 8aE KYEYAXÎ • ^MUbpipNA l5g np’lN 12 kxtka Ba (|)i NErpEoiiT tnImiae, cay VN NXMbp nprt MapE: iui $iiNA ki> aatcTb yi<|>pb ny noaTE cb TpîiKb npECTE g , AYbM g nENTpy K<ETYA AY1 .
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nbTpaTXAYl 3EniwÎAOp, TIYN£M ^NTpEÎryA npOAYKTYAYl 3£-
MiMÎAOp npiN n cair 3.20.g=54o; iie xpMb nbTpaTYA ayÎ g cav 81, mi ^mmyajjîm CYMa 1821 npiN g ^aKa jjicfipa vNi* MÎAop Ba <|>i g,npoAYKTVA ap TpEByi cb <|>i£ A’onoTpiBb ky pbMbUliga cav Mai MÎKb AS K-KT ASNCa, nENTpy Kb K H ix-aokva anscra <|>ai£M nE kate TpEÎ nbpiţiAE KapE KonpÎNAe
84	APfTMETTK'h
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ll£CT llpOAVKT Ktiu-isp- 8
îuuijie iie i5g52; ae xn- i3 g.5a
A£ CL-BfcAÎ Kb XNi.VHAE l3 6 52 C&NT <C 9- ^îtpsbM cl-	Q	1821 jy44
C£M£isi> ii£ 8, uii qjb-	^	g
k&natot anii iipuiib, a-	i838g i5g52
(J)AbM ky CKjMubrarE
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Vt&M 4.
5°. Cb KOBOpXM ASNrb pbMblllijja 4 AEClTbpiji-p'fe ypMbtoape 3o5, aîn KapE AsciibpyiM AOb jjic^pe o5, ini cb /jvMnbpjjÎM ii£ 43 npiN 12, ^NTpEmA rrbTpaT aA
Ji'ujlpi at|)Aar£. iv-KrXA 3 TpEBYE Cb CE-4£plI6 AXllb K1(M SÎCEpbM, ini BEAEM Kb CVTEAE C/KNT 3 Uli pbMblUJKIja l38 .
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28 PMbHÎNb
12
34
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tiotepi mi PTU'bmm	8$
mi ama fMaî |nkoao . Iuti TiriXA cokoteaî .
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69. AplaTiiM ani aceMEN'B Ka mi Mai Nairm kt>,
1°. PbAiliiNa KyBlK'b SIVEI (ţjpaSNţUpî CE-acţlATj ae BOM CKOaTE n£ a (|)i£ KbpXfâ ĂlN TEpMENi £1 ; &Z BOp <J)i KtpfemONaAl, a^SHEM I1E NXMrrOpXA (65) /J.N KXE SKtaKT, ^MMVAjjiNA ne 4>ie KapE TEpMtN npÎN irbTpaTXA nxm'ito-
- V 5	V5*49	3
pSASl . y' —=y --------=4y/a45.
7	73
2° . K/HNA, XN NXMT>p ^NTpEr NX apE p’bA'bmNb KXEÎ-kt> ■ţ.NTp'ferb, ars mi Ea nx noaTE <J>i m«n (ţip^NţlEpoa-cb (53,5°.): *ap jixtem Cb ne anponiEM nexott»-paiT. Ka cba<|)Ai>M 3y3 Mai nxjiiN kx |, pviMXAjjiM ne 3 npÎN kxexa axi 4, mi aBEM 3.64 cas 192, a Kbpxia pb-
AbHlNb KXC'lKb -J.N NXMbp ^,NTp£r ECTE 5 , f,lHl ECTE NXMbpXA <!EC£-«I£pE, mi 3y/3 Ka^E fNTpE mi . AcE-men!) riENTpy 3y/3 4 Maî nxjj’iN kx t*ţ ; aBEM ......
3 f X i > 3=4g43 -f, mi pbAbMÎNa ecte 17 ; ^eii J-\ ecte anponiaT 3y/3 $ mi nxjiiN kv .
5° . Ka CT» NE anpOQÎEM npÎN aîKXTOpXA 3£HÎMaAE/Op , MXTbM siprxAa ae arxrb opî kx TpEi Tptim, A*nb eş»

86	APITMETIKT?
TE gi<|>p£ 3£q’lMaAE BOÎM Aa p’bA'bUÎN'b ‘ IIENTpX KapE 8-ATiOrbM VN NVMTjp KXBiÎNUOC AE NXAE AE Ba <J>1 AE TpEBV-înjji» • Aula Kaci>aB£M 3y/->,3 Maî nxgiN	ax-
■bM 3y/3oO OGO KapE £CT£ 67, A£ XNAE 3y/o,3 = 0,67 . Acemen'B 3v/5,7 MaxnxjjiN kx c£-a^)AT» axxna . . r . 3y/’5700 Kap£ ECTE 18 iui aBEM 1,8. C(|>;Kpm;T ... *^3,2178 Mainxgiri kx ^ ecte^J^ 3^/3217=1,5 .
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Iarb îcoKOT'BAa mNTpx *^477
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3y^—r 3ţ/245=f X 6,2573=0,8939. Acemen1>........
3V'17!= V¥ = -3-'3/477; a*» V477=7>8i539. A-ma ptATiuiNa ue ţe-HEpe ecte a,6o4463.
147	18252
168	234

IIETEPI 1III FbA'b^INI
87
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ecte a Tpsia napTE a hcavi a8at . Noî bom aBt a ^ Mm>p«» JJ*1 npE MEA ‘AÎN TBK npÎN MEA A*aA AOIaT) .
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MENYA H£A A’aAAoiA'fe C£-NYM£ipe A £ - M i 3KA O K II p O -nopjiiowaA.
72. ^ana pbMbmigiAE a AOb CKbAEpî io—8 ini 7—3
C.SNT A'onOTplB'b cav NV, BOp (|)i aC£MEN'f> A’onOTpiBTj ca»
ny mi A^nb M£ ae BOM aAbora gymb 8 + 5 a KxrbgiMiAop ae CKi>3yT; napENEAi» io + 5 mi 7 + 8; ae *nae YpM"fe3b Kb, KiRNA aBEM £KÎAi(|)£pENga 10—8=7—5, CXMa 98-Aop AE-MapţtÎNE £ C T £ a’o IIO T p i B b KY89£AOp  £ m i x a o k, mi aîn nporiBl», A»Ka 10+5 = 7+8 aBEM EKÎAi+EpENga 10—8=7—5 -
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12
#
90	APITMETIKT»
Tpisb, fpfcsxe cb vpRie3£ iioTpiBÎpt panopTypiAop Cav npouopgia |-= l^-cav 6 : 3 :: i4 : 7 . IL-NrpY kt>tot A’ajrNa ry (JrbKbTopi a AOb npoAYKTYpi A»0 noxpiBb noa-Tt cb c£'4>op»JE3£ o nponopuiE (Btaî w°. 33).
2°. IJpOAYKTYA HEAOp^E MiaCAOK '(|>aUE YN m>Tp3T , AEfiop <f>i A’onoTpÎBb; asmi hea asmîjkaok nop-IJOpfâiONaA N T p £ AOb N Y M £ p £ ECTE p b A b U i -wanbxpaxb a np o a ykt y avi a o p .	^ n t p e 3
iui 12 UE A A£ MÎaîAOK npOnOpglONEA ECTE X=y/5X 12=6. A,în npOTiBb Aana aBEts 62 = 3X*2, iiytem ^>au£ o nponopjps KORjj’iNYTb “3:6: 12.
3°. Aana o nponopjjÎE KonpÎNAE yn TepMEN NtKYNrr-
ckyt npEKYM 6:3:: i4 : x ; ^îîna Rb ae 3 opî i4 caY'
4a TpEBYE Cb ^»Î£ a’u nOTpÎBb KY A£ 6 Opî NEKYNOCKY-TYA, EA ECTE £5) K&TVA AY1 42 4>Mllbp|jiT lipiN 6 C3Y *3 — 7 . A.£ OBIJIE SSÎA A1N UE1 ASMapţllNE CE fl_ cJ)Ab jvMnbpyiNA II p O A YK TY A UEAOp A E M i -KAOK n plN UE A fa £ M apţllN E KYNOCKYT. AaKa NEKYNOCKYTYA ECTE YNYA A£ M13KA0K , ap TpEBYl Cb fM-nbpjjÎM npOAYKTYA UEAOp AE MapŞUNE npiPt UEA At MÎar-AGK KYNOCKYT.
4°. IIytem. ^>bpb acE-CKÎMBa npEjiYA ynei nponopyu,
Cb <f>a<I£M Ka A£OC£Bijii TEpMENl AÎN K3p£ CE-KOMriYNE Cb lipilMtcRb TOaTE CKÎMBbpÎAE R3p£ (JiaK ^NKb Cb A^ npO-AYKTYA UEAOp tAE MapţtÎNE A’onOTplBb KY aA UEAOp A£ MÎ -*aok. Ama TiEKTpv 6:3:: i4: 7, Rapt a^^X?—3X*4 av nxrij.
nponop^ii	91
I. Ct> ckîmbtjM np£ mei ae Mapi/iNE 4-Ntpî cine cax npc mei A£ mîsaok fNTpE cÎne Kaps CE-ap&Tb npiN Alternan* do ) ama.
6	; i4 :: 5 : 7 cax 7 :	3 ::i4 : 6
cav 7 : i4 :: 3	6
II.	Ob flYNEM HEI AE MapijlÎNE AOKXA «AOp A* Ml-JtAOE ^ KapE CE-NYM£iji£ Invertendo ) •
3	: 6 :: 7 : i4
III.	ccţt^pmiT ct> j.MMYAijiM cax ci> ^MniipgiM na a-Mj'knaoi Anteheasnui cax aM£NAoî xpMtTopi tot npiNTp’xN
NXMTjp .
73 . Aavkxna TEOpEMa aeah n°. 33 fN nponopjjia.... 3o : 6 :: i5 : 3, cax ~ — ~^» a^AiM.
3o+i5	i5	3o + i5	3o—15
----— mi-------------=---------,
9 + 3	3	6 + 3	6—3
JL,tm i°. cxMa cax AÎ$£pENjja ÂNTEHeAENBi-/op C£-ap£ KT>TpS a XpMTjTOpÎAOp, npeKXM X N aNTEHEAENT KT> Tp £ XpMl»TOpYA CbX.
2°. CxMa aNT EHEA ENJii AOp C£-apS KTbTpe AÎ^EpSNÎia Aop KaCXMa XpMTjTOpî AOp KT»-xpe aî<|> epsNjja Aop.
92	APITMETIIvh
3°. <|)k vn uixp as panopTvpî a’o noTpÎBT»
« - IO- 14
5 —6	T
6 + ^o + !4 + 3o i4 3o
3BEM
AS-
3+ 5+ 7 + i5 7	5
ii|n opî he uiJKp as panopTvpî ajon o t p i b t>
CVM3 aNTEHEIENJjiAOp C£-ap£ KbTp£ a V p M b-TOpiAOp Ka V N SNTE'IEASNŢ KtTpE îpMtTO-p VA CbY .
4°. ^,e bom j.NToap'iE nponopipa AaTb aBEM . . . . 3<>±6	6
3o : i5 :: 6 : 3, a£xnas-= —.
,	i5_+3	3
74. IIvTEM Cb (,MMVAJjiM"'"A01» nponopîiiî TEpMEN KVTEpMEN; IIENTpV Bb 3o : l5 ” 6 : 3 Uli 2 : 3 :: 4 : 6 Aav ^paîNţtEpiAE A’o'noTpiBb	un
-|=^; II£ KapE AtlAE BOM j.MMVAiii a(|)AbM...
3oX2 : 15X3:: 6X't : 3X6.
ĂS *NA£ VpM"fe3b KbnVTEM CbapAlKbM OIipO-
nopjiiE AanbTpaT a a k v b..... mi* a'in npoTÎBb
CbCKOaTtM AÎNTpANCa p b A T> HÎ N a nbTpaTb, K V B i K b •.,.
2, II £N T p V PerVAlAE ASTpEI.
KjXNA EAEMENTVpÎAE VNEI npOBAEME nOT Cb c]>aKb O npo-HOpîiiE aA Kbpia kekvnockvtva £CT£ MEA A*nb xpwb TEp-MtN, IJpEJJXA aHEipia m’a Ab O ClMCIAb COKOriiAb (72, 3°.)
mKaps onvmîm PtrvAb Asipsi: ama 3o ASAVKpb-i
I
i	PEFYAI AE TPEI	93
TOpt av AVKpaT 20 METpXpî, 21 AXKpbTOpl KATE ap AX«
Kpa Tor^NTp’aq'fe BpEME? AcfiAbM 5o : 20 :: 21 : x, apb-
| TANA npÎN X NXMbpXA METpVpÎAOp HE CE-U£p£; Uli BBEM....
