saqarTvelos eklesiis mamamTavarni D
ODEN mTavarepikoposni
1. ioane 335 – 363.
2. iakob 363 – 375.
3. iobi 375 – 390.
4. elia 390 – 400.
5. svimon 1 400 – 410.
6. mose 410 – 425.
7. iona 425 – 429.
8. ieremia 429 – 433.
9. grigol 1 433 – 434.
10. basil 1 434 – 436.
11. mobidani 436 – 448.
12. iovel 1 448 – 452.
13. miqel 1 452 – 467.
kaTalikos – mTavarepikoposni.
14. petre 1 467 – 474.
15. samoel 1 474 – 502.
16. gabriel 1 502 – 510.
17. TavfeCaR 1 510 – 516.
18. Cirmagi-CiRirmane 516 – 523.
19. saba 1 523 – 532.
20. evlavi 533 – 569.
21. samoel 2 569 – 535 ?
22. makari 553 – 569 ?
23. svimon 2 569 – 575.
24. samoel 3 575 – 582.
25. samoel 4 582 – 591.
26. barTlome 591 – 595.
27. kirion 1 595 – 610. amis dros moxda somex-qarTvelTa religiuri ganxeTqileba.
28. ioane 2 610 – 619.
29. babila 619 – 629. aman TbilsSi aago metoqed anCisxatis taZari.
30. Tabori 629 – 634.
31. samoel 5 634 – 640.
32. evnoni 640 – 649.
33. TavfeSag 2 649 – 664.
34. evlade 664 – 668.
35. iovel 6 668 – 670.
36. samoel 6 670 – 677.
37. giorgi 1 677 – 678.
38. kirion 2 678 – 683.
39. izil-bozili 683 – 685.
40. Teodore 1 Teodisi 685 – 689.
41. petre svimon 2 689 – 720. TavfeSat 2-dan am petremde kaTalikosebi colosani yofila.
42. Talale 720 – 731.
43. mamai 731 – 744.
44. ioane 3 744 – 760. antioqiaSi ukanasknelad nakurTxi.
45. grigol 2 760 – 767.
46. sarmeane 767 – 774.
47. miqael 2 774 – 780.
48. samoel 7 780 – 790. wm. abos cxovrebis aRmweri.
49. kirile 791 – 802.
50. grigol 3 802 – 814.
51. samoel 8 814 – 826.
52. giorgi 2 826 – 838.
53. gabriel 2 838 – 860.
54. arseni 1 860 – 887.
55. evsuqi 887 – 908.
56. klimtos 908 – 914.
57. basili 2 914 – 930.
58. miqel 3 930 – 944.
59. daviT 1 944 – 955.
60. arsen 2 955 – 980. qarTvel wmindanebis cxovrebis aRmweri.
61. oqropiri ioane 1 980 – 1001.
62. svimon 3 1001 – 1012.
kaTalikos – patriarqni
63. melqisedek 1 1012 – 1030, 1039 – 1045. sveticxovlis gamamSvenierebel-aRmadgeneli.
64. oqropiri ioane 2 1031 – 1039 – 1049.
65. eqvTime 1 1049 – 1055.
66. giorgi 3 1055 – 1065.
67. gabriel 3 safareli 1065 – 1080.
68. dimitri 1080 – 1090.
69. basil 3 1090 – 1100.
70. ioane 4 safareli 1100 – 1142. ruis-urbnisis saeklesio krebis Tavjdomare.
71. svimon 4 gulaberiZe 1142 – 1146.
72. saba 2 1146 – 1150.
73. nikoloz 1 gulaberiZe, Zmiswuli svimonisa 1150 – 1178. sveticxovlis svinaqsaris aRmweri.
74. miqel 4 mirianes Ze 1178 – 1187. Tamaris mefed makurTxebeli.
75. Teodore 2 miranes Ze 1187 – 1206.
76. basili 2 1206 – 1208.
77. ioane 5 1208 – 1210. ` angelozTa swori ”.
78. epifane 1210 – 1220.
79. eqvTime 2 1220 – 1222.
80. arseni 3 1222 – 1225.
81. giorgi 4 1225 – 1230.
82. arseni 4 gulmaisis Ze 1230 – 1240.
83. nikoloz 2 1240 – 1280. mefe dimitri Tavdadebulis Tanamedrove.
84. abram 1 1280 – 1310.
85. eqvTime 3 1310 – 1325.
86. miqel 5 1325 – 1330.
87. basil 5 1330 – 1350. giorgi brwyinvales Tanamedrove.
88. doroTeoz 1 1350 – 1356.
89. Sio 1 1356 – 1364.
90. nikoloz 3 1364 – 1380.
91. giorgi 5 1380 – 1397.
92. elioz gobiramis Ze 1399 – 1411. Temurlengis SemosevaTa mowme.
93. miqael 6 1411 – 1425.
94. daviT 2 1425 – 1430.
95. Teodore 3 1430 – 1435.
96. daviT 3 gobelas Ze 1435 – 1439, 1443 – 1459.
97. Sio 2 1440 – 14343.
98. markoz 1460 – 1466.
99. daviT 4 1466 – 1479.
100. evagre 1480 – 1492, 1500 – 1537.
101. abram 2 abalaki 1492 – 1497.
102. efrem 1 1497 – 1500.
103. doroTeos 2 1503 – 1510, 1511 – 1516.
104. dionise 1510 – 1511.
105. basili 6 1523 – 1526.
106. malaqia 1528 – 1538.
107. melqisedek 2 1538 – 1541.
108. germane 1541 – 1547.
109. svimon 5 1547 – 1550.
110. zebede 1 1550 – 1557.
111. nikoloz 2 baraTaSvili 1562 – 1584.
112. nikoloz 5 Ze kaxTa mefis leonisa 1584 – 1591.
113. doroTeoz 3 1592 – 1599.
114. domenti 1 1599 – 1603.
115. zebede 2 1603 – 1610.
116. ioane 6 avaliSvili 1610 – 1613.
117. zaqaria jorjaZe 1613 – 1630.
