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... in the dialogs Timaeus and Critias written by the Greek philosopher Plato (428-347 BC). An Egyptian priest was supposed to have described it to the... ...tian priest was supposed to have described it to the Greek statesman Solon (638-559 BC). The priest insisted that Atlantis was enormous - bigger ... ...echnologically advanced civilization, recounted the priest, in the 10th millennium BC (c. 12,000 years ago). Curiously, he also said that the A... ...an island in the Aegean Sea (Thera, or Santorini it suffered an earthquake in 1640 BC and housed the flourishing Cycladic civilization), through th... ...ed to Numa Pompilius, the second of Rome's seven kings (said to have ruled 715-673 BC). Stories during the Renaissance describe "do it yourself" se... ... Colombia (77), Kenya (10), Nigeria (45), South Africa (101), Algeria (59), Egypt (78), Iraq (26), Jordan (10), Lebanon (19) and dozens of other co... ... Each wall of the Pentagon is more than 920 feet long (=300 meters). It is almost 78 feet high (or a little short of 25 meters). It should have be...

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...tructures in S-loops 74 3.8 Smarandache mixed direct product loops 78 3.9 Smarandache cosets in loops 84 3.10 Some special type of Smar... ...generally, if a, b, c are elements in a Moufang loop G such that (ab)c = a(bc) then a, b, c generate an associative loop. The proof is left for t... ...= b, b < a. (ii) if a < b and b < c then a < c. (iii) if a < b then ac < bc and ca < c b. The relation a > b is interpreted as usual, to mean b <... ... triple a, b, c ∈ L is said to be pseudo associative if (ab) (xc) = (ax) (bc) for all x ∈ L. If (ab) (xc) = (ax) (bc) for some x ∈ L we say the trip... ...ciative loop L if for a non-associative triple a, b, c in L we have (ax) (bc) = (ab) (xc) then for all x ∈ L, we say the triple is strongly pseudo a... ...w we proceed onto another type of loop called Jordan loop. DEFINITION [78]: Let L be a loop. We say L is a Jordan loop if ab = ba. a 2 (ba) = (a ... ...y ≠ z and yz ≠ x. Now x ∈ N λ (L n (m)) implies (x, y, z) = e which is 78 possible only when x = z. However e ∈ N λ (L n (m)) as (e, x, y) = e fo... ...8). 7. Bruck.R.H, Some theorems on Moufang loops, Math. Z., Vol. 73, 59-78 (1960). 8. Burn.R.P, Finite Bol loops, Math. Proc. Camb. Phil. Soc.,... ...). 77. Vasantha.W.B, On Quasi loops, Octogon, Vol. VI, 63-65 (1998). 78. Vasantha.W.B, On a new class of Jordan loops and their loop rings, J. o...

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..................................................................................78 UP THE LADDER ......................................................... ...etter to not want, than to want and not have, or in the words of Lao-tzu (604 BC - 531 BC), “Manifest plainness; embrace simplicity; reduce selfishn... ... worlds and the corporeal world. ��������� �������� ������� � ��������� ����� 78 KABBALAH REVEALED being. It is already evolving within us, and it is...

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...rance had to be where Tuthmosis’ granite Dream Stela was. During the period of 1427-1401 BC, Tuthmosis had placed the Dream Stela in front of the Sp... ...e light- house was built by Ptolemy Soter, Alexander the Great’s commander, at around…290 BC, I believe. The lighthouse was completely destroyed by e... ...uys! We have something you should see!” It was Jack and Bob. CHAPTER 78 CONFESSIONS MITCH and Alex were shocked when J...

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...be publicly burned in London, he also turned theologian and wrote a book of 78 quarto pages dedicated to the pope, denouncing Luther and defending t... ...ss us to accept their opinions as articles of faith (as I have said above). 78 The third captivity of this sacrament is by far the most wicked abus... ... et catholica, cap. 1, sec. 3. Corpus luris Canonici, op. cit., II col. 5. 78 Cf. p. 28. 79 Though not actually present, one could obtain spiritu... ... between the various monastic orders and theological factions. E.g., cf. p. 78 n. 138. 129 This was the position of Thomas Aquinas, going back to A... ...bservantia, which also means “observance,” a fling at the Observants. Cf. p. 78 n. 138. 159 Cf. pp. 18 and 109. 1 Luther, M. (1999, c1959). Vol. 3...