20.21
x = ------=i4. Beaem kt> AECAtrap’ii auEUiiî uspEpi
3o
!	CTb fN pEI'XAa Tpe", KANA CriVNEpk CE-<|>OpMl33b AiN
j	aotj nepioaAE ; aî ueaxi aÎn taix aoi TEpMENi cant omo-
! I,I£NÎ K0pbCUXN3bT0pî KXaiHEAXl A’aAAOiA'fe, aAiKb TOT AS
I XN (j)£A KATE A01 AOl; Uli Kb |NKb aiEipî TEpMENÎ ITOT Cb
c|>i£ |mmxajpijî npÎNTp’xN tot auEA ,NXMbp. Auia ps npo-
EAEM8 NOaCTpb 5o AXKpbTOpl , IUI 21 AXKpbTOpl CANT
| OMOGENI , mi 3M îmi) aHECTE NXMEpE Cb AE /pVUMVAjpM
. npÎN 2, 3,.... <|)bpb a CE-CKÎMBa npOBAEMa .f.NTpX NiMÎK.
I A»N npOTÎBb [lipEMt nANb KANA O nîaTpb Cb K33b AOC
N6(|)iiNA ^NAOÎTb KANA fNbAjjilu'b ECTE -jvNAoirb , O BYTE 1 • ^ NE^EOlbpTANAXCE -J>N ^NTpElTb BpEME KANA Ea ECTE AE TpEl
opl Mai RiapE : aiSCTE EAEMENTXpî NX nOT a CE 8AXHE ^N
j psrxAa ae TpEi.
I
,	76. Axni q£ aM apbTaT A«Ka AECAErap'b xnei npo-
EAEME nOaTE Cb CE A’fc npiNTp’o npOnOpftlE , NX pbMANS AE KAT a XOTbpA- eJhE KbpXKl TEpMEN Tpi>IITa K3pE Tp£-EXE Cb ML. ^EA A*Hb XpMb Uli UEA A’aATpEiA^ CANT NE-KXNOCKXTXA Uli 3A CbX OMOGEN, ciNrxpXA KapE noaTE a CE KOMUbpa KX AXNCXA. ^EpEp'B ^NCEMN^Sb ^NKb mi KapE AÎNTp’aUECTE AOb NXMEpE KOBApUiaiJIS UE HEA aAUATj pape xoTbpaipE aokxa meaxî aîn ta» tui ueaxi a’sa aoîa$
t
94
APITMETIICb
T£pMf.N, IIENTpX KT. aNTETEAENgi TpSGXE Cb (£iE A*IN np£X-nt MaiMapî cay Mai m'l’ii as kxt spMbiopi Aop .
Ama Axnb qg nxctpbM Maî cxo 20 MErpxpî mi x me-
Tpypî , BEACM Kb 2 1 AXKpbTOOl TpEEXE Cb AXKpf 3E M81 nXJi'lN AS KXT OO , mi KT» XpMbTOpXA X ECTE < 20 ; AÎN
AOb NVMEps A»p 5o mi 21, 3o ecn 4ea aîn tsb, mi a-B£M 3o : 21 :: 20 : x-
TTpMbTOaptAE AOT> £KC£MnAXpl BOp apbTa Mai ASCBOAT
B£ ii as ai'iî .
Yn AXKpX c’a CbBSpm'lT p* 5 3ÎA£ KX 57 AXKp'bTOp] , KXTE 3ÎAE TpEBXECK KX 10 AXKpbTOpî Cb CE CbBXpmaCKb TOT aqEA AOKpX ? (|)iiNA Kb 3‘iAE aM nXT'Ij Cb AXbM ae
AOb cay as 3 opî Mai mxat mi AXKpbropî as aTAcrfe opî Maînxym,'ispsp'fe ce A£CA"ferb npm nponopjiu. IIxnem Mâî ^.NTSUV 5 3*1 A8: X 3*1 AS, mi ^»iiNA Kb Aa 19 AXKpbTOpî Tpe-BXSCK Mai MXATE 3ÎAE AS SXT Aa 57 , Ka Cb C£-CbB*pma-CKb TOT aiEA AXBpX , XpMbTOpXA X ECTE > 5; ECTE Aap XpMbTOpXA panOpTXAXl «JEAVl AÎNTS1X, mi 3BEM
5.57
ig AXKp: 57 AXKp .	5 3Îas:x sîae =-----= i5 3Îae .
19
Ka Cb C£-pMBpaq£ O MOEÎAb a TpÎBXÎT 6 METpypî AS CTO(|>b ABTb AE	TOT IIENTpX aqlâCTb MOBlAb KXTE METpX-
pî BOp TpEBxi AS o CTO<|>b AaTb AS -f- ? KxTOaTE Kb a'li KXTS narpx TSpMENl C«NT METpypî , A»p BEASM Kb 6 METpXpî ECTE OMOIJEN KXHEA NEKXNOCKXT, IKNrpV Kb aMJKNAOÎ a-f
PErtfAI AE TPEI	95
part axmjhme; ama npouopuia CE-TEpMÎNfeb kx 6 me-Tpxpî iui X METpXpî . A1'” AS O CTOtjp'b K3pE EC.TE Maî Aa-■xb TpEBxtiji£ Maî nxyÎMj axnj^îme : niNTpx Kb|>|, a-B£M|X> 6; iiua ECT£ aNTEBEAtRTXA panOpTXAXl BEAU
aîn UK iui ac[)AbM |6 : x as xnae x=6X1=6|.
77 . Kx ToaTS Kb tot A’axNa ects aecne a (JiaBS asiorb sxAÎKarb, Aap AtnbpTiBNAVNE ae AMNca, uxtem AXKpa Maî kte cOHOT^Aa . Abem AOb ^>£ATfpî AEpanopTxpt,
ApEnT KapE CE ^)OpM'i53'b A>N NXMEpE K8p£ KpECK Uli CKaA AÎNnpEXR'b , uli 3ATXA f N T O p C , f N K8p£ XN NX-Mbp CK3AE KXNA BEA 8A3AT KpîipS. 3o AXKpbTOpî ID1 20 MEMTpXpî AEAa Bipip'fc AÎN TJK1-X CXKT fN panopT AptnT, TIENTptf Kb AXKptTOpi CASNT Mal MVAJjî Uli AXKpX CE-^)a-be Maî m^at; ,j,n ui A’a Aoa aîn npOTÎBb., £7 AXKpbropî mi 5 3Îae cmnt panopT -pnopc nENTpx Kb AXKpbTOpiî C1KNT Maî MX A ai, Ulî Ka Cb CE- (£aKb XN AXKpX TpEEXE Maî 11 X ai N £ 3Îa£ .
KaU'U TfpMENl XNE1 UEpEpî CIKNT p8II0pT Ap^T, CE n*N TOT |NTp’aUEA£ TpEliyî KapE TpkBXE Cb aîfib /JiN IipO” nopyiE, nERTpy Kb ajknaxce urpEpi, ce-aTj iniiOTaufA P*NA TEpMENl AOp OMOJJEN1 -f.N aMSNAOb IIEpioaAEAE . A.aP ASKa npOBAEMa aps panopTXpÎAE CâAE ,(,NTOapC£, TEpME-wi TpEBXE Cb CE-axXKb fNTp’xN fNJlEAEC AÎN npOTÎBb 4>N nponopjiiE , DENTpy Kb BEA AÎN XpMb AÎN NXMEpÎAE AaTE CE-CKpÎE BEA AÎN TA1IX J, U1BA.... NEKXNOCKXTXA ^)ilNA TOT
A’axwa aokya bea A’aA naipxAi , Kape xpMÎ3b AÎN BEAE 3ÎC6 .
06	APITMETIKT)
Maiiarb iniaAts EKCEMriAxpî ^nkTj riENTpx ptr¥AiA8 A£ Tp£l .
I.	Xnom a AVKpaT 5o ae CTxmxm 8 3Îae , 80 as CTiKNsiNÎ -jvN kxte 3Îae Ba Axnpa ? PerxAb ApklTrb: auia 5o : 8 :: 80 : x= 12 f.
II.	OM a <|rbKXT XN ApXM ,f>N 8 31AE MEprXNA KA5-T£ 7 H'icxpî 11£ 31 , KSTb BpEME TpEEXKl c’bA ^)aKTi AEMEpljb K/gTE IO H'fecypl n£ 3i ? PfirXAb ^NToapci»; AehÎ io : 7 :: 8 : x=5, 6.
III.	A,a«a 17 MapHE 5 onmu 4 rpbXNye AE-apţiiNf av npsjjxiT 869 AiBps i5 coaau rmi 6 AÎNapî, kst ap npEijxi i4 Mapie 3 onhu 2 rpbXNjj£-|-? PerxAb Aplî-mb; aemi 17M 5° 4r:86g aîb. iSq 6a:u4m 3° 2r £:x aIb .
CoHOT^Aa CE'fNAECNEipE ^MMXAljiNA nE aMXNAOl aNTE-
heaenjji npÎN 16 tui aBEM 283m : 869AB . i5c. 6a.::23om 5°:x. lipi» Kape CE-a^At x=7o8a 16c. O J-a •
jy. 6 CKaxpoaNE ax cbBxpmiT 0Mara3ÎE -ps54A£ 31AE, 9 CKaApOaNE fNKXTE 31AE ap ChBXpiuio ? PtrX-Ab ^rrroapcb, ae y«AE 9: 54 :: 6 : X = 56.
Y. O KOpaBlE aps <JiNKT> IIENTpX 10 31AE McplKAE j Aap nEMapE O Cb 3bE0BlîCKb l5 3ÎAE, Aa KXT TpEBXE Cb CE-aAXKb ^)ÎE K-apE nopHÎE? Ani NX a<J)AbM nETEpMENl KXTE naipx ; A»P tCTE 4.NBEAEpaT Kb XNXA CE-CX&T^NJJE-AEIJCE mi KbllpOBAEMa TptlîXE Cb CS»^NHEA'fer'b f.NTp’a’UCT
kîikae ce-stofii 10 3Îas ne Mape^ap cj>i abt {fiie Kbpxia
PEL'KAi 4.E TPEI	97
bM K/"KT£ OnapTE, O Cb 3bE0Bl5CKb l5 , KMTE KJKT A»p
o cb ce- A"b ? pEnfAb ^NTOapcb; ama i5 îrkjy: 1: x=f.
78. PervAi a £ t p e î KOMnxcs. AE myate opt CE-nponvN fN nponopjiiî ispEpi, KapE KoripÎNA Mai mya* as K-KT TpEl TEp.MENI AaU,l. AtYNiÎ 81ECTE lEpEpi TpEBYE Cb C£-(J)aKb AÎN AOb nspioa^fi, KapENYMEpi/S OMOţIENE Cb AE feo ipÎN3b K/KTE AOb AOb, ilENTpY KapE fâTb YN EKCEMIIAY .
Aasa ao^oaoaMENi aYAYKpaT 160 MSTpypî l5 31AE, 3o OaMENl KXX OaM. MSTp. 31AS. BOp AVKpa ^N12 3ÎA£? AE 3H1 ^NaÎN- 20	l6o	l5
TE BOM fMnpEVNa TEpMeNl OMOGENI 50	X	12
Ăvnb KYM CE-BEAE fjvNlipOTÎBb .
Am BEAEM AOb ^NTXMrlAbpî: aA*IKb KXNA TEpMENl KapE ny pb'cnyRA nekynockytyayi cxnt panopT Ap£nT cay j^NTopc. Am 20 oaMENÎ iui i5 3Îae c*nt panopT ^,NTOpC; nVTEM Aap Cb ^NAOÎM Cb ^NTpElM .... IIE YNYA A1N NYMfpE , HENTpy Kb n£ MEA HA 3AT fA ^MnbpgÎM lipii» 2,3,... Ulî BEpEp'fe pbM/ENE TOT aH£"6. Cb ^MMVAjjiltt 20 'oa meni np'm i5, mi a bem 3oo oaMENÎ mi 1 si; a cemen^ cb fMMyAjiiM 3o oaMENÎ npii» 12, mi bom aBt 36o oaMENÎ mi 1 si. Ae'iî lEpEpt aKYM cb tfiant, AaKa 3oo oaMENÎ ax ay- Osme. METp. sîa. KpaT 160 METpypî fNTp’osi, 36o	3oo	160	1
K*r Bop AXKpa? TiMnYA <|>iiNA	36o	x	1
TOT a<l£A3 f A AbCbM, m’l aBEM p£-
pEi YAa Ap^nTb 3oo:. 60 :: 36o : x== 192 MtTpypî,
13
98	APITMETIK'b
KaN'A panOpTXA £CT£ ApEIlT C£-riOaT£ (|»as£ llXATS
<j>£AXpl J CnpE nÎAAb A»Ka 20	oa-			
MENI ax AKKpaT 160 METpypi	fN	OaM.	METp .	3ÎAE t
15 31AE KjKTE s'lAE BOp TpBli	Aa	20	160	l5
So OaMENl Ka Cb CE-AXKp£3£ ig2 METpVpl .		3o	192	X
Aui OaMÎNl C/KNT Mal MXAIJ1 mi METpVpl Mai MXATE AX' Kpl33T>;	20 OaMEKl' mi 160 METpXpî C<KNT ţN paiIOpT
ApEnr. Ama, Axnb he bom pMMVAiji vNa AÎNTp’aHECTE k«-TbJjiMl npiN 2, 3,.... TpEEXE aCEMSlsii Cb fMMVAJjîiM mi npE 1EA 3A3AT TOT npÎNTp’aHEA NIMbp . Cb AXbM 118 192 nENrpV (|>bKbTOp AII 20 OaMENl mi l6o METpXpl; nE Xp» Mb n£ 160 nENTpx 3o obmenÎ mi 192 METpxpî, mi Ecre ^NBEAEpaT KbN^MbpXA AC METpIpî	Ba <|>i ţN aMXN-
AOb ^NTXMnAbpiAE ig2 X l6o . BoM 11Xt1j aAXBE Aap aMÎCTb BEpEpE} A^Ka 20 X I92 OaMENpaX CbB«KpmÎT IN AIKpy j>N l5 3ÎAE, Aa 3o X 160 OaMENl KJRTE 31AE BOp ipEBli? antCTb pErVAb ECTE fNTOapCb mi UBEM........