118. evdomoz 1 diasamiZe 1630 – 1643, rostom mefem muslimanobis winaaRmdegobisaTvis
kldeze gadaagdebina.
119. qristefore udurbegisZe amilaxori 1643 – 1660.
120. domenti 2 qaixosro muxran batonis Ze 1660 – 1675. aman ganaaxla dasamreklo auSenaanCisxatis eklesias da sof. Walidan gadmoasvena macxovris xelTuqmneli xati RvTisa.
121. nikoloz 6 maRalaZe 1675 – 1676.
122. nikoloz 7 diasamiZe 1676 – 1696.
123. ioane 7 diasamiZe 1696 – 1700.
124. evdomoz 2 doasamiZe 1700 – 1703.
125. domenti 3 1704 – 1729, 1739 – 1742.
126. besarion orbeliani 1724 - 1737. gremlis avtori.
127. nikoloz 8 xerxeuliZe 1742 – 1744.
128. anton 1 didi, iese mefis Ze 1744 – 1756, 1763 – 1788.
129. ioseb jandieri 1756 – 1763.
130. anton 2 erekle mefis Ze 1788 – 1810 gardaicvala 1827 w. niJni-novgorodSi.
SeniSvna: 1811 wlidan 1917 wlamde saqarTvelos eklesiis avtokefalia ZaliT-administraciuli wesiT gauqmebuli iqna, ruseTis imperialisturi mTavrobis mier. eklesias ganagebdnen ruseTis uwmindesi sinodis egzarqosebi, tomiT rusebi /pirvelis gamoklebiT/. 1917 wlis 12 – 25 marts abtokefalia aRdgenili iqna.
131. kirion 3 saZagliSvili 1917 – 1918. ivniss 13 26. eris Tavdadebuli moZRvari, mokles
mis rezidenciaSi sof. martyofis RvTismSoblis taZridan gamosvlis dros.
132. leonide oqropiriZe 1918 – 1921.
133. ambrosi xelaia 1921 – 1927. erTerTi sveti da burji qarTuli marTmadidebluri
sarwmunoebisa.
134. qristefore 2 cicqiSvili 1927 – 1932.
135. kalistrate cincaZe 1932 – 1952.
136. melqisedek 3 fxalaZe 1952 – 1960.
137. efrem 2 sidamoniZe 1962 – 1972.
138. ilia 2 SiolaSvili 1972 – ZmaTa sisxlisRvrisa da ukanono mTavrobis mosvlis mowame. saqarTvelos Znelbedobis JamTa mxilveli
dasavleT saqarTvelos kaTalikosni
Semonaxulia 1390 wlidan isic arasruli, qronologiurad daulagebeli.
1. arseni 1390.
2. ioene – iakime 1455 – 1474.
3. stefane 1490 – 1516.
4. malaqia 1 abaSiZe 1529 – 1532.
5. evdemoz 1 CxetiZe 1543 – 1575.
6. eqvTime 1 sayvareliZe 1578 – 1605.
7. grigol 1 1612 – 1659.
8. malaqia 2 gureli 1605 – 1639.
9. maqsime 1 matutaZe 1628 – 1647. ierusalimSi gardaicvala.
10. besarion 1 1647 – 1656.
11. zaqaria qvariani 1657 – 1659. aman kaTalikozis kaTedra biWvinTidan gelaTs gadmoitana.
12. svimon 1 CxeiZe 1659 – 1666.
13. daviT nemsaZe 1667 – 1682.
14. evdemoz 2 sayvareliZe 1667 – 1669.
15. eqvTime 2 sayvareliZe 1669 – 1674.
16. svimon 2 1665 – 1681.
17. giorgi 1701 – 1703.
18. nikoloz 1703 – 1710.
19. grigol 2 lorTqifaniZe 1710 – 1742.
20. germane wulukiZe 1742 – 1754.
21. besarion 2 erisTavi 1755 – 1766.
22. iosebi, mefis solomon 1 Zma 1767 – 1776.
23. maqsime 2 abaSiZe 1775 – 1795.
24. kaTalikosis mosaydre quTaTeli mitropoliti dosiTeos wereTeli 1795 – 1815.
`qebai”–s teqstis qristianuli sarwmunoebis
wina periodad mesaxeba
da ese enai mZinarea dZesamomde, saxarebasa Sina amas enasa lazare hquian
da axalma nino moaqcia da helene dedofalmanese arian orni dani viTarca mariam damarTai
da saxarebasa Sina qarTulsa Tavsa xolo maTeissa wvlili zis romel asoi da ityvis
yovlad oTx aTassa maragsa. da ese ars oTxi dRei da oTxisa dRisa mkudari, amisTuis misTanve
dafluli skudiliTa naTlis Zebisa misisaiTa da ese enai Semkuli da kurTxeuli saxeliTa
uflisaiTa, mdabali da dawunebuli moelis dResa mas meored mosvlisa uflisasa.
gavarkvioT, ras warmoadgens Zili? – Zili sxeulis fizikuri umoqmedobaa.
`Zilis dros suli sxeuls ar tovebs, samagierod mZinareSi aRiZreba sifxizlis dros dafaruli gsiqikuri SesaZleblobani, maT Soris mTavaria naTelxedva, momavlis winaswarganWvretisa da Sors manZilzemimdinare movlenebis Setyobis unari. erTsac da meoresac mZinare aRiqvams saidumlo wesiT, grZnobis organoTa monawileobis gareSe da mas rogorc sizmars ise ganicdis”.
/l. vasilievi – adamianis fsiqikis idumali movlenebi gv. 9/.
maSasadame, qarTuli ena mZinarea, magram aqvs naTelxedva, momavlis ganWvretis da movlenebis Setyobis unari.
`saxareba” – samyaros RvTiuri gzis maCvenebeliaanu sabas ganmartebiT `saxareba
ars sibrZne, simarTle da Zliereba, samive swor da erT”.
