nbUfnbujljt !txbwmfcb!!WJJ!lmbtTj! - Ganatleba

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- 26 - xSirad moxdeba, rom maswavlebelica da mSobelic, maTda gasakvirad, aRmoaCenen, rom saSualo moswavlesac arc ise gauWirdebodes iqneba erTi SexedviT Zneli da didi davalebis Sesruleba... roca gonebrivad normalur moswavles uWirs `saymawvilo ma- TematikiT~ swavla, ver igebs mas da ver xsnis amocanebs _ amis mizezi, rogorc wesi, erTia: am moswavles Sinagan an gare mizezTa gamo daqveiTebuli aqvs teqstis wakiTxvisa da misi gaazrebis unarebi, moswavle ver kiTxulobs. amgvari SemTxvevebi gacilebiT xSiria im klasebSi, romlebsac wina wlebSi Cveneuli saxelmZRvaneloebiT ar uswavliaT da pirvelad iwyeben `saymawvilo maTematikas~. ra vqnaT? jobs gvian, vidre arasdroso. V klasi iqneba Tu IX, maswavlebelma pirvel rigSi unda Seamowmos moswavleTa kiTxvis unari: gadaaSlevinos maT saxelmZRvanelo romelime axal gakveTilze da daavalos teqstis xmamaRla wakiTxva. uceb gamoCndeba, romel moswavleebs uWirT kiTxva (umjobesia, SeirCes iseTi teqsti, romelSic mravaldaa rTuli qvewyobili winadadebebi). meore safexuria sityvis amokiTxvis sizusteze muSaoba _ yvela aso zustad da mkafiod unda warmoiTqvas. moswavleTa (da mozrdilTa) umravlesobas erTmaneTSi eSleba msgavsi bgeriTi Semadgenlobis mqone sityvebi, magaliTad: erTerTi \ erTaderTi, marTebuli \ marTobuli, gamarTuli \ gamarTlebuli, gamkeTebeli \ gakeTebuli, miuwvevia \ miuRwevia... Tuki sityvebi zustad araa amokiTxuli _ romel azrovnebaze, logikaze da maTematikazea saubari? mesame safexuria sasveni niSnebis amokiTxva. maT TiTqmis sul ugulebelyofen rogorc kiTxvis, ise weris dros. gansakuTrebiT iCagreba mZime, orwertili da tire _ swored is sasveni niSnebi, romlebic gadamwyvetia azris logikisaTvis. amitom moswavle unda mieCvios teqstis wakiTxvisas sasveni niSnebis gacnobierebas, rac kiTxvisas mcire SeCerebebiT (azrobrivi pauzebiT) unda gamovlindes. sasveni niSnebi teqstSi tyuilad ar weria, maT
- 27 - jerovani yuradRebis miqceva sWirdeba! meoTxe safexuri yvelaze mniSvnelovania _ wakiTxulis gaazreba. es teqstis wakiTxvisas marTebuli azrobrivi aqcentebiT unda gamovilindes. arafrad ar varda Tundac zusti, magram meqanikur-monotonuri wakiTxva. mxatvruli teqstebis wakiTxvisas ZiriTadad mxatvrul-grZnobiTi aqcentebia saWiro, samecniero teqstebis wakiTxvisas ki _ logikur-azrobrivi aqcentebi. maxvili unda daesves im sityvas, romelic yvelaze mniSvnelovani da arsebiTia logikuri Sinaarsis TvalsazrisiT. es oTxi safexuri unda damuSavdes ara mxolod teqstis wakiTxvisaTvis, aramed agreTve zepiri metyvelebisaTvis da werisaTvis: sisrule, sizuste, sasveni niSnebi da azri. maTematikis gakveTilebze es dafasTan zepiri msjelobisas da sakontrolo weris samsjelo amocanebis amoxsnis dros unda damuSavdes. araa sakmarisi amocanis mxolod amoxsna anda Teoremis damtkiceba _ saWiroa kargad gamarTuli msjelobac. amaze maswavlebelma sagangebod unda imuSaos _ ese igi, unda Seasworos, Caasworos, Seavsos, gamarTos, daxvewos moswavlis zepiri Tu werilobiTi teqstebi. magram mxolod Sesworeba da Secdomis gacnobiereba araa sakmarisi _ moswavlem aucilebelad Tavidan unda gaimeoros (zepirad Camoayalibos an gadaweros) Sesworebul-daxvewili sruli teqsti. swored amgvari muSaobiT viTardeba gonebrivi unarebi da azrovneba. swored esaa mTavari _ da ara leqsisa Tu gramatikuli wesis gazepireba, formulis damaxsovreba, damtkicebis damaxsovreba da meore dRes moyola da gamoTvlagardaqmnebis sxapasxupiT keTeba. mTavaria ara programis gavla, aramed moswavlis gonebis gamdidreba da ganviTareba, misi SemZleobis, xelwifebis amaRleba. amgvari savarjiSoebisaTvis araa sakmarisi mxolod qarTuli literaturis teqstebi, moswavle abstraqtul-specialuri teqstebis wakiTxva-gaazrebasac da Seqmnasac unda mieCvios. amitom