20.192.15
3o X 160: i5 :« 20 X 192 : * — -— --------ca? .. * .
3o.i6o
2.192.5	192
X =----------=--------= 12 .
_ 1.100	16
•^BTTOarE- ^NTSMnAbp’lAE TOT A*ltb KÎdVA aaECTa AI-KpbM , mi BEAEM Kb ^NTOpKXNA lipOBAEMa IIXTEM (jiaiE npoea AiKpbpil. Ian> ^NKb mi bat ercenhai aectva ae /J>NK*pKaT .
PEI'XAI AE TPEI	99
AaKa 40 AVKplTOpî aY	OaME.	METp .	3U£.
AYKpaT 300 METpYpl jvN 8	4o	3oo	8 7
3ÎAE AYKpXNA RAITE 7 H'feCY-pî n£3i; AaSi AYKp : Ka	5i	45g	x 6
CT» CE-AYKp£3E 45g METpYpl 3‘lA€ Bop TpEEYi?	KSTE 6	«dicypî	ns si, kxte
Mai	BEAEM Kl> AYKpTjTOpi Uli <d5CYplAE CSNT |N pa-
nopT fNropc; o ci» tivisem Aap 4oX7 H'fecvpî A’onapTE mi 10 X<î itiCYpî AEaAT8,^NT*p3i-
ÎNA Kv 0 31, Kaps Al» AOK qEpEpi 1TI)CVpî . METp .	S1A5.
me c£-apaTi> ^NiipoTiBij mi Kaps 4oX7	3oo	8
nyecte aexpEExiNUT» a CE-am . 5iX6	45g	x
HtcypiAE i mi METpvpÎAE
CJKNT panOpT .pN'TOpC; O	OoMENl.	31AS.
ci> cfiaHEM Aap ne 45g j-MMYA- 4oX7X45g 8 U'iTop TEpMtNÎAop riEpioAY- 5iX6X3oo X
AY1 HEAY1 AiNTXH?, IipEKYM mî
3oo Ba <|>i acEMENi heayÎ A’aAAoiA’fe; AYKpY KapE Ba aAVie
NYM"bpYA METpYp'lAOp CT» <|>Σ TOT aHEAa mi AE O liapTE, mi A£ aATa mi aBEM ama o pErvAT» A£ Tp£i ^NToapci», nc Kaps o bom jiyne ^NTp’anecT Kin ....	....
4o.7.45g.8
5iX6X3oo : 8 ::'4oX7X45g : x=---	‘—; ca?
01.6.000
40.7.8
x =--------=11 -5- •
2.100.
FIytEW ^NKT» CT» NE Atnl>pn>M A£ a^ECTE <|>£AYpiMl A* AYKpipî lai SYAEKtttl , IHNTpY Kt p£npO*YKiNAYA« •-
TTMETIKT)
‘J&-;**'***	, y,
» ^>Σ-O^^MCpMFN H£ CE-KOMni>p,63'b KV NEKYNO-i
bsaIs ktj k * n a panopTYA Ba
faT, TEpMENYA TptBÎE Ci CIUMBE AO-K Y A K V OMOţIENÎA C i £ ; nEKTpî Ki ţaEa p a -nOpTÎA ECTE j>NTOpC /JvAAiCiAl ama II p £ K î M E C T £ . 'f'NC(|)*pUliT^MMyA|liM TOaTSNYMEpi-ae îe C£-Konp|NA ^N(J»i£-Kap£ pasNA,inino-T p i B i M npOAVKŢypiAE ^ N T p £ £A£. Aula ţN AYITb YpMb MEpspE AYKpbTQpi mi 3Î A£A£ CtfNT pailopT
^Nropc, np£RVM ini «rfîcypi ae ini
3JAEAE; METpypÎAE j^NCi UII 3IA£A£ 4oX45gX8X7
«jian vNpanopT AptiiT.CKiaiGiiM Aap 5iX3ooXxX6 a'in aok NRMaî n£ 3oo mi 459; <J>a-
1EM npOAYKTYA NYMEpÎAOp H£ C£-KOnpi«A fN <|>i£ - KapE
AirnE mi noTpiBWA CE-<J)aHE.....................
4oX45gX8X7 —5iX5ooX6Xx nape beaem KbapE tot a^EA npEjj kym mi Mai ^Nain ( 5 ) .
AnicTi ATKpapE noan ciNrvpi ci cE-a^Ki ps-TYaÎAE A£ TpEl C1MIIAE .
7g. PfiryAT» as ToBipinjis. Tptî TOBapiurî ax nsc -p NeryjjbTopiE ynta 12000 <|>pa>n. batya 8000 ^>pN., mi n£A a’ba TpEÎAl» 4ooo <J>pN. t mi ay Kxiţiirar 543o ^>paN ., ce—4f.p£ a CE-A£enipjji KSipirvA anscra AYm> KaniTaAYA Aop.
CvMa ^NTpiri a4ooo <J>pari. a *aT 543o <|>paN. ci 4>a*WM A«p anEcte TpEÎ .nponopjjiî.
PEHFAI TPEI	101
s4 ooo:543o ca? 24oo : 543 :: 12000 : x = 27i5 <};pN.
24oo : 543 :: 8000 : x = 1810 24oo:543:: 4ooo : x = 905 Ct ce-nporm -psKt ini npOBAEMa xpMfroap£ .
Tpsi NtrxiiiiTopî ax nxc -j.n NErxjjtTopÎE xnxa 1 cooo
4>pN . fN lîpEME AE 7 AXNÎ , 8A1XA 8000	5 AXN1 UH MEA
^’aA TpElA't) 4000 fN 20 AXNÎ; C£»MEp£ Aap KXTi liapTE a-fpe c|)i£ Kapt aîn K*qiirxA i5oo <|>paN.
Ct /JvNcemnTjM Kt Kbn'iTaavpi ae ini TÎMm'pi/E cxnt panopT jvNTopc ; ^mmxajjînaxae n£ <J>îe Kapt npiv m1> ac Axrb axncxa, benîm mpb ^NTp’o pErxAb a£ <|>eaxa M£A AÎN TAiEX, aAÎKT> XNXA AÎN TOBapblUÎ CE*COKOTEEJJE Kt a nxc 70 (>0O <ţ)pN . , MEA a’^A AOÎA^I 4oOOO <|>pNK . mi MEA AÎN XpMt 80000; BpEMÎAE CJINT a’o nOTplBt 3KXM, 1111
ama ac])AbM 552,63....tjjpaN. 3i5,79...c£>p. 63i,58...<|>p.
XlENTpX KSIţlirxpiAE |)i£ KtpVKl.
80, pErxAb as A o e x n a T». Ckoiixa aMEipiî p£-
TXAE ECTE a a<|)Aa CXMa AE nAtTlT nENTpX B3N1 ^Mnpx-MXTauî Axnt oapE Kap£ ^mboeai : aobxnab aM^CTa c£-a-umt fN AOt KÎnxpi: cax aptTXNA meIj me ai» ioo Kape ce-apaTt npÎN BOpBEAE 4,5... AaocxTt ^mics-cKpie ama 5a.J) cax xortpxNA cxMa KapETpEBxc ctA^Ao-BXNAt XNXA ; AlNapXA l4 /J.NC£MNi3t Kt l4 tjlpaN : Aax XN 4>paNIi .
PEAajjia KapE A^rt aMECTE AQt Kinxpî ae a amt3a ao-BALNA3 , CE aq>At npiN nponopjjie, AAÎKt AÎaapxA a5
I
402.	APITMETHxb
, s tot a^eii kx 4 a. $ mNTpy kt> nvÎNA perxAa ae Tptt AaKa 25 Aav i,me joexnaii Aav îoo, atfiAbM /i. A-CEiMEN'fe iui AÎwapyA 2 bine Aa 5o Aa AiNapyA 20 Aa 5 a $ (be31, uiENa i*a., Acta II a CrxpqiTVAVÎ ax! MoAisp).
Un ercemiiax aA psrxAi aobnsî ecte aectva cb ne apa-TE KXM TpEBVE a AECAEl'3 TOaTE qEpEpixE AE aHECT (J)£A . A,aKa 100 Aay ^ ^Np’o AXNb, 10000 ,p 7 avni kst Bop
Aa? Aq'feCTb pErVAb AE TpEl CE-AEGAijrb A*tlb OfiiqEHf (78) Aap TiyTEM CbOAEOAErbM IUI Aynb KyM ypM'feîb j	100 :	:: 10 000 : x=25 aobainab avi 10 000 nso AXNb 1
AOEXNAa Aap he CE-MEp£ ecte 7X25 ax 175 .
81 . PETXAb A6 G Kb3bMXNT. KxNA O CXMb £-CT8 Cb CE-nAbTebcKb ACTb O EHOXb /J.NKb fNASAVNratb , uiionpiiMÎM aTXNit ^NAaTb, nvmîm Ckhihant AOBSNAa Kaps <|>aq£ ns au^ BpEME . AAÎKb AaKa oape Kaps aps cbnpiÎM^CKb 10000 (J>paN. Axrib 7 axnÎ, AlNrp’au'fcCTb CVMb JiiiNA AOBALNAa KXTE A . £ Ilb AX-|	Nb, TpEEXE Cb CKbAEM lj5 <|>p . , Uli pbMSNE 9826.
|	A4ECT (|>£A AS AyKpapE CE-31HE Kb CE-ia CKb3bMSN-
TXAacţiapb. iui ecte npi> OBiqNviTb kxToaTE Kb ce-onpsijiE AOBXNAa avt 10000 mi j*n <J>iisjjb cE-nAbTEips
1	NVM31 9,825 4>P •
riENTpy CK'bSbMXNTSA N AbVNTpX TpEBVE Cb CE-cKoajib NXMai AOEXNAa cyMi Kaps CE-nAbTEips: mi la-!l	Tb IţyM TpEBVE Cb C^aiEM . Ilfi <J)iE KapE AVNb TpEBVE Cb
li	oupiM | f|>p. nENTpv îoo, ab^Î AWb 7 axni îoo-f*
%
PETIT AI &E TPEI	103
CE-sop cf>aMS 100 (|>p. ini ama iixnem acrb nponopjjie, A8K8 101 | (Jp* c’ax 4)'bt;yT 100,10 OOOKIKT CE-BOp (£a-
qt? mi ac|)AbM 9828 cţop.	(JmNjjTj, alipii cxmî
At’i bom altora aob«na3 ti k&te a. ■§• m> AXNb , bom aufc ţapi» 10 000 cjij).
82. PerxAb KoisxiyraTTi. KacbapbTbM a^fecTb pETXAb , Cb AXbM XpMbTOpXA EKOEMlIAX I 5o AÎBpE AE lJapic npiijxECK 5i AfiXa&iBxpr, 25 ae XaMBxpr npEjjv-ECK jfţ AE (J)paK4*0pT, C£-H£p£ 3 KXhl pailbpTXA AlBpl UapicxAxî KbTpE a <ţ)paK(|)uprxAXÎ.