`lazare” – RvTiT kurTxeulia da saxarebis Semadgeneli /sulieri/ nawilia, qristes
megobari da qarTuli enis /eris/ saxiereba.
lazare qarTul anbanSi kodiT amoikiTxeba da mas anbanis asoniSanTa ganxilvisas warmogidgenT. maSasadame, es ena anu eri or bunebovania RvTiuri da samyaroseuli /adamianuri/, es RvTiuri buneba saxarebis Semadgeneli nawilia da mas `lazare hquian” romelic dRemde mZinarea samyaroseuli /adamianuri/ buneba – dedamiwaze adamianis moqmedebis unaria. ukeT gadmocemisaTvis gamoviyeneb baton revaz siraZis ganmartebas:
`adamianebs Soris sikeTis mixedviT did sxvaobas xedavdnen sikeTis aRmavlobis bisi safexurebi ase jgufdebodnen: araqristiani, - qristiani, - RvTismosavi eriskaci, - sasuliero piri, - samRvdeloni, - martvilebi, - mociqulebi, - gankacebuli RvTaeba”.
adamianis yoveli gamorCeuli qmedeba zepirsityviT da weriTi masalebiT gadaecema Stamomavlobas.
`da axalma nino moaqcia da helene dedofalman”
aq upirvelesad yuradReba unda mieqces sityvis fuZeze darTul moqmedebis gamomxatvel man – s. `axalman” /qristianoba/ da `dedofalman” igulisxmeba zeca da samyaro, mociquli da morwmune, beri da mrevli. nino mociqulia, helene morwmune. e.i. axals nino mociqulad mouqcevia, da dedofals helene morwmuned mouqcevia. `ese arian orni dani”, e.i. orives qmedeba erT mizans emsaxureba, magram Sesrulebis sxvadasxva safexurebiT `viTarca mariam da marTa”- rogorc RvTis mSobeli mariami da misi da marTa. logikuria mariami ninos mociqulad moagcevda da marTa morwmuned moaqcevda helenes. `axalman” da `dedofalman” aq igulisxmeba mistiuri Sedareba. `axalman” – Zv. sarwmunoebis axliT Secvlis mimdinareobaa, romelic mama RmerTis nebaa. dedamiwa mdedrad aRiqmeba amdenad `dedofalman”- sityvaSi igulisxmeba dedamiwis mTeli mosaxleoba – eklesiebi, morwmuneTa sakrebuloebi.
nino – mociquli da helene morwmune gamoyvanili arian, rogorc dedebi Stamomavlobis gasagrZeleblad – sarwmunoebis gadasacemad.
` da saxarebasa Sina qarTulsa Tavsa, xolo maTeissa
werili zis, romeli asoi aTs ityuis
uovlad oTx aTassa maragsa ”.
saxareba, rogorc zemoT avRniSneT RvTaebrivi gzaa. amave Sinaarsisaa qarTuli anbani. `saxarebasa Sina qarTulsa Tavsa” unda gavigoT – anbansa Sina qarTulisa enisa, `xolo maTeissa werili zis”. maTe wmindania, `werili” – sityvis /saubris/ dokumenturi wyaroa, `zis” – arseboba, yofna. e.i. teqsti waikiTxeba: wminda dokumenturi faqti arsebobs. marTlac, maTes saxarebaSi aRwerilia qristes da misi Tormeti mowafis samyaroSi saswaulmoqmedebebze e. i. faqtobriv - xilul–ambebze. `romeli asoi ars da ityvis yovlad oTx aTassa maragsa” – anbanSi aseTi aso aris `wil”, romlis ricxviTi
mniSvnelobas sityvis 4 000 – s.
`qebais”- s teqstSi miniSnebuli `wil”= 4 000 maragi, unda niSnavdes, rogorc qarTuli enis gavlil RvTaebriv gzas, 2895 + 1000 =4000 wels
`maragTa” raodenobas 36 X 4000 = 144 000.
samyaroseul – materialistur wil-4000 maragis gagebas unda warmoadgendes dafaruli damarxuli g a n Z i. anbanis ganxilvis dasasruls SemogTavazebT, qarTul
enaSi damarxul saidumloebaTa anbanur wils.
`da ese ars oTxi dRei da oTxisa dRis mkudari, amisTuis misTanve dafuli sikudiliTa naTlis Rebisa misisaiTa”.
gavarkvioT, romel oTx dReze migvaniSnebs, romelnic oTxisa dRisa mkvdarad
cxaddeba. Tu gaviTvaliswinebT amave strofis wina nawils naTlad Cans, rom pirdapir migviTiTebs `da ese ars oTxi dRei”, maSin oTxi dRis meoTxe dRe yofila `wil”, maSasadame, `oTxi dRei” aris: Cin – i amaRlebuli, can – i naTeli, Zil – i naTelmxilveli – momavlis winaswargamWvreti da wil – i misi moqmedebis wil –xvedri, fasi.
`qebai”-s teqstSi arsebuli citata `weli aTasi viTarca erTi dRei”- dan gamomdinare:
erTi dRe Cin – 1000.
ori dRe can – 2000.
sami dRe Zil- 3000.
oTxi dRe wil- 4000.
maSasadame, adamianis moqmedebis unari Tavisi cxovrebis gzaze gamoxatulia oTxi dRiT.
`da oTxisa dRisa mkudari”, is rac adamianma moipova: amaRleba, naTeli, naTelxedva da ranairi wilic ar unda qondes vxovrebaSi garduvalia sikvdili. vinc meti sikeTe gaakeTa dafluli iqneba `sikudiliTa naTlis Rebisa misasaiTa”
anbanSi oTxi dRis mkvdars gamoxatavs:
erTi dRe hoe – 10 000
ori dRe bor – 20 000
sami dRe kil – 30 000
oTxi dRe jvar– 40 000
ufro konkretulad,
erTi dRe hoe – mkvdris dasaflavebamde periodi
ori dRe bor sami dRe kil sami are /samare/.
oTxi dRe jvar
ufro dawvrilebiT asoniSan hoe-s gamnartebaSi.