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... rYix kY ............... 77 mhlw 4 CMq muMD ieAwxI pyeIAVY ............. 78 mhlw 5 CMq mn ipAwirAw jIau imqRw ......... 79 swihb qy syvku syv ...... ...drsnu Bytq pwp ............... 915 isKhu sbid ipAwrho ........... 916 mn bc /im rwm nwmu ........... 916 mhlw 3 AnMd AnMdu BieAw myrI ............... ...31 bwrh mih rwvl.............. 1332 sMqw kI ryxu swD jn sMgiq ... 1332 78 mhlw 3 gurmuiK ivrlw koeI .......... 1332 inrguxIAwry kau bKis lY ...... ...o kry ijsu ibnsY haumY qwpu ] nwnk kau guru ByitAw ibnsy sgl sMqwp ]4]8]78] isrIrwgu mhlw 5 ] ieku pCwxU jIA kw ieko rKxhwru ] ieks kw min Awsrw ... ...imqRw qyrw drgh bylI hoie ] gurmuiK nwmu smwil prwxI AMqy hoie sKweI ] 78 iehu mohu mwieAw qyrY sMig n cwlY JUTI pRIiq lgweI ] sglI rYix gudrI ... ...whI ikCu pwrwvwru ] dws Apny kau dIjY dwnu ] kbhU n ivsrY nwnk nwmu ]5]9]78] gauVI guAwryrI mhlw 5 ] Aink jqn nhI hoq Cutwrw ] bhuqu isAwxp Awgl ... ...vK nsy ]1] swDsMig kIrqn Plu pwieAw ] jm kw mwrgu idRsit n AwieAw ]2] mn bc /m goivMd ADwru ] qw qy CuitE ibKu sMswru ]3] kir ikrpw pRiB kIno Apnw... ...m hY insqwr ]2] inrml gux gwvhu inq nIq ] geI ibAwiD aubry jn mIq ]3] mn bc /m pRBu Apnw iDAweI ] nwnk dws qyrI srxweI ]4]102]171] gauVI mhlw 5 ]... ...y ibnu aubr n hoaU ] XwhU qrn qwrn smrwQw ] rwiK lyhu inrgun nrnwQw ] mn bc /m ijh Awip jnweI ] nwnk iqh miq pRgtI AweI ]43] sloku ] rosu n kwhU ...

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...rY rYix kY................ 77 mhlw 4 CMq muMD ieAwxI pyeIAVY.............. 78 mhlw 5 CMq mn ipAwirAw jIau imqRw ........ 79 swihb qy syvku syv...... ...5 drsnu Bytq pwp.................915 isKhu sbid ipAwrho............916 mn bc k®im rwm nwmu...........916 mhlw 3 AnMd Anµdu BieAw myrI............... ... so kry ijsu ibnsY haumY qwpu ] nwnk kau guru ByitAw ibnsy sgl sMqwp ]4]8]78] isrIrwgu mhlw 5 ] ieku pCwxU jIA kw ieko rKxhwru ] ieks kw min Aws... ... ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ 78 ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ hoie sKweI ] iehu mohu mwieAw qyrY ... ...nwhI ikCu pwrwvwru ] dws Apny kau dIjY dwnu ] kbhU n ivsrY nwnk nwmu ]5]9]78] gauVI guAwryrI mhlw 5 ] Aink jqn nhI hoq Cutwrw ] bhuqu isAwxp Awg... ...suK swgr ]4] pwrbRhm qyrI srxwie ] bMDn kwit qrY hir nwie ]1] rhwau dUjw ]78]147] gauVI mhlw 5 ] Apny loB kau kIno mIqu ] sgl mnorQ mukiq pdu dI... ...ivK nsy ]1] swDsMig kIrqn Plu pwieAw ] jm kw mwrgu idRsit n AwieAw ]2] mn bc k®m goivMd ADwru ] qw qy CuitE ibKu sMswru ]3] kir ikrpw pRiB kIno ... ...im hY insqwr ]2] inrml gux gwvhu inq nIq ] geI ibAwiD aubry jn mIq ]3] mn bc k®m pRBu Apnw iDAweI ] nwnk dws qyrI srxweI ]4]102] 171] gauVI mhlw... ...py ibnu aubr n hoaU ] XwhU qrn qwrn smrwQw ] rwiK lyhu inrgun nrnwQw ] mn bc k®m ijh Awip jnweI ] nwnk iqh miq pRgtI AweI ]43] sloku ] rosu n kw...