(|)iiKA Kb 5o AÎBpe A£llapic=i5i AÎBps AtXaMExpr
aBEM f --J AÎB. n. = 1 A1B. X • j (hEAEAIN T£Hr AÎtE-
V5i'
pE [I., X. (|). fNC£Mr)Î3b Ilapic, XaMBxpr, <J)pai»K-
s4
^lopT); aBtM aCEMEisi 1 aîb. X=^—^ aîb (J).; a^Î*
(—) AiB.n^C^AÎB.^.; oi	Kafy
cav 5oX25 aîb . II. == 24 X 5i, Kaps ecte panopiXA %
CE-MEpE , mi NXMtpÎAE ASTE AE CKp'lM CVBT 4>0pMa ERSafiii A>nb KXM CE-BEAE fN npOTÎ-
Bb, (f)bK.XNA.KaaAOa 5o AÎB. n. == 5l AÎB X. napTE a EKxajiii hei 25 aîb. X. =24aîb <|). a iN T/5B Cb 4>i'E TOT AE
ONaTxpb KxiNTxia napTE aEKxajjii îei a’î A o a; mi anoî cb immvauîm ansete EKxayiî TEpMEit
i04	ÂPITMETlKi)
TEpMEN, m.3iNA Aa Iiap-rT) aîn T*W, BEA AÎN TîKHf <J)6K As xn'im'Î ,-nnAa nii A’a Aoa bea Avnt ypMî>.
IIoaTS ct> cE-A'fe vn Maî Mape nvmt>p ae pâuopTypî, Ka-pE cE-jiiK AaNji. Aaîktj, Kape Iecte pariopfyA MErpyAXi Ki)Tps^B£pra^ENrAmpi, ipiÎNA kt> g BEprju npcyvEOK 7 «Oîiî A^l^paNJii, IuiKT>KOTXA rtpE^VEqiE 1,1821 M£-Tpvpî? AVliM nENipy HEA A1N T/Hiy TEpM£N 8A pErVAi KON6 3<vraTS g cepi^i , napc ecte as ^)£AVA BECE-BEpE ,'llli tlYNEM g gB. = 7K.
BEpJ1Il=7 KOIJÎ ; ll£ypMl> CKpÎM 1K. =l,l821M; m MEAE AaATE panOpTYpî ETjlHENA IM- = XB. clîMa Aa pErvAa nii ae cvc mi a-
Axhem ne beae a’in rxnx aot> panopTVpî ^NTp’ywyA ciNryţi gXE BEpi,ii=:7 X i5i82i METpvpî. ITe ypMT> nywM 1 METpy =: X BEpjjlt , mi BEAEVI KTj pEA^KXNAyAE aceMEN'fe, aBEM g X 1 X 1 Baprb—7 X 1,1821 X x METpypî, Ka« pe ne a Avne cb Mai ^mvajjîm ^nktj âBECTE Tpeî EKyajjiî TfpMiN Ky TEpMEN , mi ama aBEM g iiepi,!! =z8,*2747 opî
9
NEKyNOCKvryA x, aexnas x=±--------, (5) ini |N ccjiaîp-
8,2747
X = 1,087 BEp. == 1 METpy .
^■NCEMNhM KT> TtpMENXA BEA AÎN TXB îlli BEA AYITb Xp-Mb X, <J>iiNA TOT AS XN (J)EA , 3MA>NAQb ntpJpAE /pUIIAl-NECK aCEMENi TOT ai'fe KONAijjiS AXIVb HE fMMXAljiM, TEp-MENl HEI AE Ml/KAOK (JniNA NyMEpE aBCTpâtîTE; BCEMEnI) BE-
jft A01» n&piji ^n EKyajiia A^nb vpMt ce-ba^k tot Aa a-a<rl> xftiMe, *tap% tot A’avNa ecte as TpEByiNflTj
nporpF.cn		105
♦n ccfixptiiiT mitt> uii a/ri Cnaisia kxijÎ <|>paNHÎ <J»aK ■,	sEpepe: ioo	xoniî xe
ipiiNX* Ki 1 x^KaT xe Cnama	3 <J>p. ==	32 x.ct.
iipeyyEiiiE 95 xÎNapi Xt|rpoc	24o x.ct. =	1 A.CT.
XE AMCTEpxaM , KT> 34 COAXU	1 A.CT. =	34 c.rp..
XE rpoc npEljyir.CK 1 AlBpi	1 c.rp.=	i2X.rp.
CTEpAiM'l XE AoNXpa, Ulî K1	g5 x.rp.=	1 x*k .
32 XÎNapi CTEpAiNţtl HpEyX£CK	1 x*k.=	375 Map.
3qJpaNHi? I}Jîm Kixonia xe	io88 Map. =	1 nicx.
CnaNia npfejjîfEqiE 1088 Mapa-	ioo xon. ■==	*$P-
beai , xe Kape vn Avi>aT ape
3y5; AiBpa ah rpoc ini AÎBpa CTEpAiNri npegvecK 20 coxxiî
3.24o.g5.io88.ioo XE 12 AIKapî <|)itK0pE. A<f>AiM x==-----------------~
32.34.12.375
itapt ce-pEAV'ie /ax = 4X 19X20; Xe^i ioo xoniî iipEjjvECK i52o <jip. Alieri AYKpape he ce-rmuijiE Ap-BiTpas Mai axEci opî CE-j.NTpEBviNjjîja'b fN CKÎMCbpr.
3. IlENTpv Ilporpeciîi
83. O xpMape xe TspMENÎ xîn Kape ^>ie kape KOBXp-magie ne a«UAa KapE -ja npeiExe cax ecte KOBspuiÎT kx a-
VEini KAÎTlIjiME J ECTE aME^ *JE NVmÎM FI p O P p E C 1 E npiN xi ^epENjii: ac<j)£A cjknt KXM£pi/£ i, 4, 7,
10,.... n£KapE ©apiriM auda~i.4.7.io.i3.i6,.........
mi KVBarfTyx a'ii sere 3.
14
/
106	APITMETIK'b
Ect£ j>NBEAtpaT ’fel» aA AOÎAii TEpMf N'” CCT6 A’oîlOTpIBb HSAX1 AIN T&VS Mai MXAT KXBXNTXA ; BEA	TpHAlî H£-
AX1 a’îIA AOÎA'fe Mai MXAT KXBXNTXA, ai'lKb MEAX1 AIN'TAUX'
Mai mxat ae 2 opt kxbxntxa ; «Ua A 3a na rpxa'5 £CT£ acEMErrfe KOMnvc aîn iea aîn t*h Mai mxat as 3 opt kx-> B/KNTTA UIHA . AE OBIJIE Opl-RapE TEpMEN aA X N E
nporpEcit ripiN AÎ^spENUT» ecte so»nyo Air» 41 a aîn t&yx Mai mvat kvbsbtva ae ais-t1> opt, AVni K iK JJ î TEpMENl TI p E 4 £ A • ,J,E XN-At xpMfctfe:
i° . Kb nvTEM ci» aifiAtM xn TEpMEN aA xneÎ nporpE*» cil, (|>bpb CbCOKOUM UE'lEÎAaAiy KapE UpElf-A • Aaî-Kb Kb aA NOCTpX aA 10O~a13 TEpMEN ECTE = 1 + 5 X 99 cax 298.
a°. Ka cbnxNEM ^NTpE 4 mi 32 rnacE aemîhcaok npo-nopjjioNtAÎ npiN Ai^EpfNIi15 > aAÎKb KacbAErbM a-«1ECTE AOb NXMEpE II p i N T p*a A T £ 6 A î N T p E £ A E, KapE (|>aK onporpEcÎE KOMnxcb aîn 8 tep—
MENI, jiKCEMNXM K b M £ A A*nb XpMb TEpMEN
32 aA nporpEcii <|>iiNA A’onoTpiBb meaxi Ain tsix 4 aAioraT bxkxbxntxa Axat ae 7 opt, 3a—4 ax 28 ecte ae 7 opt kxbxntxa nekxnockxt;
ae XNAE KXBJKNTXA ECTE M — 4, (5).' OGIJ1E Ka Cb Eb-
n>M, fNTpE AOb NXMEps, aemixaok nponopjiioNEAi npiN Ai-<|>EpENJJ,b, ^MnbpjjiM Al^EpENJia a4£CT0p AOb K & Tb JJ î M 1 npÎNNVMbpXA 1 £ A 0 p AE MiîKAOK
MC
nPOI'PECII	107
moimvat y n yj sasha Ba<|)i kvbsnixa. n p o -i-pscia -it A6 c*c ecte ~r 4.8.12.16.20.24.28.32 . AcEMEN'B Ka Cb EbrbM OnT AE MUKAOK 1-NTpE 4 iui 1 l ii —4 .	7
a<|)AbM kybxntya =---------=— • nporpEcia ecte...
9	9
f-4.4*.5*.6f 7f 7f ■ 8f- 9f 11.
y
84. O nporpeciE npiN kst ecte o YpMapE ae TEpMENi aîn Kaps cj)ie KapE KonpiNAE nps «a KapE fA npaqeAE caii C£-KOnp‘lNAE j,NTpXNCKA TOT £E aTSTt Opi . Ac^)EA ECTE
râ yp.MbToape -H- 3 : 6: 12 : a4 : 48 : 96.... $ kybsn-
tva ecte 2.
^ÎEA A’aA AOlAt TEpMEN ECTE a’o IIOTpBT» «1EAY1 A1N TiKHf •^MMYAJjiT npÎN KYBXNT ; HEA A^A TpEÎAi ECTE A*0 nOTpi-BT> HEAY1 AE a A AOlA'fe ^MHVAglT npÎN KYBSNT , CaY Hf AY1 AÎN T*K iJ.MMVAJJÎt npÎN nbTpaTVA KVBXNTVAyî; aCEMEN^
aA 4-a^ ecte npoAVKTVA heaxi aîn tjkw npi« kvbva ky-BXNTVAyî HI1A : ae OBqiE opî H E TEpMEN a A Y N £ 1 nporpEciî npiN kxt ecte npOAifktva heayi AÎN TXHf np ÎN K V B XNTYA apAlKaT AaOIIYTE-pE a p ITâTIj npiN NYMtpTA TEpMENÎAOp Ka-pi np£ 1 £ A • IIytem Aap)
1°. Cb COKOT1M npEJJYA YNYÎ TEpMEN (Jbp'b Cb d?ÎU
ciAi&î ae a rpEiE npiN tojji Kapi j>A npE«i£A. Aa 3E>UAi
TEpMEN iaA nporpEcii NoacTpe ae cyc ecte..........
3 X a9 = 3 X 5ia = i536.
ios	APITMF.TIIvb
2°. CbBbrbM, |.NTpE AO b NYMEpE AaTE, AŞ MÎ/E/iOK npQ«i nopu‘iQN£Ai ; aAiKb Ka Cb aBtM oiit ae m'iîkaok ^,NTp£ 3 mi 1536 , ^ncemntjM kb mea ayiii> ypivrb TtpMEN x536 aA nporpscii tjiii.NA A’onoTpiBb ueayÎ aîn txb 5 ^simyah’it HpÎN KYB.KNT apAlKaT A3 nYTEp’fe g, 'ae BOM ^Mllbpgi i356 npiw 3 , kxtva 512 ecte a 9-a nxTEpe a ky-BJRNTyAXl, AE YNAE CE'BEAE Kb KXBXNTYA —9y/512 = 2, ( 6o ) .	» «a C b B b Ţ h> M ^NŢpE A O b N V M £ p £
A.aTE, AE M i 5K A O K npOnOpgiONEAl, T p £ B V £ C b A V b M K X T £ A AOp Uli AiN TpXNCÎA Cb CKOa-T£M O pbAbliN b a*NEl Tp £ I] T £ a’o TI O T p l B T> NYMbpYAXl 4 £ A O p A E M i 3K A O K Mai M X A T 1-iu a, k a p £ ptAT»*iiNi> Ba <|ii kxbxntka.
An'fecTTj EKCTpai^EpE a pbAbmMAOp ECTE O AYKpapE AECTYA AE rp’fe , Aap NY ECTE AE KXT YN JKOK npÎN aîKYTO-pYA cJ)pyMoac£Aop nponpÎETbgi a AorapÎTMÎAop . Ka ct Bbl bM 4 AE MI'/KAOIs j»NTp£ 8 Uli 6 i, ap TpfiBYÎ Cb EKCTpa-ytM pbAbHÎNa a 5-a. aîn ^ cav 5y/8 KSTbipME NEpagi-
OKaAb £63) AE41 AECbBIKpLUÎT -J.N NYMEpE NY IIXTEM Cb
apbTbM auEipî AEMi*AOK, Aap NEanponiEM utxt kxt BoiM U1ÎBEAEM Op'fe KYpXNA Kb 5y/8=l,5l57 ECTE KY-
bjkntya mi riporpEcia «ie c£-4£p£ ecte
-H- 8 : 12,1257 : 18,5792 : 27,8676 : 42,2243 : 64.
Acxnpa aHEipiî npi4i.Ni be31 £i53, io°).
4. IIentpY AorapitîSÎ.
85. Cb AYbM aoIi nporpEciî xwa npix kxt mi aAxa
AOrAPITMI	409
ppÎN AÎ*î>£p£NHT» a KTjpOp Ţ£pM£nî CC-pbCnXNA K*TE AOl
2,01 , nptKXM .
rr i : 3 : 9 : 27 ; 81 : 243 : 729 : 2187.N\Mtpe.
-r 0.2.4. 6	8 . 10 . 12 • 14 ........AorapÎŢaiî.