`da ese enai Semkuli da kurTxeuli saxeliTa uflisaiTa”, romelSic Cadebulia da dafarulia adamianTa sazogadoebis ganviTarebis kanonzomiereba dasabamidan dasasrulamde
mdabali da dawunebulisa anu misi enidan Seiqmna `sxvaTa” enebi e.i. daamdables da daiwunes, magram `meored mosvlisa uflisasa” qarTul enaze ametyveldeba.
qarTuli anbanis asoniSanTa wyoba
qarTuli anbanis asoniSnebi awyobilia zeciuri velisa da samyaros asaxvisSinaarsiT. zemoT Cven gamovTqviT mosazreba, rom zeciur vels warmoadgens anbanis aTi asoniSani sameba /a, b, g/, samyaros Seqmna /d, e, v, z, T/ da maTi /samebis/ `i” gansasvenebeli are.
eaca yovelTvis dadebiTi muxtis matarebelia. RmsrTi mowyalea da samarTliani, radganac adamianebs aZlevs Tavisi danaSaulis gamosyidvis saSualebas da adamianeba es RvTaebrivi mowyaleba maqsimalurad unda gamoviyenoT sibrZniT siyvaruliT da vodvebis monaniebiT. RmerTi Semqmnelia xilulisa da uxilavisa.
samyaro – es aris: dedamiwa fauna da flora, wyali haeri anu Tevzi da frinveli, da cis mnaTobebi dadmianis bedis ganmkarguleblebi arian:
zuali /saturni/ - mrisxane da boroti batonia.
muSTari /iupiteri/ - zenaesTa da adamianTa gamgebeli.
aspiroz /venera/ - siyvarulis batonia.
maric /marsi/ - Semoqmedi /radikalurad /
otrali /merkuri/ - mozerzebulobisa da gamWriazobis gamgea.
mze – mnaTobTa sistemis patroni.
mTvare – dedamiwis uaxloesi Tanamgzavri da megobari.
samyaros warmoadgens qarTuli anbanis 30 asoniSani da ganlagebulia samyaros aRmniSvnel wreze – sam yarad. | |||
| |||
 |  | ||
frinveli cxoveli 
u merve -Tan- i Tevzi kaci
 |
subieqti - vini - vini |
sur. 4.
zeciuri velis da samyaros urTierT mdebareobis
grafikuli asaxva
T h b z 
b bb zec. veli a g
d e v |
oTxi dRe
 |
20 s.
21 t.
sur. 5.
qarTul anbanSi adamianis gasavleli gza mis rigiTobaSi devs, moqmedeba asoniSanTa
ricxviT mniSvelobaSi, saxe – asoniSanTa grafikul moxazulobaSi.
adamianis amqveyniuri cxovreba /yofa/ qarTul mxedrul anbanSi gamoxatulia sami
a, p, h asoniSniT da warmoadgens anbanis RerZs.
rigobiTi ganxilviT
a – rigiT pirvelia
p – rigiT meCvidmete
h – rigiT damamTavrebeli
moqmedebis anu riCxviTi mniSvnelobis mixedviT:
a – moqmedebis area 17 weli /rigiTobidan/
p – moqmedebis area me- 100 weli, (p = 80, J = 90, r = 100)
h – moqmedebis area zeCa maradisoba.
maTi yofierebiT
a – warmoiTqmeba adamianis dabadebisTanave.
p – warmoiTqmeba adamianis bageTa moqmedebiT..
h – warmoiTqmeba filtvebidan haeris dacliT.
asoniSanTa grafikuli gamosaxulebiT:
a – erTi a.
p – ori a, a
h – sami a, a, a,
masasadame, RvTiT movlenili adamiani (a- yrma) gaivlis ra swavla – aRzrdis periods a- dan h-mde, e. i. xdeba 17 wlis miviRebT a + a = h kacs, romlis moqmedeba asaxulia 80 – 100 wliT.
qarTuli anbanis asoniSanTa saxis warmavloba.
 |
zeciuri are
 |
qarTuli anbanis asiniSanTa ganxilvis dros logikuri msjekobiT da maTematikuri
analiziT gamovTqviT mosazreba, rom qarTuli anbanis ormoci asonoSnidan, sawyisi
asoniSani zeciur areSi RmerTis – samebis mieraa Seqmnili da asaxavs samyaros
Seqmnas. ricxobrovad 94 – s /oTxmeoc aToTxmets/, Semdgomi 30 asoniSani ki gansazRvravs samyaroSi adamianTa sazogadoebis ganviTarebis kanonzomierebas
dabadebidan dasasrulamde. maSasadame, qarTuli anbanis 10 + 30 asoniSani gamoxatavs
zeciuri velisa da samyaros urTier kavSirs. aramed asoniSanTa saxec aqedan unda
gamomdinareobdes amasve migvaniSnebs “ qebai ‘’- s teqstic:
“da megobrobai /asoisa/ amisTvis Tqua viTarmed yoveli.
saidumlo amas enasa miwa damarxuls ars”
moviyvaneT faqtobrivi masalac, rom uZveles saxelmwifiebs qaldevelebs /qarTvelebs/, egviptelebs da indoelebs hqondaT mTvaris kalendari. aqedan mxilod qarTuli iyo mamrad aRiarebuli. mTvaris fazebi adamianis bed – iRblis ganmkargulebelia, razedac uamravi gamonTqvamia qarTuli tradiciebidan gamomdinare.
azri imisa, rom TiTqos qarTuli anbanis asoniSnebis grafikuli saxe miRebuli yofiliyos sasoflo iaraRis asaxviT., nakleb savaraudoa, radgan RvTis metyvelebac da mecnierebac qurumebisgan da samRvdeloebisgan mimdinareobda. amdenad, RvTis msaxurni upiratesobas RvTiur aRqmas miscemdnen aqedan gamomdinare, asoniSnebis grafikuli saxec RvTis metyvelebaSi unda veZioT.