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...rightly glowing bulb with the quote "I have an idea." THE POWER IN YOU 78 2. The bulb in square two has lost some of its glow and says, "A word o...

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...iane lungi, ca sforile, care se agaţă şi de care se folosea Tarzan în 78 film – se întind de sus spre p ământ şi apoi se înfig în sol, se îngroa... ...eun ă cu George P. Coatmundi publicaser ă o carte la Trafford (Victoria – BC, Canada), „A New Copernican Revolution”, pe care Greg a prezentat-o. ...

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...main completely abstruse to us. Q: The Zohar was written in the second century BC, but was first discovered in approximately the 13th century. Why di... ...es them. They begin to obtain forc- T H E K A B B A L A H E X P E R I E N C E 78 es with which they can shape nature correctly. They also recognize t...

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... felt my naked knee, pressing a stone: it seemed VOICES FROM THE PAST 78 another knee although I felt the stone. I thought: nature tries to cl...

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...The Republic is a Socratic dialogue written by Plato around 380 BC concerning the definition of justice and the order and character of the just city-state and the just man....

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...alian plezuron, ne estas mirinde. Ĉu vi samopinias?” “Jes,” li respondis. 78 390 Parto Tri “Nu, kion pri kiam la plej saĝa viro diras ke laŭ lia opin... ...s ja.” “Kaj ankaŭ la militarto?” “Nepre jes.” “Do Palamedo en la tragedioj 78 ĉiam montras ke Agamemnono estis ridinda generalo. Palamedo pretendas, ... ...r homo.” “Ĉu vi scias kion mi opinias pri tiu studo?” mi demandis. “Kion?” 78 Palamedo estis posthomera heroo, rolanta en nun perdita tragedio de Eŭr...

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...E ATOM AND MATHEMATICS 57 INTRODUCTION 57 THE EARLY STORY OF MATHEMATICS 58 THE MATHEMATICS OF THE CLASSIC GREEK ERA 60 PYTHAGORAS (560 - 480 BC) - GREEK PHILOSOPHER AND MATHEMATICIAN. 61 EUCLID (325 - 270 BC) - GREEK MATHEMATICIAN 61 APOLLONIUS (262 - 190 BC) - GREEK MATHEMATICIAN 61 ERATOSTHENES (276 - 196 BC) - GREEK ASTRONOMER AND MATHEMATICIAN 62 C...

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...0 ;C 0 be the feet of the altitudes of an acute-angled triangle ABC (A 0 2 BC, B 0 2 AC, C 0 2 AB). Let a 0 ;b 0 ;b 0 denote the sides of the podaire ... ...lds true (see Theorem 25 in page 112): Let AD and AE be two cevians (D;E2 (BC)) forming angles ; with the sides AB;AC, respectively. If b A 90 an... ... b p By 2 + p z a p Ax p x c p Cz 2 0; or equivalently, y +z x bc aA + z +x y ca bB + x +y z ab cC 2 a p BC + b p CA + c p AB : ... ...CA + c p AB : (3) By using again the A.M.-G.M. inequality, we obtain a p BC + b p CA + c p AB 3 abc ABC 1 3 : Then, on base of (iii), one gets... ...b p CA + c p AB 3 abc ABC 1 3 : Then, on base of (iii), one gets a p BC + b p CA + c p AB 6s : (4) Now (4) and (3) implies that (iv) y +z x ... ...rslanagi c, D.M. Milosevi c, Problem 1827, Crux Math. (Canada) 19(1993), 78. 2. D.S. Mitrinovi c et. al., Recent advances in geometric inequalities... ...A 2 b 2 + 3S 2 ; where T = 2S. Similarly, bc =M 2 + 3R 2 =A 2 d 2 + 3R 2 ; 78 where P = 2R: (10) Therefore x =z +ab; w =y +ad; z = ab +T 2 = 2N +... ...ih aly Bencze, OQ.58, Octogon Mathematical Magazine, Vol.4, No.2, 2000, p.78. 2. P.N. de Souza, J.N. Silva, Berkely problems in mathematics, Springer... ...sical Functions of Number Theory, Smarandache Notions J., 9(1998), No.1-2, 78-81. 157 2. K. Kashihara, Comments and Topics on Smarandache Notions and...