(plt Kap£ TfpMEN SA^EAlî A’aA AOIA-!» £CTE' AOrapÎTMYA NYMT>pYAJiî K0pT»CIIYN3T>TOp H£Alî AÎN TIlî , O £CT£ AO-
rapiTMVA ayi 1, 2 sa ayj 3 5 4 ayi 9 ; 6 ayi 27 iuia : AorapiTMl Aap csni n Y m £ p £ fN nporpEcifi n P I N AÎ<J)tpENgT>, Kap£ p T» C H Y N A TEpMţN KY t £ p m £ n a a a a t £ NYMp£ ^NnporpEcic n p i N KXT.*
(J)iiN£ Kt AOrapÎTMÎ NY NE CMNT ^»OAOClTOpi AC KST NYMaî fN îlYTEp'fe npOnpiETBIjjAOp K3p£ N£ apT»T KT» 3HE-cte nporpEciî fNieri YNa acab i mi aATa aeab nya3 , bom aB'fe j,NaiNT£ Aap aiEAE nporpEciî itaps ^miiaîneck anii-CTT» KONAÎjiiE . B'b3Yp'bM KT» paMVAgipiAE Ulî fMm>pgi-piAE Kaps ^>aq£M <j»n oap£ Kap£ ^NT*MnAT»pi acvnpa nv-McpiAop nporptcii hei aîn tauy , ptcHYNA Aa aAYNipî iui CKT>A£pi -j.n A’a Aoa ; iiytem a np£B£A"fe ki» Aora-p'lTMi BOp ^NAECNi MYAT COKOTEaÎAE , AYKpY KBpE NYMaî fNAan» CE-Ba api»Ta .
86. nponpi£TT>gî a AorapÎTMÎAop . TTpMfr-3T> aîn iea£ 4e bm ăic ( 83 mi 84 ) mi aîn a^at ki» npo-
rp£ciÎA£ NOaCTpS 4NUEII YNa ACA3 YNY mi Hlî> A3ATT. A£A3 NYAT» , KT» Opî KapE TEpMEN C£«^OpM^3T> AÎN KYBXNT AC ararb opî <J)T»KT»Top, mjwpY ni a'in rare} uuAC.ăţ&tf»
t
110	APITMETIKT)
Opî 3AT>0raT IlENTpy A’a AOa, AVnb KSţjî TEpMENÎ BOp <|)i jvNaiNT'fe axÎ. ^IeÎ A’araacEA’fe TepsitNÎ, cnpe ri'iA-Ai> oxnt 243 mi io; pxTp’xNx* kvbxntxa ecte 3 apAi* KaT Aa a 5-a nxtEps, uii ţN bea aAa at ecte 2 aAtoraT a£ 5 opî. Kvbssntxa a a p ae aTSii opî ecte (£t>-
K t T 0 p -(.NTp’xN TEpRIET* aA 1 E A i î AiN T X. 1* , a£ KSTE opî ECTE a^torar N KOpECnyNŞbTO-p y a ciî,
yS,E BOM ^MMVAÎji ^NTpE c'lNE AOl TEpMEPtî aî npOrpS.Cti npiN kst npEKVM g mi 243, kxbkntxa 3 Ba (J)i ae 7 opî ^>bKbT0p (>N npOAXKT, IIENTpy K"b A6 2 Opî ECTE 9 mi ae 5 opî /(vN 243. npoAXKTXA Aap gX243 cax 2187 Ba <|)i aA onTXAÎi TEpMSN aA nporpccii. Iap as bom aA"b-ora TEpMENÎ 4 mi 10 KopEcnxN3bTopî .pxnporpEcia npiN Ai^EpESgT» , KXBSNTyA 2 Ba ^>i aCEMEN^ ae 7 opî aAto-raT pN cxMa i4; AS’iî npoAVktxa 2186 mi cxMa i4 cxnt T£pM£NÎ KOp£CnXN3bTOpî , KapE CE- apaTTj 31KSNA K Tj cxMa AorapinviiAop aAOb NVMEpe ecte Aora-p i TM V A npOAVKTVAyî Aop.
A,£ vnae ypivrifob kt> Aorap’iTMXA jcNAOÎT aA yNyî Nywbp ECTE AOrapiTMyA nbTpaTXAXl Avî; fNTpEiT ECTE aA KXEX-AXÎ mi ae OBtpE /JvMMXAgiNA AOrap'lTRlXA aAXNXÎ NXMTjp npiN opî 1 S (Jj bK'bTOp, SBSH AOTa-piTMXA nxTEpi a^ECTXÎ nxmt>p apbTaT npiN aîECT ^IKMOp. IlENrpy 93 , âBEM 3X4—12» Kaps pEcnxNAE Aa72g = 93 .
87. ^MnpOTÎBiTOapEAE aiECTOp AyKpypî caint aecne
AOFAPITMI	111
a cs-aptra rif.NTpx Kt AorapiTMYA hiktxatÎ Maî mvat BA ^.MntpLiiTOpVAXÎ TpEESÎNA Ct a1> HE aA -JiMIltpJjÎTXAXÎ f XpMl>3b Ka AOrapÎTMyA KSTSAÎ1 a AOt SVME* p £ ci ^)it Ait^EpENga AorapiTMiAOp a>it* CTOpNVMEpE.
AcemenIj a o r a p i t m y a opî Kt pi a ptA'h'HN1 a
YNYlNYMbp, tCTt K/KTXA A OTa piîM* AJ1 a-
y £ c t y î n y m t () 4» m ri t p u, i t n p i n t p t n t a a b 8 -
ipi.l p tA t 4ÎiS î .
88. A* Ka aok ae a Aya 3* aai aAf.ţlE nfrnpy ky-BXNTXA tlporpscii rip’lN KST , O KXTtyiME KY MXAT Mai wiKt arSNHI NYMEpi AE AÎN KapE ta ECTE KOMnvet ap <J)i 4>oct waî anpoaiiE ynya aematxa, niinpiN anponitpE aai t|)i ac{)AaT -p TpaiNca j, 2, 3, 4, 5. Ct cokotIm
Aap Kt ECtE (JlbKYTb o T3EAb , p KapE âp (J)i CKplCE a-*X£CT£ NîfMtpE mi AoraplTMU AOp , CKOfJ/KNA prp’BAT KlU HETOIJÎ qElţjiAaAJil TEpMENl AE MIÎKAOK, IipiNMinXpÎAE KapE
aptTaptM ap cpi <|)oct a’o noTÎBb aAfBtpaxE. Ct p-Kinxiai Kt a^torb TaBAt ecte ţţttKYTt: beaem Kt.
1°. KaCtfMMVAftÎM AOt KiMtpE A^TE ECTE AECTVA Ct AXbM p TaBAt AoraplTMU AOp Ct*! aAYNbM, mi ct Kty* TbM C.y»ia pps AOrplTMi: NXMtpyA KOptCnXN3tTOp ECTE ITpOAVKTyA 4E CE-BEpE .
3°. Ka Ct pinbpJjÎM AOt NVMEpe CK03TEM AorapÎT-MYA pntpjjiTOpYAXÎ AÎKTp’aA ^MTItpaiTyAXl, KbXTbM ptMtmijja pTpe Aoraph’MÎ; mi NYMtpyA Kop£cnîN3b-Top ECTE KXTYA 'IE CE-HSpE .
112	APITMET1KT)
•3°. Iîa cb (|>a'i£\î o pervAU ae Tptî âAVjrhivî Aorap‘n\\il
MEAOp Ai MÎîKAOK , CKOaTEM nE aA >*EAOp 4E MaplJlNE KX-NOCKXT, NXMTjpXA Hţ. pbCnSNAc EIUÎTYAXÎ Ba (^1 HEA N£KXa NOCKVT j
4°. Ka ci» aBEM Aorap'iTMVa xmi ^>pxN\iEpî pETpaysa
AOrap’lTMVA NSfMiTOpVAyî AÎNTp’aA NXM'bpTjTOpX AX1 , p b-
Mbiuiga Ba c[)i Aorapîtmya he c£-4£ps . TaEASAg KorrpiNA NVM3Î AOrapifMXA NYMEpÎAOp ^NTpETjEl j Tc O p£ M 3 a'ltx.Ta ^NTÎNAE fNTp£BviN}iap'fe AOp Aa (Jlp-KNJ.tEpî.	).
5°. Ka ct> apAÎKtM xn NXMbp Aa o nvTEps ^mmxajjîm
AOrap'iTxMXA cty npiN Tp'bnTa nxTepi; KbxrbM npcuxK-TXA ^NTpE AOrapiTMl, NXMbpXA KapE CE-pEriOapTb Aa A*N-CXA £CT£ nmp’fo HZ CZ-HEpZ .
6°. Ka Cb CKOafEM O pbAtmNb AlNTp’XxN NXMbp , -f,M-nbpjjÎM AorapixMYA aaECTxî NXMbp npm rpiinia pbAb-mtU , iui nE K/KT ^A KbXTbM ^NTpE AOrapiTMl; NXMbpXA *i£ CE-pbCnVNAE KX ASNCXA Ba (|)i pbATm'lNa H£ CE H£pE .
BeAEM Aap Kb ’IEAE Mai KOMliAETiTE COKOTEAl 3KXM NX cxnt ae kxt o acxKbpis Ka cb 3hem ama . ^MMXAgipÎAE mi j,Mm>pgipiAE cE-fMiiAiNEcK upiN aAXNbpî mi ckt»ae-
pî; apAÎKbpiAE nvTEpÎAop mi EKCTpaţtepiAE pbAbHÎNiAOp CE»aAXK ^MMY/gipi mi -pMribpgipiu A'iecte cÎMnAÎ-^inagu C/KNT AaTOapE AX1 NE11EP BECITO I^EOMETpX CKOgiaw, atJiAbropxA AOrapÎMÎAup mi a Kbpxm memo-pie CE-KXBIPiE a (Ji CKXMntb TXTXAOp lVBITOpiAOp At mi-ÎNUE .
ÂOrAPiTMt	113
’8§. <|)a<lep£ a Ta BAUOp . PbMJKNS 8KXM Cb a-pbTbM KXM nXTEM Cb atf)AbM AOrapiTMl TXTXAOp NXM£-p’iAop ^rdpti.ufisisb a<ii nporpEciÎAE NoacTps npm Aif)£piNJib iui upiN K/Rt ax <^oct iui XNa mi aATa Ka TOt 04£A INXMbp Cb aiBb O MXAJjÎME M AOrapiTMl. IleCTE rix-H'iN 3KXM BOM B£At KXB&NTXA Kap£ a iJnsKXT Cb aA£I,ItM ne 4£a£ xpMbToape.
-7T i : îb : 100 : Ibooio obo:.... Nx'Mcpe.
~ o . i .	2 .	3 .	4 .:.... Abrapi™!.
O, 1, 2 ... CfiNT AOrapiTMl AX1 1, IO, ÎOO,;.... IUI pbMfi-ne cb a(ţ>AbM ne ai axi 2, 3, 4,... Kapi fMB£A£paT ce ko-
iipiNA f NTpe 6 uii 1; aî axi 11 , 12.99 cxnt fNTps
1 mi 2 uiMA . A4eipî AOrapiTMl nx nxT£M cbl aatM A£ K/KT npÎN ahponiepe; Maî OBriNxiT Ne mVajjtmîm kx 7 âtuiMUAt.
Cb BbrbM A£ CfeMb Kb AaKâ lNTp*OnpOrpecΣ, np£KXM *7“ 0.2* 4.6.8. IO..,. AbCbM XN T£pM£N lipECTE A01
koNceKXTÎBÎ, 2 nptcxe 3.... c«-(|)aK aTXN'ii aATe npo-rpeciî t- o. 4 . 8 . 12 ..., cax ■— o. 6 . 12 ... IIxtem A3p cb ne iNKirixiM Kb aokxa auefiTopa A6 CXC aM AX-aT aATtAe a[Kbpopa TepMENÎ ap <ţ>i cJjoct kx mxat Mai aiipoane /psrpe A^rmii, iui Kbpopa a^eipia ap (|)i aa:X-TaT a (J)i napTS .
Ama cb nxNEM Kb aivi nvc Risipe 1 uii 10 xn <|>oapTe Mape NXMbp as nponopjjtoNEAÎ A£ mîxaok npiis kst ; a-TXN41 <ţ>i‘)NA KbNeexÎM A£Aa 1 KbTpe IO hp’lN Tpf.nT£ (|)oapT£ crp.KNce, BOM aB'B fNTpe aneiirî ac mixaok nxme-
15
m
APITMETIM)
p'iAE 2, 5, 4..,. /.a 4În 3f.'iE M'uioaNE anpoans. Aasa • ’ap ii?ne yNacEMEN'fe Nvuip ae nponopjjioNEAi a& Mi-ÎKaOK npiN AHptpENglj /(.NTpE O Uli 1 ; aHEIJIl AS MÎ/KAOK he Bop aB'b tot ainb Tp'fcriTh kx 2, o, 4,... Bop (J)i Aora-pmii aiecTop isyMfps. Tot acEMtN't (JianEM mi A£Aa io
IlSSl A3 ICO UI'IA .