zeciuri are, an rac igivea, veli, warmodgeba wriul sibrtyed “ “ romlis
xelebi zvidan da gverdidan warmoadgens swor xazs. ` ` asevea samyaros grafikuli asaxvac, im gansxvavebiT, rom zeciuri veli asoniSnis zeda nawilSia, samyarosi ki qveda nawilSi. zeciur velidan samyarosaken momarTulia naTeli sxivi, romlis grafikuli yovelTvis swori xazia..maTi urTierT ganlageba gansazRvravs anbanis ama Tu im asoniSnis grafikul saxes. asonisanTa saxis Seqmna pirobiTad kverTxiT sruldeba, romelsac warmoadgens zeciuri velis amsaxveli grafika – swori xazi da naTeli sxivi, romelic zeniT samyaros miedineba. kverTxis amsaxbeli saxea. |
mama sameba Ze 
Ze suliwminda naT. sxivi
naT. sxivi
samyaro samyaro  |
maSasadame, qarTuli anbanis sawyisi asoniSani unda warmoadgendes zeciuri velisa
` -- -- -- “, ` 0 “ da misgan warmomavali naTeli saxis anu sxivis - ` 1 “-is erTobas,
magram radgan qarTveli eri mTvares aRmerTebda, amitom anbanis sawyiss asoniSnad miiRes mTvaris xilvadi gza ` “, ` “ da zeciuri velis amsaxveli grafikulisaxe ` ------ `. maSasadame,
zeciuri veli ` -------- `
 |
mTvaris xilvadi gza –
maTi `megobrobai` - erTadyofna gvaZlevs sawyisi asoniSnis grafikul saxes
anbanis ganviTarebiT – transformaciiT miRebulia qarTuli anbanis mxedruli
` a ` asoniSnis saxe.
qarTuli anbanis sawyisi asoniSanTa rigi daricxviTi mniSvneloba erTi da igivea.
uwin qarTul enaSi TviT asoniSnebi aRniSnavdnen ricxvebs. Tanamedrove ricxviTi
mniSvnelobiT miRebulia a = 1, b = 2, g = 3 da a.S. maSasadame,
qarTuli anbanis yvela asoniSans aqvs Tavisi saxeli, romlis saxelis pirveli asoniSania TviT asoniSani. saxelis momdevno asoniSnebi RvTiuri dogmatis maCvenebelia, mTlianad saxeli ki qarTul enaSi damarxuli – dafaruli saidumleobis
matarebelia. imisda mixedviT, zeciuri veli, naTeli sxivi da samyaros amsaxveli maTi grafika rogoraa urTierT ganlagebuli, iZleva anbanis asoniSnebis grafikul saxes.
anbanis sawyisi asoniSnis saxelia ` aan ` metyvelebis ganviTarebis gamo
` aan ` - idan miRebulia ` an ` rac unda niSnavdes `RmerTi Zzliers` Sumerebis uZvelesi firfitebis gaSifriT gaxda cnlbili, rom mTavar RmerTs `anu` erqva.
maSasadame, anbanis asoniSSanTa mTliani Sinaarsi gadmoicema maTi rigiTobiT—
--mizeziT, grafikuli saxiT – subieqtiT, ricxviTi mniSvnelobiT – qmedebiT da saxeliT – dafaruli saidumlos mTliani Sinaarsis arsiT. e.i. anbanis mTliani wyoba gveqneba
1. 
– a = 1 an-i.
– a = 1 an-i. a – suli /asuli/ - RvTiuri arseba.
aR – marTi /aRmarTi/ - zesvlaa.
an – bani /anbani/ - RvTiuri xmis bgeriTi metyveleba.
a – Ti /aTi/ a + T = 10 RmerT-kaci.
ar – wivi /arwivi/ ar wivis, ar tiris. /ariol ar wivis/
aR – viri /aRviri/ roca cxens aRvirs /lagams/ amosdeb viriviTaa.
anbanis rigiT meore asoniSani
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igi warmoadgens mama RmerTis anu sawyisi asoniSnis asaxvidan gamomdinare Sinaarsi e.i.
mamisigan gamomavali Ze, romelic samyaros naTels hfens. misi grafikuli saxe miRebulia zeciuri velidan ` 0 ` gamomavali naTeli sxivisa ` 1 ` da samyaros asaxvasTan ` ---- ` erTad yofna, rac niSnavs zecis samyaroSi movlenil Zes.
zeciuri veli
naTeli sxivi
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samyaro
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misi Sesatyvisi mxedruli asoniSania ` b `. e. i.
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maTi ricxviTi mniSvnelobaa 2 – ori, saxeli ban-i /b – an/ maSasadame, anbanis rigiT
meore asoniSnis wyoba iqneba
2. 
b = 2 ban-i
b = 2 ban-i3.
beri – Ze eris wmindani
buxari- bu xari, bu – keriis /ojaxis/ mama: xari erovnuli Zlierebis gamoxatuleba.
Zveli qarTuli tradiciebidan – buxars rac metad daanTebdnen miT met pativiscemas
gamoxatavden stumris mimarT.
anbanis rigiT mesame asoniSani aris ` g `
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asebe mama RmerTisgan momdinareobs. ` g `-goni samyaros RvTiuri Zaiaa- da mas suliwmindas veZaxiT. suli – uflis naTel saydars niSnavs. zeciuri velidan gamosuli siTbo, romelic mTels qveyanas aTbobs aris mamisgan gamosuli suliwmida. maTi erTad yofna iZleva anbanis rigiT mesame asoniSanis grafikul saxes. maSasadame,
zeciuri beli `-----`
gamosuli siTbo ` `
samyaro `--------`
maTi erTad yofna gvaZlevs asoniSnis grafikul saxes. e.i.
sxivi
g. veli |
samyaro
misi Sesatyvisi mxedruli anbanis asoniSnis saxea ` g ` maTi ricxviTi mniSvnelobaa 3 – sami, saxeli gan-i. maSasadame, anbanis rigiT mesame asoniSnis wyoba iqneba
4. 
g 3 gan-i.
g 3 gan-i.5.
qarTuli anbanis meoTxe rigis asoniSania `d` don-i
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RmerTis mier samyaros Seqmnis pirveli dRe, da am dRes Seqmna uxilavi qveyana –angelozebi.