Page 1 and 2: - 1 - nbUfnbujljt q o r b u d a !tx
Page 3 and 4: - 3 - maTematikis maswavleblis mecx
Page 5 and 6: - 5 - gonebrivi unarebi, romlebic u
Page 7 and 8: - 7 - li sakiTxebis gasameoreblad _
Page 9 and 10: - 9 - veswrafviT moswavlis aramarto
Page 11 and 12: - 11 - xuli unda iyos SiSi. SiSze d
Page 13 and 14: - 13 - ganviTarebaSi da gaZlierebaS
Page 15 and 16: - 15 - mxolod `Sav Sromaze~ damyare
Page 17 and 18: - 17 - pasuxi moswavleebs aTqmevino
Page 19 and 20: - 19 - emateba. samagierod, amgvari
Page 21 and 22: - 21 - (cxadia, ubralo ariTmetikis
Page 23 and 24: - 23 - lia sazogadod klasifikaciuri
Page 25: - 25 - moswavle, romelsac kiTxva uW
Page 29 and 30: - 29 - gadauWreli SesaWiria. xolo d
Page 31 and 32: - 31 - moswavlem daaklo raime sityv
Page 33 and 34: - 33 - moklea. am dros umjobesia, r
Page 35 and 36: - 35 - rialos~ axal an Znel sakiTxT
Page 37 and 38: - 37 - yvela moswavles ar moeTxoveb
Page 39 and 40: - 39 - moswavlemac gaiazros isini,
Page 41 and 42: - 41 - ramdenimewuTian saklaso wera
Page 43 and 44: - 43 - dasaTvleli Tu sxva saklaso s
Page 45 and 46: - 45 - Cveneuli meTodikiT momuSave
Page 47 and 48: - 47 - (ara damatebiTi Zneli) sakiT
Page 49 and 50: - 49 - miviCnevT maswavleblis nakla
Page 51 and 52: - 51 - klasSi mainc amoxsnis. amito
Page 53 and 54: - 53 - im terminebis farglebSi, rom
Page 55 and 56: - 55 - `saymawvilo maTematikis~ kid
Page 57 and 58: - 57 - farTobi {fuZis perimetrisa d
Page 59 and 60: - 59 - tronomiis, logikis, filosofi
Page 61 and 62: - 61 - mTliani simravlis tolZalovan
Page 63 and 64: - 63 - es asea, magram saamisod ram
Page 65 and 66: - 65 - amis ramdenime konkretuli ni
Page 67 and 68: - 67 - magram es yovelive _ gumanis
Page 69 and 70: - 69 - kiTxi ukve karga xnis ganmav
Page 71 and 72: - 71 - ar varga. kanonzomierebas ki
Page 73 and 74: - 73 - mniSvneloba gansakuTrebiT di
Page 75 and 76: - 75 - klasSi Cven nivTieri TvalsaC
Page 77 and 78:
- 77 - programa gverdiT darCeba. xo
Page 79 and 80:
- 79 - naxevarsfero, cilindri, naxe
Page 81 and 82:
- 81 - 14. CamowereT, romel nivTebs
Page 83 and 84:
- 83 - nfdbejofpcb/! Tuki damatebiT
Page 85 and 86:
- 85 - sxva. sakontrolo weris rveul
Page 87 and 88:
- 87 - `10~-s an `5+ ~-s Cveulebriv
Page 89 and 90:
- 89 - moswavlem mimdinare gakveTil
Page 91 and 92:
5. 4/16 4/30 - 91 - sw # 13 sw # 14
Page 93 and 94:
- 93 - C(1,5), D(1,75), K(3), E(3,5
Page 95 and 96:
- 95 - kg. 2. I. 53 sm; II. 950 g;
Page 97 and 98:
- 97 - 6. ara, radgan 12m-ic da 8n-
Page 99 and 100:
- 99 - II. 8 ⋅100000 + 9 ⋅10000
Page 101 and 102:
- 101 - 3. 2), 3), 2) da 4). saSual
Page 103 and 104:
- 103 - meore SemTxvevaSi: u ≈ 40
Page 105 and 106:
- 105 - S0 ⊂ S . 5. aguredi (marT
Page 107 and 108:
- 107 - denoba ar aRemateba mocemul
Page 109 and 110:
- 109 - 7. uTvalavi yofiTi sityvaa
Page 111 and 112:
- 111 - 7. pasuxi unda SevarCioT mi
Page 113 and 114:
- 113 - (1; 4)II, (2; 4)II }. {(7;
Page 115 and 116:
- 115 - g. 4. 1. I. +7, +3,1, 3,1,
Page 117 and 118:
- 117 - Tavi X. g. 1. 1. I. {1; 3,0
Page 119 and 120:
g. 8. 1. I. -3; II. ( 4 2) - 119 -
Page 121 and 122:
- 121 - zisgan. aqvs simetriis 4 Re
Page 123 and 124:
- 123 - iqneba Semoxazuli wrexazis
Page 125 and 126:
- 125 - 3. I. 25; II. -11. 4. orive
Page 127 and 128:
- 127 - jixuri, 31-e - Zelskami. II
Page 129 and 130:
- 129 - 5. I. katis myol mobinadreT
Page 131 and 132:
- 131 - nawili tolia 21 km-is (1 q)
Page 133 and 134:
- 133 - sakontrolo wera # 7 rigi I
Page 135 and 136:
- 135 - II meoTxedSi (1 q). 5. xali
Page 137 and 138:
- 137 - 2. I. 2a - 5 (2 q); II. y +
Page 139 and 140:
- 139 - 1 x + 1 x nawils, rac 1 mTe
Page 141:
- 141 - математики. М.-1
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