EcTE aAtBipaT Kb Ka Cb HVNEM XN NXMbp Mapr AETEp-MEN1 AE MÎaJAOK npiN KXT ap TpEExi Cb ECTpaţIEM o pbAb'lINb AE O Tpl>I!Tb npE apAlRaTT» £84), Aap NEATj-ntpTbM a£ aaEcvrb rpsxTaTE upÎN aasxTopxA aeoeebîteaop pbAb'UM > IlbTpaTf. CXKCECÎBS. CllpE IUAAb Cb KbX-TbM AofapiTM^A AXI 5: HEa AE MÎ3CAOK npiN KST pNTpE t ini IO ECTE 3,16227766, mi npiN AUjnpENIJb /J.NTp£
0	mi 1 ecte 0,5; 0,5 ecte AorapiTMXA axi 5,1622 ...nx-Mtp anxM anpoanE as 3. O acEMtNij AXKpapE nsNTpx
1	mi 3,1622 ... ae o napTE, mi nENTpy o mi o,5 ae aATa, A"b 0,25 nENTpy AorapiTM avi 1,77827941. AccMEnS ^NTpE 1,7782 ... mi 3,1622... ae o napTE,mii fwp£ o,25 mi o,5 as aATa , acţiAbM nENTpy ae mokaok 2,37167370 mi 0,675 . XpMXNA ae a Mat tot Minuiopa acEMENfc aiE-cte xoTapf, ai^AiM 0,30102999 mi 0,47712125. nENTpy AorapÎTMi Ayî 2, mi 3.
AntCTE COKOTEAÎ CXNT <J)OapT£ OCTENÎTOapE; ECTE /J.N-BEAtpaT KT» AE AyKpbM NXMaî lIENTpy NXMEPÎAE UEAE A1N-txk: nENTpy ktj Hei AaAjji AorapiTMÎ CE-aejiAb aîn Tpx\-mi. ^,ap Ky tobte anECT'b tot pbMXNE Ka AECTyA ci o-CTENtcKi» mi ii Mat cxcJsprroapE pbBAaps. Ama noi apirbM anierb cokot'Bat» nvmbi k’xn mkkaok as a ne
AOr APITM.I	•	415
<Şaa£ o Uee ae $au£pl3 TaBAEAOp, KbXTXNA a^aMai^N-AtcNiToape (575).
90. Ecte aecne aKXM aapbra nENTpx m cb aAti^&M meae Mai a£ cxc AOb nporpaciî. Tot AorapiTMXA ce-<|)OpM'I>3b AlNTp’o napTE j.NTp’lirb KapE CE-NXM£lpE X a-pEKTipiCTiK’b mi AlNTp’o (fipXNIJEpE 3E<UMaAb *£'11 .
1°. Aorap'lTMÎ NXMEplAOp IE CE-KOnpifU fNTpE..
1, IO, 100,... CE-KOnpiNA fNTpE O, 1, 2,... aAUtb AO-rapÎTMXA ap£ nENTpx xapaKTipicTÎKb aTS* tIj XN1M1, KSTE U, î cj} p E ^NTpEJJl apENXMb-p x a, MainvgÎN «Na, KapE ne ^naecneipe a ipi a -
*1ECT NXMbp AE IiicJjpE, EiBNA XapaKTÎpiCTÎKa NE ECTE AHTb iui ĂÎN npOTlBb . NxMbpXA 543, 21 apE 2 XNIM1 jiNTpE-ţrî 4NAorapÎTMVA cbx1, mi 3,47712125 ecte AorapmiXA xnxi NXMbp, a Kbpxia napTE ^Nrpirb aps naTpx ui-<J)p£. ITp'b A'C NE AEnbpTbM AE 8 XMnA*b TOEAEAE KS a-utCTb XapaKTEpiCTlKb, KapE ECT£ aKOAO £ NE(|)OAOciTOapE.
2°. KaNA Bp£M Cb 4MMVAJ1ÎM Cax Cb ^MnbpyÎM XN NX-Mbp npÎN IO, 100, ÎOOO,... TpEEYE Cb 3A'bOIbM Cax Cb CK08TEM AOrapiTMXAVl CbX 1, 2, 3,... XN1MÎ, AEXNAE xp-îufeb Kb a Mbpi cax a MÎKiuopa xapaKTEpicTÎKa kx 1, 2, 3,... ECTE a pMMXAţji Cax a fMnbpui NXMbpXA Kop£cnxN3bTop npÎN io, ioo,... cax aaAbora 1, 2, 3,... NXAE, opî aAE CKOaTE, jvN C^XpUUT ECTE a MXT3 BlpI'XAa kx 1, 2, 3,... TpEriTE cnp£ Ap^nTa cax cnps CTXNra. AorapÎTMi NXMSpÎAOp 3,4578; 34,578; 345,78 ax TOT a»rf> napTE 3EHÎMaAb; iui NXMaî xapaKTEpiemiAE Kopb-
A PJTMETTIvb
CITTNSBTOapE C*NT O, I, 9,...
8p£M Cb3Î4£M Kt O KXTbljiME ECTE YN AOFap’lTMV
TaBXAEp |a aptTtM npiN camnya L; abc;kna fNCEMNa». pf) Log: /jN ^.NTXMrvA'bpî kxna cicTtMa Ba (|)i apsirpa-, pb cav NtXOTtpXTt .
91. ^NTpEByÎNIjapE TaBAEAOp. TpfBYE Cb TŞM Aa .jNVbMXNb TOBAS AS AOFapiTMl Ka Cb f N1JF, AEţIEM |NTp£BsiNUap’î) AOp . TaBAEAS AVI KaAET, BopAa, ini ^E-, AaMBpV CAkNT 'l£A£ Mai PfiiqNviTE. Noi aii NY BOM <JiNTp£—
npÎNAE AEaaptTa ^NTpEB.vÎNjiap'fc /op; Aap cx.vr oapE, KapE nVNTVpî KapE TpEB.VECK AVMlNaTE , KbH; CXNT TpE-BviNnoacE <j.n ^MBbjjbŢvpb..	,
i°. AorapirMVA NXMEp’uop <i ax o rp.£VTaT£: ae ob-IţlE £8.8,4°) TpiBVE 0/b p£TpaI,I£M AOrap'lTMVA N.XMÎTOpVAVl AlNTp’aA NVM'bptTOpVAVl Ka Cb aBEM ITS 3A YNtl (JipSNT.lE-pî: Aap KXNA Ea £CT£ M«î MiKt A£ KXT XNY , CKBAtpl». NYCF.-TTOaTE lţ>a,q£ . Cnp£ n'lAAt» Ka CB ^MMVAJJÎM 5 np’lN, 4, (piÎNA KB ECTE A’onOTpÎBB KVa^Mnbpjji ll£ 5 npiN , ecte tot anEfc a aAbora Li Aa L 5 ; cav a pETpaijE L *y aîn Li 5 ; iui aTVNit aAEijEM Maî b'ine anLcTb Avnb vpnb AVRpaps. Bea'M Aap kb TpeuvE ctTpaţtEM Aora-piTMVA NVMbpbTOpVAVl AÎNTp’aA NYMiTOpVAVl, iui Kb CB fNTpEBV’lNJJBM <JiNCb au£CT AOrapiTM	f. NJJEAEC A1N npO-
TJBb; a Al KB Cb’A CKBţEM A£ Ş» TplBvi Cb*A 8AYNBM, Uit
a'in nporiBb. Ilp^jivpiAop aiECTopa Ai e*a ast nvme a£ AorapiTMÎ NşraTiBÎ nENrpv kbce-^ncemn^sb kt
CEMNVA----IE C£-nVNE ^NaiNTE .
Ecte aectva nvji'iNB BbrapE ae cLmb Ka cb CKanc ui-
AOrAPVTMI	H7
mna as rpnuiAi. IaTh m;u mxate «JiEAxpf ae EKCfMiiAXpx «lECTOlNIHE a fN/ECNÎ ^NJţEAf^fpli, aMEaop OOKOTIAl.
4o,2I2X-§-	’	3y/0,00027
1'. X —
o,o4
y4;
5°.
32,41
♦ ntshi,avk pa pE.
*
Lî= 0,6989700 Li or— 2,0000000 L3— 0,4771216 Li=r 0,6020600
Li=----0,22 18487 Lo,o4=---1 ,0979 IOO
Î-j42,212=: 1,6254369	i,4o358"2
1,4035872 Lx= 2,8016272 x-655,18
A ioa AXKpapE.
Ka Oh 3(|)AKM NXMhpXA ME ph-
ctixnae a>if.CTSi AorapiTM NtraTiB ,	L5= 0,6989700
fA pETpaţtEM AÎN J, AXKpX KapE	’Li'j— o,845og8o
4>aHE NXMhpXA AE îoopî MblMa-	L4=—ro,» 461280
ps; aBEM 0,9269660 KapE ph-cnxNAE axÎ 8,4515 ; aehi x=o,845i5.	Lx=—0,0730640
A T p £ ia A X k p	ape
CKoaTEM a’in 3 aqtcT ao-rapiTM Lx, KapE (JiaiE nx-WhpVA AE 1OOO A? Opi Mai Maps; aBEM 0,2997766 Ka-pe phcnxNAE Aa i ,9942; îmi x=ooi9942.
L 100000:=	5,0000000
L 27=	i,45i3658
Li 0,00027==—3,5686362 —i,i8g5454 L 02,4i—	1,5106799
Lx=-r-2,7002244
I
118	APITMETIltt)
Axnpli aMiNTE qe CE-nepE Aa coKorbAa AorapirMÎAop KeraTiBi, ne cjims Fa aokxa AOp cb aAEţiEM Mai eîne HEaHEia aKbpop NXMaî xapaKTEpic.TiKa ecte NEra-Tim» auia Ka cb sbem L^ — Li 3 — L 5, <J>a>iEM cKbAE-p"6 â <J>i nvTÎN'ioac'b, aAborxNA î Aa xapaKTEpicTÎKa AX1 3; fNCb BaTpEGXÎ Cb CKbAEM 1 A*IN KOBXpIllipE mi BOM sbT) Lf =—i + o,778i5i3 nEKapE ^a cKpiw ama.... i,778i5i3. Aii <f)u'|A NXMaî xapaKTEpicTÎKa NEraiiBij, apbTbll KT» ^N COKOT&ATJ XNAE Ba ÎNTpa a^ECT (|>£A AE AO-rapmi, ne iibsiM acKbA't a>ii>crb xnîme. AcemenTî.... Lo, '4 — L 4—Lioo = L4 — 2 = 2,60206 10 . IIx-
TEM BEaIj KATb jiNAECNÎpE A"b a>l£CT METOA TIENTpX (JjpXN-ţlEpÎAE 3E'UMaA£. COKOTEAÎAE AS CXC CE-(|)aK KXM Xp-
MÎ3b:		
L^.=t,778i5i3	L5z=o, 6989700	Lo,06027^=4,43 i3638
L42,212—1,62.54359	L7—o,845og8o	a^ioriM iui ckt>x6m
i,4o35872	L*r=x.8538720	2, mi axim acXMi- j
Ix>,o4—-ş-,6020600	axionm micKi-	TaT'S	
Lx=2,8016272	XEM 1, IDlAXlM	■2,8io4546
	xxviiTaT'S		L32.4i—1.5106790
	Lx=t,926936o	Lx=3,2997756
Ac<|>£A BENÎM Aa SUIEaIjUIÎ pE3XAT3TXpî . Cb ^NCEMNbM KT> jvN HEAE AÎN XpMb AOb EKCEMIlAXpî K&NA 3M 3BXT Cb 4>Mnbpu’iM xn AorapiTM ^ncemn3t kx o xapaKTEpicTÎKb WEraTlBT», Maî jvNTXHf *AaM (JybKXT a tj)î AE-fMnbpJjÎT a-A'bOrSNA'Xl XN NXMbp KXBUNHOC AS XN1M1 . Auia Ka Cb
AxbM 4 L 2, aM nxc L c'fBT tjiopMa—2 + 1,8538720. Bii^ticrb TTpEfjNrpiacipe TpEBXE tot A’axNa aoxxa ţN
BbrâpE ae (+Mb.
119
AOI’APITMI
3°. Tipii MXAT Cb np£-CKXpTi>3b AXKpbpiAE HplN ^vNTpETVBiNyapi k o m ii Ai-ti i p i a o p; cokot'6at» ain npOTÎBT» C£-p£noapTb A3MEA AIN TJE1Y EKCEMI1AX SE aBXpbM ^NaÎNTE: Ka Ch AXbM AorapÎT-MXA AX1 aAbOrbM L3 KOMnAÎKipEl AX1 L5 ^BC3I î»° io) .