angelozebi arian sulni usxeulni, gonierni da Tavisufalni. sityva angelozi niSnavs moambes, mauwyebels, isini nwodebian moambed imitom, rom, RvTis gangebiT, isini miiRebdnen kacis sazes, gamoecxadebodnen RvTis kacebs da uambobdnen, anu auwyebdnen maT RvTis nebas. erTi mTavar angelozTagani gaamoartavanda da moindoma RmerTTan gaTanabreba. ampartavnobam is RmerTs ganaSora da Seqmna boroti, mas veZaxiT satanas.
zeciuri velis da samyaros urTierT kavSiri Cadebuli da dafarulia saidumlo anbanis meoTxe rigis asoniSanSi ` g ` don-is saxiT, da gansazRvravs adamianis gasavlel mTlian gzas
dabadebidan – maradisobaSi gadasvlis CaTvliT. zeciur velsa da samyaros Soris manZili aRebulia rogorc gadasvlis /gardacvlilis/ manZiliT – gziT, romelic `qebais`-s teqstSi moxsenebulia rogorc `oTxi dRis` mkvdarad. mkvdris 40 dRian samgloviaro ritualisa,
`weli aTasi viTarca erTi dRei`-s da `daasi ese wili anbanisai`-s gaTvaliswinebiT miiReba:
qarTveli eris winaprebs mTvare miaCndaT mTavar RmerTaT. manZili mTvaridan dedamiwamde Cadebuli anbanSi warmoadgens 4.10/5. km – s. dRevandeli uaxlesi teqnikiT gazomili manZili mTvaresa da dedamiwas Soris miRebulia 3,910 km – ad.
C,jhybr pflfx gj c,otve rehce abpbrb 372 cn&
~ D& C& Dtkmrtyintby `&
maSasadame, zeciuri velis `------` samtaros `0` da maT Soris gasavleli `oTxi dRis` gza
`1` warmoadgens anbanis rigiT meoTxe asoniSans. anbanSi zeciuru velis gamomsaxveli wre,
samyaros aRmniSvnel wris Tavze horizontalurad devs, amitom wre – xazaT Cans.
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e.i. miiRo aseTi saxe - ` ` da ewoda don-i.
zeciuri veli
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gardasvlis gza
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samyaromisi Sesatyvisi mzedruli asoniSani aris `d`.
maTi ricxviTi mniSvneloba aris 4 – oTxi. saxeli don-i.
maSasadame, anbanis rigiT meoTxe asoniSnis wyoba iqneba
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-- d – 4 don-i. Zveli aRqmis saRvTo istoria da qarTuli anbanuri wyoba migvaniSnebs, rom RmerTma anu samebam (3), pirvel (1) dRes, anu anbanis meoTxe (4) rigiT, Seqmna uxilavi qveyana. Tu ricxvebs sasveni niSnianad grafikulad gadmovitanT, gveqneba 3, 1, 4 veduri codna gveubneba:
`RmerTis pirovneba srulyofilia da mTliani: da radgan igi yovlad dasrulebulia, yovelive misgan warmomavali, rogoricaa es fenomenaluri samyaro, bolomde aRwurvilia srulis TvisebiT, yoveli rac srulia mTelisgan warmoiqmneba,srulia TavisTavad da raki srulia mTelia: misgan warmomavali esoden uricxvi erTeulis miuxedavad, mainc srul wonasworobas inarCunebs`.
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zeciuri are don-is anbanuri xedi.
oTxi dRei
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samyaro
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zeciuri 
don-is xedi don-is izometria samyaro zemodan.
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don-is samyaros wrexazis Sefardeba zeciuri ares xazTan gvaZlevs ricxvs 3,14. . . da dausruleblad grZeldeba. asec unda iyos, radgan zeciuri – samyaros, RmerTisgan (mTelisgan) warmoqmnili usasrulo erTeulebi anu 1415926535. . . varT. cnobilia, rom rocxvi 3,1415926535. amoxsnes 10 000 noSnamde, sadac perioduloba erTxelac ar dagiqsirebula. Cemi Rrma rwmeniT qarTuli anbanidan gamomdinare perioduloba aucileblad miiReba mxolod 40 000 niSnamde amoxsnis Semdeg, romlis dasawyisi iqneba ricxvTa igive wyoba. e.i. perioduloba 40 000 niSniania. es ki imas niSnavs, rom samyaros ganviTarebis kanonzomiereba Cadebuli da dafarulia qarTuli anbanis 40 asoniSanSi. meormoce asoniSnis ricxviTi mniSvneloba aris 40 000, rac ciklSi welTa raodenobas miuTiTebs, romlis gavlis Semdeg moxdeba ganaxleba anu axali ciklis dasawyisi e.i. boxdeba perioduloba.
sakvirvelia, magram faqtia is rac Cvenma winaprebma 5 000 wlis winaT qarTul anbanSi Cades
da dafares rogor miesadageba dRes uaxlesi teqnikiT gamomSvebs.
Tu qarTuli anbanis meormoce asoniSanis hoe-s rigiTobisa da ricxviTi mniSvnelobis jams
e.i. 40 + 40 000 = 40 040 gavyofT don-is wrexazisa da xazis fardobaze e.i. 3,14-ze miviRebT
dedamiwis diametrs. maSasadame,
40 040 * 1000 : 3,14 = 12, 752 km.
abanis rigiT mexuTe asoniSani `e`
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RmerTma samwaros Seqmnis meore dges anu anbanis mexuTe rigiT Segmna miwa da wyali erTad.
anbanis meore asoniSnis saxe warmogvidgeba zeciuri velis `------` misgan momdinare sxivs `1`
da wylisa da xmeleTis qaoturi masis aRmniSvnel xazs, romelic zeciuri velis marcxnidan
gamodis. maSasadame,
misi Sesatyvisi mxedruli asoniSani aris `e`
qaoturi masa
zeciuri veli naTeli sxivi 
maTi ricxviTi mniSvnelobaa 5-xuTi, saxeli en-i anbanis rigiT mexuTe asoniSnis wuoba warmogvidgeba Semdegnairad 5. ----- e = 5 en-i.