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...d the path ABC. The tangent vector on the path formed by the segments AB and BC has the same total change in direction θ, but all of this change ... ...lso passes through a point of the segment AC, or through a point of the segment BC. Probably the most intuitive notion of a point C lying between ... ...lso passes through a point of the segment AC, or through a point of the segment BC. 40 This is Pasch’s axiom, and it states roughly that an s-l... ...′B′ is also congruent to the segment A′′B′′. III-3. On the line a, let AB and BC be two segments which except for B have no point in common. Furth... ...r B′ also have no point in common. In that case, if AB is congruent to A′B′ and BC is congruent to B′C′, then AC is congruent to A′C′. III-4. Ever... ...r, so there is a difference in the properties of large and small objects. For 78 example, the large triangle GHI in Figure 7 has no interior. The ... ... 77, 81 parallel 21, 26 paradoxist 53 partially between 35 Pasch’s axiom 39, 78 q-congruent 43 regularly hyperbolic point 45 relative angle 21 ... ...7 SAS criterion 44 s-circle 25, 62 s-congruent 41 S-denied 6 s-Klein bottle 78 s-line 11 s-manifold 9, 11 s-manifold with boundary 63 s-proto...

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...re and more evolved, the images defining divinity will be more and more 78 agreeing with one another and we will see that this problem is not an e...

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...entem ab alio Quovis curvae pun&o g agatur ZR’ .difiantk S P parallela , Bc aemittatur .$& T perpendicularis ad diltantiam illam SP : vis centripe... ...~6 ut 'T'zt.fk sequalis ipfi Tv ; deinde cape z~lv, quz fit ad vG ut eit ‘BC q@ad. ad T C pad. Et quoniam ex conicis efi $9-v q~d. ad T v G ut ZICg... ...antur tria puntia fit folvitur expeditius. Dentur pun&a B, C, I), Juntias BC, C2) produc ad E, F, ut fit EB ad E Cut SB ad SC, 8~ FC ad FB ut SC ad ... ...ifim EC-CA ad CA-CCL, fei. 23 A ad A,!&~& Fompof& EA ad EA=-kAL feu EL ut BC ad E C+CA feu EB; ideoque, ob knilitudinem triangularurn EA.& EL I, E C... ...s velockas &. loco quovis C ej dd velocitatem cwpo~is centro B inferv&lo BC c&&m defiribmtis, in fidbdtiplicata n&one qzmm AC, ++&a corporis a circ... ... pIen= non majorem h&&at proportionem ad refiitentiam pyxidis vacua? quam 78 ad 77. Nam fi squriles dent ambarum refiitentia?, pyxis plena ob vim fu... ...o diutius confervare deberet, atque ideo completis femper 06 +llationibus 78 ad loca illa notata redire. Rediit autem ad eadenl completis ofcillatio... ...ternis fint ut materia, feu numerus particularum quibus refiilitur : erit 78 13’ refiiientia pyxi- 3s pIenae in ipfius partibus interni-s : ideo,que... ...acua r<efi- fientia tota A+B erit ad pyxidis plenz refiitentiam totam A-1-78 B ut 77 ad 78, & divifim A+B ad 77 B, ut 77 ad I, indeque A+B ad. B ut...