4°. Tune £cte at^a^E EcnpEciÎAE Mai cîmiiae Mai Na'm-te AsaanAtKa coKor'feAa AorapmiiKb; auia ecemiiay no-
3.422,12
CTpy mea aîntaux CE-pEAX'iS Aa x=---------; uii NXMaî
2
Ka ct> beaem Mai eîne jkokxa AorapÎTMÎAop NEraTiBi aM a-
AEC Cb TpaKTbM (JlOpMXAa AlNaipiTE .
5°. Cb (J)i£ ’mpxT AorapiTMXA aA xisxî NXMbp «ap£ TpEME IlECTE XOTapbAE TaBAEAOp M£ CE-pNTXMIlAb , Clips niAAb |N T8BAE/E AX1 Cillet} KapE NX n/KIUbCR Mat NaiNTE A£ 108 Mlî . KsNA BOIM UE AOrap’lTMXA AXl....
5487344, KbXTbM Mai ^NTIKIY AOrapiTMXA AXl 54873,44 a Kbpxia napili 3EMÎMaAb ecte tot antb , iui nENTpy a-M^CTa (JnifU Kb /a AurapitMXA axi 54873 KopbcnxNAE jvN TaBAb 73g3587, 4>aqtM aTxrm aM'fecTb nponopjiiE. .1 £ ,I,i<|spENJja ^.NTp£ NXMEpfi) CE-apE KbTpE 79 (]aÎ-
^)Ep: j.KTpEAor, Axî 54873 iui54874) Ka 0,44 (aî<|>.
^NTpE 54873 mi 54873,44 ) KbTpe x; ae xnae..........
x=o,4:^'X'jq=35 Kaps CE-aAaon> nbpiji semimb/e a L54873, mi a bem 7393622: ecte ae npicoc cb apbTbM Kb 7g ini 35 jjin aok	nponopjjia woacrpb ae 0,0000079
L5=o, 4771213 Km. l5=t,3oio3oo
LÎ2,2 12=1,6254559 1\m. Lo,o4=i,3979400 LX=2,8016272
120	APITMETIKi)
nu o,ooooo35. Âkym NXMaî pbMANE AEKXTamrNE xâ» paHTEpicTina KyBiiNHoacb Axnb aokxa BiprxAEÎ nx-MtpvA hea nponxc .
Aî’Serb ptrYAb *£ TpEl KapE CXBTUXNE Kb NXMEpiAE KpECK nponopjjjiE KXAOrapirMi Aop ecie .pBEAepaT
rpEiiiiri: fNCb NXMEpiAE i, iob îoo...... aBXNA nENTpy
AoraiTMi o, i, 2,... Aorpiwi NXMtpiAop AtAa 1 haini» Aa 10 ibKNb Aa 100,...». .^MnapTE ^NTpt a*nuiî atrioTpi-BÎT O XNIME ; A£ XNAE XpadjAb Kb KX K&T NXMpIAE CA.m waî Mapî j kx arXTa AorapirMi KOCEKxriisî ( ie b'in xnxa AXllb âATXA) CE-AEOc'lBECK Maî ‘mtyÎN jvNTpe a an ou . NxMEpÎAE A£ HINHl Jji(J)p£ tpCEXE Cb aiEb fiavrpX AOl'O-pÎTMi Aop, HEA nxjiiN HANb Aa XN AOK , O antlUl pENijTj, iui Mbpj^itviiVAXce n&Nb Aa 7 SE'nivta/E ; ama be-AEM fN TaBAb Kb anpoanE A£ 100 NXMEpE koncekxtîbe , BE'UNE A£ 5487.3, ax 79 HENTpX Ai<J)£p£lYJJb AOrapiTJMÎKb .
6°. îîa Cb a(|)AbM NXMbpXA Hl pbCIlYNAE AOl'apÎTMX— AX1 7,7095622, BEAEM M31 .fiNTAIHf Kb KHA& fNTpE NXMfc-p)AE 54873 iui 5^8/4 ; iui Kb AÎ^EpENga ^NTp£ aHECT
AorapÎTM mi aAAxî 54873 ecu 35; ama pxKinxKVA 8 x-hîmi ţNTpElju Aa xapaKTEpicTiKa AdrapiTMXAXi nponxc ea
ia pbcnxNAe Aa 54873 aAbotaT kx o cjipxNj.itpf. ne Kape
0	acpAbu ^NTOpKSNA nponopjiia ae cxc . Ab;M Aapb
79	35
1	-=-------, âe xnae x= ’2. = o,44 ; 0111,7390622
1	X
tCTE AorapiTMMXA A'il 0,5487544.
CfjjJKpllriT i
NOTE
jva
APTTMETIKT»
* ACEMEN'S apIKT'B llNSim C7. aAK7iT^I8.CE7» AECnT.pyipiAS a iţi as aob cax naxpx yicţipE; ^ncb aTXNiî a*na*cs xn NxMip, aM aB'fi ^.ntp’o-fNT^MnAape Mai mxats Atcmpyipî, uii fNxp’aAXa Maî nuHÎNE: nsNxpn Kaps ispisxxNx xoxapBAs xxMspiAop iscs-
■tNTptBîiNJJ^Zl Mai ASC ECT8 ASCNE a BEA® Kt c’a (JlBKXX -j-MBOlpe
a cs-Axa o MicXpi KXBiiNioacB -fNTpe aiuxNAOB nxpjjiAe.
2 Tot avKCT T8MSW IlOaTE CB C AX/KacKB CUpS a CKpî XOaxfi NXMEplAE ftX Mâl MX ATS CAX Mal MlJlNE Biceps . Cb NE ^NKinXiM cnps ni aab kb NsaM jmboIt a jNTpEKxiNHa NXMaî naTpx xapan-Tspî, aTxNiî o imf>pb nxcx A’acxxNra aAxia ap xpsitti cb »f>i© AS naxpx opî Mai Maps Âs kxt AaKa a p cpi (|)oct -fN aokxa cbx ; io aTXNHi apnpsyxi naxpx, n ii Nai, 12 maca, i3 manxe, 20
bnT , 21 NOB IUIa :
I(,t>na na noi lintna cb ijt’Bckb în NîMBp cxpic cax aîk npo-xii:B , ca ,jnt-t,ANi |NXAiMiiAapi ai'IicTa Maî mxaxe rptSxBjiî aek.t.x cicTEMa zsiiMaAB , nsNxpx kb (J>eax a apBxxpi nx ce-i:a -j MBoi kx aiicxB nxob AÎcnozijjieN Cnps ni aab na cb liTÎM NXMBpXA CKpic nplN4l23 -[N ClCXSMa NtMEpa^iil AS1ÎN1Î Jiicfips
o , 1, 2,3 , 4 , [ aAÎKB k«na o jucfipB nxcB A’acx*Nra aAxia Ects as ii mii opî Mai Maps ask®x A'aita ap tfii <|)ocx aokxa tks] aTXNiî TptBxt cb ^.MMXAyiM ne 2 npiN 5, ns i irpiN 52 cax
i«-5 , tis •! iic'fMKpurix npiN 53 cax 125 111 i a hem...........
rG
NOTE
AXisS-j- 1X25 + 2X5 + 3 ca? 538 ntMTfw nps.uVA N?M7.psATÎ
irpanxc, cKpic fu cicTtina zsuiMaAi.
A,în npoTim cil kcttcm iiifJ)pEA£ Kaps ci apaTE numi, pta 434 AÎH cicTEMa ie 5 xapaKTEpî. IIsNTpT auficTa ci> Încânt. m kt> COiţOT'j^Aa se cuc noaTE a cE-rţja'iE fn opawAxiaAa -f-NToapcîr; a-AÎki ^MMXAUNiA ne 4 aîn 4i23 npiN 5 mi a^orasNA 1 cnps apB-JiTa KapE ai 2i,- ireXpMi. p mmâajuna ne 21 npiN 5 mi a»ora-.na 2, iui IN c<î>a:pmiT nEEmiTTfA 107 npiN 5 mi a ai ora, na 3, a-^ai.m tot UE 538 : ae?n.xe beaem k! 4 c’a fMMS'Ajji'r ae Tpa opî JTpiH 5 , 1 ae aov opî, mi 2 oaati .
aa'BcTi aspasTaps ce-beae kî, TpEBTE ci fMni pniw nâ-SiipTA npoxrec 434 npiN 5, piMtmiira 4 na cpi l-a yirţspi ae-cnpE ApinTTa , mi kjstxa 86 ca rf)i np£jj?A asaop aaate niPps ckojixna'Sce 4; .j.Ajin,puiNA aîn nSoî ns 86 npiN 5, piMimisia i cărţii a 2-a jiicţipl; fMixipjjiNA rnpnE K*'rx.\ 17 npiN 5, bom a-aai nSNTpy a 3-a iiiţipi piMlmina 2, mi hsntp a 4-a nsKXTiA 3 KapsAC (ţiiiNA waî mîk aekirt 5 ccjvTpmarpE AWpap'fi. Ama ecnpEcia ca? apT.Tapfi HEpTTi ecte 32x4.
Beaem acEMENi ki 566 CKpic KxnaTpv xapaKxf.pî ac 2o3 12 Ki fNcicTEMEAE ae6, 9, mi 12 ijiţipE NA-Mhp-SA 5o35 ce-apaTi npi»35i5i, 68x4, uab7, a mi b ^.ncemn,t,na zehe mixN-cnpEzeiE cicTEMa xs aoîcnpţzsVE xapaKTEpî • Atect aîn ■spun. rjiiEA ae NtMspanifi ecte mu rţtOAOCÎToapE se k.y.t ceas aaate TOATE, nENTpK KT. AOl,cnpEZETg apE Mai MXAJJl -fMMnipŢjÎTOpî ae KSt zETE ; jNCt ap rţai Sn AXKpx rpoapTE ks i’pE? a CE-CTaTopNÎ-ai aKXM,'nENTpxr kc ap TpEcxi cj; ckîmkim NtMspÎAE mi toate nk-
MEpOacSAE pVTpECSijIgCpî NE IUN AiN EAE .
3 Jîif’P1 KXTKAKÎ ECTE rpEmjTl Mai KĂ'AEOCEBlpS K/T.NA a AOa ciţlpT) a -t-Mtll» pIjiTOpSA-Sl l!3pbi 7> 5 , nENTplf KT» HpOAĂ'KTlfA AIN npiaiwa ex Ba ani an Mat Map£~NXMCp as xnîmÎ. Ama (pis -^9 > îMacpaiNA» t—7 -X7' o cirjipi np'S Mape.- -jn axion ^NTSMAaps I1XTGM aCEMENÎă irXNE fN AOKĂ'A -pMMpljiTOp'SATfî 287 X1E 300 IC)
i 216
A A -■'pfTMETIK'b
ţ>x zînenem lf :== 4 i aTWii ^ncx pxxxNip’B ua^ii ain npoxinx ki.nî bom auB ojii^pi wiitx, kx xoaTE kx teri Mai anpoanE ie aASBXpaTXA K.TiT Kap£ ECTE 5 .
Sn k*t nsNTpx •HepKape, noaxa. NiNtna cx o cpaKx axkp.T.NA ae Aa cTX\ra cnpe ApBnTa; ngvrpx kx AaKa axiix ij£a MaÎMapE kx-BiRNT ckxaepB xnxî npo-WHT nu sexe nxTiNNoacx , nx ecte iixtîn-Voaci aCCMtNÎ) NlTL KXNA NeaE II,iN$Te Bop MXpi NXMXpXA a£ cio>-zxr? Auia na cx NepKxM kxtxa5	1914 npin 3aţ),
zi'iEM 6X3=î8, Tpac aîn 19, pxMXNE 1, KapE aAXTXpaT a«n-rx 1 ne ypM'Bz'h ax 11; 2X6—12 ncKape nxa iis tem xpaţiE :s,în 11 ; AENi 6 ecxe Maps ini Tpcxxa cx ’iEpKXM he 5 .
AaNÎNÎ o ^NT/TiiinAaps m(ţ>pa jji\xTx nx noaTE c x cpiE a '0110-xpinx kx pMMîanixopxa , nENXpN kx Aaita ap 5 ap Tpaxxi Ka ni ppa ^mmxaUÎtx cx (pi£:=io, Ka cx irxem iAnB 2 . Auia A»Ka bom (fiaxs xox £ OAaxx ini .preAjiipTi mi ct;xa£P^>> nicjipa jjînxtx 13 a <ţ>i Mai ncxpinixi; nx ^ m m y a ni t o px a , mj Aaua kikna ,(|>aNtM npona, Atnx kxm zicEpxn, i;om pNT.Y.ANi o pxMXmiyx A’onoxpi-BX KX I[i bpa NE NSpKXM, aTXNNl TpEEX’E CX O COKOX1M KX axB iii -cf)pT> nxects ama ae Mape. <ţ)iE cnpe ni a ax ,	-£-??£> «nixx’A 8
a\ axî ^ ecte npB Mape,- Kacx NEpnXM jie 7 , zpitM 3X7—21 , xpac AiN 25 pxM-T.NE 4 mi aBEM 4o,- 7X5=35 a!n 4o pxmxne 5; ,JN Ctf/'KpmiT 7X7=49 CROC AiN 56 pXMftNE 7, AEU1 7 ecte bxn. via OK1JIS NEpKap'S TpEBXE MlKNâTX MNX Aa o jNTMinAapS .JNKa-ps NX'HyTEM CX CKXJ6M, cax nXNX K/KNA BOM l'x'ci opXMXmXjlTi nea hxjjîn a’o nOTpiBX kx nic^pa ne NEpKapxiu .