anbanis rigiT meeqvse asoniSani `v`
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RmerTma samyaros Seqmnis mesame dRes wyali ganyara miwisagan. wina dRes wyali da miwa qaotur masas Seadgenda, es anbanSi asaxulia asoniSan `e en-iT. maSasadame en-i unda gavyoT wylad da miwad e.i. wina dRes myofi erTgvaeovani masa unda gaiyos or erTi da igive formis aRniSvniT vinaidan ganayofSi wyali metia miwaze, amitom maTi aRmniSvneli msgavsi grafikebi sxvadasxva unda iyos, ganayofi ki marcxena da marjvena saxiT dalagdes.
maSasadame, gvaqvs en-i gavyoT msgavs da sxvadasxva zomis saxed:  | |||||||||||
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misi ricxviTi mniSvneloba aris 6 – eqvsi, saxeli vin-i. Sesabami mxedruli asoniSani aris `v` e.i.
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anbanis riciT meeqvse asoniSnis wyoba gveqneba 5. ----- 3 = 6 vin-i. germaneli geofizikosi alfred vegeneri miwisa da wylis gayofas adasturebs Semdegnairad:
`zustad Seesabameba erTmaneTs kontinentis napirebi, amas Tqvenc dainaxavT Tu rukas daxedavT zogierTi materikis sanapiro xazebi ise avsebs erTmaneTs, rogorc gatexili miis ori naxevari. magaliTad, samxreT amerikis Crdilo- aRmosavleTi kuTxe da afrikis gvineis ube: gegonebaT, pirveli meoredan aris amoWrilio. aseve, Tu CrdiloeT amerikis aRmosavleT kides, mivadebT Cvens warmodgenaSi evropis dasavleT sanapiros miviRebT erT mTlians`.
vin-i subieqtis an obieqtis maCvenebelia, am SemTxvevaSi wylis da xmeleTis.
anbanis rigiT meSvide asoniSani `z` zen-i.
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Zveli qarTveli eris cxovrebaSi mnaTobTa Tayvaniscemidan mTvares /ZvelqarTulad yamari/
TeTri giorgis uzenaesi RvTaebis adgili ekava, ese igi mTvare iyo upirvelesi qarTul kosmogenur mecnierebaSi. amasTan, saqarTvelo ar iyo erTaderTi qveyana, sadac aRiarebdnen mTvaris kults. Sumerebi, babilonelebi da egviftelebic eTayvanebodnen mTvares. aseTi gaRmerTeba, gamoiwvia upirvelesad yovlisa, iman rom mTvare warmoadgenda dedamiwis mudmiv Tanamgzavrs, Zvel saqarTveloSi mamrul, xolo sxva qveynebSi mdedrul sawyisad aRiarebuls.
misi meSveobiT xdeboda ama Tu im movlenis kosmiuri Sefaseba, mTvaris fazebiT awarmoebdnen sxvadasxva saidumlo gaangariSebebs da bolos uZveles saxemwifoebs hqondaT mxolod mTvaris kalendari. drois aTvla fazebisa da misi TanavarskvlavedebSi Sesvlis aRnusxviT.
ciuri mnaTobebi adamianis bedis uSualo gamgeblebi arian. miTologiuri azrovnebiST zuali
/saturni/ `mrisxane da boroti batonia” muSTari /iupiteri/ `zenaesTa da adamianTa gamgea”
aspiroz /venera/ `siyvarulis batonia” otarili /merkuri/ moxerxebulobisa da gamWriaxobis gamgea”.
saqristiano moZRvrebidan viciT, rom `dasabamsa dasxmulni Svidni dReni da Svidni igi mnaTobi mTvaresi, Svidi heri igi sanTeli solomonisi da Svidni rqani kravisni da nivTis naxulni da lvalad igaviT me 9-e Tavsa werilni: sibrZneman iSena Tvisa Tvisisa saxeli da qveSe Seudgina Svidi svetni. ese ars wameba SvidTa maT saidumloTani, rameTu sibrZne ze RvTisa ars da saxelad iSena eklesia da svetni eklesiisani arian Svidi saidumloni”. /saba/.
cifri 7 /zen/ amave dros asaxavs `meSvide cis” miTologiasac, romelic fSav-xevsureTSi
iyo gavrcelebuli.
anbanis rigiT meSvide asoniSnis saxe warmoadgens xeciuri velis `------“ naTeli sxivis `1” da
samyaros `i” asaxvis erTobas-megobrobas.
naTeli sxivi
zeciuri veli
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samyaro 
zeciT mosuli sxivi dedamiwaze asaxavs ciur mnaTobebs. misi Sesatyvisi mxedruli asoniSani aris `z"” aq Cvenma winaprebma zeciur velsa da samyaros Soris ciuri mnaTobebis sxivi Cades.
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maTi ricxviTi mniSvneloba aris 7-Svidi, saxeli zen-i. maSasadame, anbanis rigiT meSvide asoniSnis wyoba gveqneba
7. ----- z = 7 zen-i. anbanis rigiT merve asoniSani c, hoe-merve.
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anbanis asoniSanTa merve rigiT anu samyaros Segmnis merve dRes RmerTma Segmna Tevzi da frinveli e.i. uxilavi da xiluli. asoniSnis saxeSi Cadebuli da dafarulia saidumloebaTa Sinaarsi, TviT mis grafikaSi ar figurirebs samyaro. es ki imas mianiSnebs, rom saidumlos
gaxsna mxolod RvTis nebaa.
RvTiT dadgenili saidumloebani viciT Svidi: 1. a-naTlis Reba, 2. b-qristianlba, 3. g-aRsareba,
4. d-ziareba, 5. e-sneulsa zeda zeTis kurTxeva, 6. v-mRvdlis kurTxeva /mRvdloba/, 7. z-meuRleRa
gvirgvinis kurTxeva /qorwineba/.
radgan eklesiisani arian Svidni saidumloni, unda vifiqroT rom `e- merve” unda warmoadgendes
RvTiur /uzenaesis/ saidumlos, romelsac veravin ver gaigebs da mas TviT uzenaesi gvamcnobs bolo
Jams. am azrsac adasturebs biblia /daniel winaswarmetyveli da sxvani misTanani/.