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...ecial elements in S-rings 71 3.10 Special properties about S-rings 78 4 4. Some new notions on Smarandache rings 4.1 Smarandache... ...s are satisfied. 1. The set G is non-empty. 2. If a, b, c ∈ G then a(bc) = (ab) c. 3. There are exists in G an element e such that (a) For an... ...) + (c + id) = (a + c, i(b + d)) and (a + ib) (c + id) = (ac – bd, i(ad + bc)). The unity of Z[i] is 1. DEFINITION 2.5.5: Consider the set Q[i] =... ...DB ⊂ B and BD ⊂ B; i.e., bd(and db) are in B. with 65 b(d + c) = bd + bc ∀ d, c ∈ D and b ∈ B ((d + c) b = db + cb). If B is simultaneously a S-... ...-strongly regular ring? 11. Is Z 25 S 3 a S-quasi commutative ring? 78 12. Can Z 27 have S-nilpotents? 3.10 Special Properties about Sm... ... collection of all right ideals of R. If (A + B) (A + C) (A + D) = A + BC (A + D) + BD (A + C) + DC (A + B) ∗ for all right ideals A, B, C, D in... ...g is zero. By S-subring we mean only proper S-subrings. DEFINITION 4.4.78: Let R be a ring. If every S-subring of R is S-essential S- subring then... ... a. a Q-ring (m = n and m ≠ n)? b. a S-Q-ring (m = n, and m ≠ n)? 78. Is the group ring Z p S n a F-ring, p an odd prime? 79. Classify th... ...direct products of E-inverse semigroups, J. Aust. Math. Soc., Vol. 48, 66-78, (1990). 56. Munn.W.D., Bisimple rings, Quat. J. of Math. Oxford, Vol...

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...aucracy under King David and his successors in the general period 800- 700 BC. Hebrew religious culture did not exist in isolation, but our chart does... ...quired. On the first level we find Egyptian religion of approximately 1400 BC which became codified and highly organized under King Akhenaton. 11 It w... ...eaucracy under King David and his successors in the general period 800-700 BC. Hebrew religious culture did not exist in isolation, but our chart does... ...ery pervasive influence of Mesopotamian culture. During the period 800-500 BC, a creedal statement of vast 11. Details in Cyril Aldred, Akhenaten, Tha... ...ned and regulated religious organization. 13 In the general period 500-200 BC three major new influences impinged upon the Hebrew system in Palestine ... ...rect cause of suffering, depends on being attached THE RELIGIOUS DIMENSION 78 to beliefs and craving for life at all costs. The Buddha was sub- stitu... ...is appears as darkness. Darkness within darkness. The gate to all mystery. 78 Muslim: In the market, in the cloister—only God I saw. In the valley and... ...00, as quoted in Suzuki, Introduction, p. 82. Bracketed comment by Suzuki. 78. Lao Tsu, Tao Te Ching (tr. Gia-Fu Feng and Jane English). Vintage Books... ...n individual deity, though unique, 132. Adapted from Hewitt, 1902, pp. 676-78. Some of this material is also given in Tooker, 1979. 133. Hallowell’s a...

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...-1 12 2 72 1 13 0 73 -3, -1,-1 14 2, 2, 4 76 1 17 -3, -1, -1 77 -1 20 1 78 1, 1, 3 21 -1 81 -3, -1, -1 22 1, 1, 3 84 1 25 -1 85 -1 26 1, 1, 3... ...26 3.35 3.99 Table 1. ctd n 10 11 12 13 14 15 16 17 18 Cn 3.51 3.85 3.6 3.78 3.65 3.74 3.67 3.72 3.69 Table 1. ctd n 19 20 21 22 Cn 3.71 3.69 3.... ...482 24327 2191 81 0 91 0 77 ⋅<≤⋅ n 39640 20 4 9974414 23521 2065 91 0 1 0 78 ⋅<≤ n 39222 26 4 9975179 22825 1996 Total 440402 481 65 99657140 31... ...cd. B= abcdabcdabcdabcdabcd…… i C I Period # F(i) M(i) L(i) 1 a a 2 bc bc 3 dab 1 d ab 4 cdab 1 cd ab 5 cdabc 1 cd abc 6 dabcda 1 d... ...ote that G=3 4 ⋅37⋅333667. From formulas (3) to (6) we now obtain: 78 For k=1,2,6,7 and 9: (3´) C i ⋅G=10 u ⋅(δ(j)⋅A+B(k)⋅G)⋅10 9j +E(k)... ...83 27 3 3 .31.37.333667.481549.F74 77 3.10034243.F282 28 146273.608521.F83 78 3.11.37.71.41549.F284 29 3.41.271.9091.F89 79 41.271.9091.F290 30 3....