4 Maî laTX 4NKX OnpOBX BpEANÎKX ae -fNCEMNaT JlENTpy CJM-
nAiTaTr6 ca. Cx hxnem kx c£-N£££ npOAXKTXA axî 293 iipi\ 1572; cx aeckomiixnem ne 293 fN aox nxpjrî AiN nap£ xsa Cx
tjiie pxMxmijia ^.Mnxpnipiî am 293 JipiN 9; axwiî a bem.....
293=9X32-j-5 ; AENÎ AEBOM ţMMSANi lTplN 10 72 11a pi ti iii Ai*
t*w 9X32 Ba a a tn a£-îMMX \.ujt aa axi 9. 1 n npo.vSXT;, a
fMni ptt»T j»p» 9 Tpeiree ci. aîra. tot aaf> pi.mi.mi • U$ na mi 5X'i‘V2 ■ Aap AeciţoMnxiNA axiii. acsjitv'B i;iu wi 11 s 107a, a(icM 15 7 2=9 XJ 7 '* + 6 ,■ iui fMMXAfliju npiN 5 , pi.nn,-mi.ua Mm pui ptî na (pi tot a ne% kx a axî 5X6 /sape icre 3 . Ama bex£m ki piMiiinjja is a^iui aa npojsKT t-cTsnpoAVKTXA pun, w i g i a o p <J>i>KiTopiAop.
Ama Aap fMin.puiM ne ifiiKiiTOpi mi ne npOAXKT npiv 9 mi «jEpKb’M xaaa aiiacxT. konai gie ce-$ MiiAiNeipe. AaîcTa. nxTepe Nxoape OTMaî 9, ii miopi neaA'r •pMnipuiTop; -(ncj. nponpisTa-rfc (msâ ti* 24, u5,) airxMepiAop 9 mi 11 N£i|)aii£ aaAege ne a>i8CT£ NX.mpe, nsvTpy fNAScsript; MaiMXAT A£K;kt ne opi 'ie a*T NXMlip •'
Cnpe niAxa* aMacJuaT Kt 53 687X9°8—^8 747 796 ; j»a ci. 'lepKiM a'i'fecxii cokot'Sai , axKNiM Toaie gi^peae ipiKtTopi-Aop aii aA£ npoAXKTXAxi, ffirpixiNA na cs citoaiiM ne 9 ie kikts opîcxMa f a na KOBAîpmi ; piiMiigiAS aijiAaTe ac^>eA c-isnt : 2,8 mi 7; MHi 2X8—16 mi 7 ecTe pt un. ungă axî ^ (neNTpx in. 6-f-i— 7): Atât AXKpapîi nx ecTe j peniiti.
AceMea li fMnxpuivA ne 700200031 npiN 683 679, aneM ne\j Tpx k.kt 1021, mi ii2 735 nSNTisp puii.miuL : ^MtibpuiNA am cienaTpx «rx.neps irpin 9, a [ivi.m pi Mi mijii a£ 4 Aa fMin.pjiiT 3 Aa ^MiinpjiiTOp ,	7 a a mKT mii ah piiMimigi . A,aiîa fM-
inipgip'îj c’ap rf)i rjn;uT eiic.iKT, puiT>mi:ia -jr.im.pjiiTx m ap <pi fpoc r a£ 3 opi 7—; 1 cixJiai nis'e 3; a.5i>or,ţc\A i KapeAe npo^
ni.vs A£Aa pimmijib , arpAi.M 4 ne.vxpx Kor„T,pmipîi junipniTx-
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5 Aufic’n, nponpitTim aAijeepiaeipe ce-apaTi. ama, n (bifau x.vsXjixp jifTpsr oapeisape, 2n apari. Toaxe NXMEpiAs Kxco.it> mi 2n+ i lieas (£>j,pt coji-
0 flxTeai a AVa k*tva npiN Kofi*pniipe cax npiN Ainoi.; Am« nevTpx ~ K,r.Tx x text 3 cax 1 , nesTps ki a5—3X7 + 1 u ‘^ “
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Ct-apaTi kSCEMOTA---Tp£B*E Ct CE-» fNTp’a«SCT fNJSEAECi
7 AayEKpiHEipE ce-2iie ki opî «£ NSMip aîn tjkw (aifiaps jfi şuii 3) ecte ae (JiopMa 6ni î, ptainpoKa nv ecte aAe&Bpari, JIENTpT KT> n*NT>‘ 3KTIM fNKl NTf C’a niTlT atJlAa O $OpMYAB K»-uiiNioaci a apî>Ta NKwai NKMtpiAE aîn t*w uii a ae KonpiNSE n* TOaTE.
* cfiis upy.a. fMnipsjiTOpi aîn t*» aî oaps KipS» NtMip N.ranp ... NTfMipTA aekjete opî Risipe KapE ecte $lKiTop; ama aBEM N=«m . jjn. yP ... Ka ci a$aiM nETOjjî iMMpuiTOpi aiî
N , ATflM TOJJJ TEpMEEli npOA»KTVAVl •
(î -(.a -f-a* 4----+ «m)(i	—.... 4-/*n)(» + y+*?::	)
Numi,prA tvttaop .pmipHiTopiAOp aHEcTOpa ecte;
(m + i) (n+i)(p + i.)
9 Ap itet® ci cE-cmiKpiuacKi îmmS Alipii ^nheidina *£aa »i-«Jipa TpenTEÎ heau Maî apaiKaTE a fMSAjjiTop«A-sî, «ttnwî cftieipe KapE sin npOA*KT£AE fN napTE TpEFS6 CT» (£is
^KaiNTE KifOTpiinTT. cnps aplinaTa. Riniu a- g34 5a8 MECTa NTfapE Ni«î OAEOCEBÎpE a ATâ AEaiEAâ 34 277 MEc’a apiTaT Aa(i5) ae k*t kb psitAfA 2 8o3 584 AÎN T*Hf c’aCKpic fN AOKSA MEaSÎ AÎNtpMl,	373 8112
«ea A’aa aoîaI» c’a cKpic fN aoksa heaSx aîn- 18 690 56
aiNT'B hea*i aîm ipMi.................ii. 6 54i 696
npÎNTp’a'i'BcTa, acsM ^NAtcNÎp'6 ae a KiNoaqie	654 1696
wax fNTAiHf uiiJpEAE KapE a? «ea Maî MapE npEji 3203 281 6a56 Uli KapE K*T£ OAaTB c-knt aectîae .
Ipis «tp*T npoaXKTîA 93,4528X3,4277 Ki 5 zE«i&iaae •	<f»n-
CE.MK1M KB fMMXAui'rOpKA au.T.NA 5 Jji^pE, TiNÎMiAE plCHîNA
>7
126
NOTE
jta a 5-a koaonb a iipo^K titani , iui aula uiprţ-A» 9314528“
ct-ua hjns |N-Tps a 4-a iui a 5-a jji<£pi, abţii k*m_____3)4277
ee-fNOEMsfBia aiN npoTiui. KVo.TptoKpi- npi.v mî- 280 3584 3kaok ; aaita ojaTi csisaxoTipx aokxa uipnt- 3738112 Atî, armui f MsnfAjjiM ne g34528 npiN 3 mi 4 ,• j 86905*
MUMi AE 2 3AE aUSCT-31 A1N KpMl npOjKKT BOp <|)i 1N	65416
a 5-a Tpîrtro AEzEHÎMaAS.	654i
/EnisnaîSX fMMîAiiip'6 ASaa 2, ns 6 aaps’ asmir 3ao,323i4 aîs 2X8=,6 fAinfHEM, uijjivtM otmaî me i , be Rips ovsîm KxaX^—i; tui ama irm>i o cm;T 2; nc-spin* 2\5~10 iuua :
/RwjlSAjjipî npi*i 7 ce-br i Nl„ru ns.mai .\E.ia ui |ipa 2 a a’u-
MÎAOp, 2X7—l lliXEM 1 <ţ>api; CX HXNfM 4, JIE pKMT> zilEM
7X5=35; 35 + 1 =36, mrxEM 6 cvet 5.- m vpMx 4X7=28 ms a: Uli ama MaîfNKOiO atIcsma AEaa cţiisqif. na,pe AimpapE kaete o ftiiţpi ar jmm'Sauî r . (pitaie Kaps ui f>px hsaxcxm o^xcemsim k» sh ntNT A’acKnpa .
AuÎctx pEi^Ai ecte mu mVat aekxi' toc A"aţ«ia 'fto-AOc i-Toape kxna (fixaiTopii Gop<ţ>i anponiagî, nssxpx ki isinx.\ hea OKi4NxiT aEobijie arwm apani aa'fe NSKwiiNux ae a npSA-snni. a* «papii a*na npOAXK'rXAKi vti npli Maps KSMxp u ui^p£, Ai* «ape itAE Ai* *pMX xpuxs a ce-ax ca -ţ-N cfc-xpuiir, -fNjiEAEiiKVAXce kx nt xpciîns anicTpa aii as k*t iu pui as zsuiMaAS as aHEÎmî
TpîlIlB KX' îţllK'uXOpii,
146 ai'm xpMB ’zsuiMaAX 'n acEM npiv mix aorta aiecTa tete rpEiuirt., «mp* Ki acxnpa u c’a a.vuorax a asii ie a ai jji'ntt aE-Aa KOAo»ia ţpMBToape, iui nEVTpx aa'fecxa xpExxs a xxxxa ozc-HiftiaAX MaiMVAT, kx ns xp>ix cb aIcih iie u'Jj ais xpMX .
J° lYi.Mni'PilipB îapx a-fiu o npscKEpxape asaAon-. fpi&
■’lî*”1, ai-11'1' ‘ie aM-u'p.iax us 4sae aix liuy aob îiH'pe a.U
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NXTAni. AlCiM at)>apl TNlMiAE 7 aA£— f sim'UÎTop'SA'si 5 ac<ţî£A bom aipAa ne a-3-a jjic|>pi a kktkasî mi pBWi.iujga 1812; actMEN'g cKoaxtr.i aifiapi iui zEuiMiAE 7 a as '^Min,puiTOp*A'xî iui aiua Mai -jnkoao. E-cts aecns aannAEKa anscT uirt ASAWcpape fNTpn KONBepcia (^piKNytpiAop iNZEuiMaAS.
lin
32o3a8iI 33277 8351 J g3452Q
11 i552o 1812 102 34
11. OEips ua ci ne anponiEM Mai nngiN k* — as npcjrSA işti X	<1
qipXNyEpî AiT£----1, OfUMSAlIlM Spin 9, uii KliiTlM JNTpEţi X
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«ii i-(-i $NTps Kape Kaae kXtka —; .— tui--------nop <£pX-
b q q
ţltpÎAE HtpSţE .
12 . ^opMa i/ENEpaA’b a ^>p*Ny£piAop uj ce-itot ain'ie txcaKT a
zs.ai.Maas ects-----; NtMip»A !ii<J>p€Aop gt'iiMaaAE ecte a’g-
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noTpiBB a ŞAHI Mai MapE aîn cniNENUi m mi n.
13. Nn ecte a ai aokka A£a AECAnwi MCToaAEAS npiNKapEc'ax kwockvt AKNţiM® met pnAni, Niuî npiN KapE ^.Nrpiaiipi TpEme a (jian; npf.ruTip'fi te CAlosaipE cnpE aatţua rpaMMXA- BezÎ t^izÎKa akî Haiiy n° 5g. Noi aii ne MipipNiM a citsne kt. Tp£b*E a ce-CAn*i un ani napam’ pNTp’o TSMBEpaTapi mi tipjcis aTMocifiEpi-m xoTtpXTE. Gi CE-rn Aap am. iicTiAaTl [cTptKapari] npiN a \ cin MaRciMUM ae AEciME ( npiN HÎS Mai MapE can mai CTpxNei ae-ciME), itaps ecte 4 rpaas lENTirpaiE Mai cnc aekxt riajia to-niri, EapoMETpn apixXNA 76 4£N'riMETp£.
1* . Tot aiE’fi aM <£i ciBXpuuT ini Kn sn <|)iKiTop Mai ciw-iun aekjkt 192; bezî aiE'B HEc’azic ntNTpn ptAXKjiia au anuarn NnMiTop (34); noi aM AnaT ani ne 192 na ci <f>atem..a Mtft Mai lins KOCEKBENJia te npM^zi.	~~'
21