`RvTiv bSVenieri swavlani, romelTa ewodebis `oqros wyaro” vkiTxulobT, `bolo Svenis
samRvdeloTa qristesTa yovelTa Sina yofad” vinaidan arian msaxur RvTisa eklesiaTa da
saidumloTa misTa”.
`xolo pavleca sTqva: rameTu yoveli-mRvdelmTavarni Sewirvad soflisa msxverplisa da Sesawiravisa dadgenil ars, romelni igi saxed afrdilisa msaxuroben zecisasa”.
`da ufali mTavari ityvis: romelman Tqven SegiwynaroT me Semiwynaros, da romelman me Semiwynaros Seiwynaros momavlinebeli Cemi mama”.
sruli dabejiTebiT SegviZlia vifiqroT, rom qarTuli anbanis merve asoniSnis saxeli `e-merve”
unda mianiSnebdes RvTiuri gagebiT e-eklesias, episkopos da `merve” uzenaesis merve saidumloebas,
romelsac veravin gaigebs bolo fazamde.
samyaroseuli /materialisturi/ gagebiT `e-merve” unda niSnavdes `e”-eros, `merve”- rigiT merves.
e.i. 1 – 8 wyoba qarTuli enis saidumloebaTa gasaTebia. vinaidan e- merves axsna gamomdinareobs
qarTuli anbanis yvela asoniSnidan, amitom mas yvela asoniSnis ganxilvis Semdeg davubrundebiT.
merve asoniSnis grafikuli saxeSi moCans zeciuri veli `e” naTeli sxivi da sxivi, romelic
samyaroskenaa mimarTuli.
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zeciuri veli
sxivi
naTeli sxivi
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misi Sesasityvi mxedruli asoniSani aris c: romlis sarkisebri xeli warmoadgens mxedruli anbanis meTormeye asoniSnis saxes –l- s. ase rom saidumlos arsebobis swori mimarTuleba icodnen, romelic merve saidumlos nawils unda Seadgendes. maSasadame,
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maTi ricxviTi mniSvnelobaa 8-rva, saxeli ucnobi `e-merve” anbanis rigiT merve asoniSnis wyoba iqneba8. 
--- c e-merve.
--- c e-merve.qarTuli anbanis rigiT mecxre asoniSani T Tan-i
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RmerTma samyaros Seqmnis meeqvse dRes, anu anbanis mecxre rigiT, `Seqmna kaci xatad da msgavsad TvisTa”.
`msgavsad TvisTa”, unda gavigoT, RvTaebrivi bunebis da suliT usxeulo. `kaci xatad TvisTa”
igulisxmeba RvTiuri bunebis mqone materialisturi asaxva – rasac xati hqvian. kaci mxolod msgavsia RmerTis da verasdros gaxdeba mama RmerTi, Ze RmerTi da suliwmida RmerTi. msgavseba ar niSnavs Tvisobriobas. RmerTma meeqvse dRes sityviT Seqmna kaci da ara adami-
-adamiani. kacuri gageba caSia da kaci adamianad warmogvidgeba, roca is ciskriT samyaros moevlineba: daiwyebs moqmedebas samwaros wrebrunvaze.
zemoT avRniSneT, rom saxeli adami /adamiani/ qarTuli enis nayofia. ` a ` - RmerTis sulia,
da `mi”-miwa,-Tixaa, romelSic RmerTma suli Cabera.
saxeli eva miRebulia qarTuli enis saxelebisagan: e-en, v-vin da a-anisagan. en-dedamiwa, vin--- --subieqti /adami/ a/n/ - RmerTi.
anbanis asoniSania rigiT mecxre asoniSani T-Tan-i. igi asaxavs mTvaris xilvad gxas, zeciur sxivs da zecaSi Seqmnil kacs.
maSasadame, mTvaris xilvadi gza - 
zeciuri sxivi -
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zecaSi Seqmnili kaci -
maTi erToba ( + + ) gvaZlevs rigiT mecxre asoniSnis grafikul saxes | | ||||||||||||||||
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misi ricxviTi mniSvnelobaa 9, saxeli Tan-i. Sesabamisi asoniSnis saxea - T
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mecxre asoniSnis wyoba gveqneba 9. ---- T = 9 Tan-ianbanis rigiT meaTe asoniSani i in-i
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`meSvide dRes RmerTman ganisvena yovelTagan saqmeTa TvisTa” e.i. axlad ara Seuqmnia ra da akurTxa dRe meSvide da dauniSna kacs es dRe /SabaTi RvTis sadideblad.
`SabaTi qveynis dabadebisaTvis idResaswauleba”
`qristeman keTilisa mizezisaTvis Sescvala udaresi uaRresad kviriakesa dResaswaulad”.
`kviriakesa dResa iwyo RmerTman qveynisa moqmedebad, masve dResa dabada naTeli saxiT naTlisa mis waruvalisa”. /saba/
kvira dRes - mose avida udabnod,
- zeviT uwvima manana puri,
- qristem waravlina mravali mociquli soflad,
- iyo yrmaTagan `osanasa” galoba,
- moufina adamierTa suli wmida,
- movals meufe Cveni gansjad.
anbanis asoniSanTa rigiT meaTe asoniSani i, in-i. meaTe asoniSani asaxavs zeciuri velidan gamosul sxivs maSasadame, zeciuri veli -------
naTeli sxivi l
maTi erTaT yofna qmnis meaTe asoniSnis grafikul saxes
misi ricxviTi mniSvnelobaa 10 aTi, saxeli in-i Sesabamisi mxedruli asoniSania `i” e.i.anbanis asoniSanTa rigiT meaTe asoniSnis wyoba iqneba
10. ---- i = 10 in-i 
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