Notes on the Greek New Testament Day 354 December 20 th Revelation 11:1-19. Works frequently referenced in these notes on the book of Revelation

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Day 354 December 20 th Revelation 11:1-19. Works frequently referenced in these notes on the book of Revelation"

Transcript

1 Notes on the Greek New Testament Day 354 December 20 th Revelation 11:1-19 Works frequently referenced in these notes on the book of Revelation Morris, Leon Mounce, Robert H The Revelation of St John (Tyndale New Testament Commentaries), Grand Rapids, Eerdmans, 1969 The Book of Revelation (New International Commentary on the New Testament), Grand Rapids, Eerdmans, 1977 Peterson, Eugene H Reversed Thunder, San Francisco, HarperCollins, 1991 Witherington, Ben Revelation (New Cambridge Bible Commentary), Cambridge University Press, Cambridge, 2003 Chapter 11 Mounce, and others, consider chapter 11 to correspond to the contents of the little book of chapter 10. This chapter is particularly difficult to interpret. Witherington comments, "Koester suggests that in Rev 11 we have an overture to the last half of the book, introducing us in summary form to the conflict between God's people and the Beast that is recounted in Rev " Verse 1 Καὶ ἐδόθη μοι κάλαμος ὅμοιος ῥάβδῳ, λέγων Ἔγειρε καὶ μέτρησον τὸν ναὸν τοῦ θεοῦ καὶ τὸ θυσιαστήριον καὶ τοὺς προσκυνοῦντας ἐν αὐτῷ. ἐδόθη Verb, aor pass indic, 3 s διδωμι καλαμος, ου m reed, measuring rod ὁμοιος, α, ον like ῥαβδος, ου f stick, rod, sceptre ἐγειρω raise μετρεω measure ναος, ου m temple, sanctuary "The measuring of the temple is a symbolic way of declaring its preservation. The background is probably Ezekiel where the prophet in a vision watches every part of the temple measured with painstaking care." Mounce. Mounce considers the temple to be a picture of the church and its measuring to be equivalent to the sealing of 7:1-8. "God will give spiritual sanctuary to the faithful believers against the demonic assault of the Antichrist." Witherington thinks that Joh's use of ναος, which means the inner sanctuary rather than the temple complex, also supports the idea of protection. θυσιαστηριον, ου n altar προσκυνεω worship Verse 2 καὶ τὴν αὐλὴν τὴν ἔξωθεν τοῦ ναοῦ ἔκβαλε ἔξωθεν, καὶ μὴ αὐτὴν μετρήσῃς, ὅτι ἐδόθη τοῖς ἔθνεσιν, καὶ τὴν πόλιν τὴν ἁγίαν πατήσουσιν μῆνας τεσσεράκοντα δύο. αὐλη, ης f court, courtyard ἐξωθεν adv & prep outside ἔκβαλε Verb, aor act imperat, 2s ἐκβαλλω throw out, cast out ἐδόθη Verb, aor pass indic, 3 s διδωμι ἔθνεσιν Noun, dat pl ἐθνος, ους n nation; τα ἐ. Gentiles "The distinction between the sanctuary and the outer court is a way of pointing up the limitations placed upon pagan hostility (cf. Morris ). It may physically decimate the witnessing church (in 11:7 the two witnesses are killed), but it cannot touch the real source of life (the witnesses are raised and ascend to heaven; 11:11-12)." Mounce. πολις, εως f city, town ἁγιος, α, ον holy Another designation for the church. πατεω trans trample μην, μηνος m month τεσσερακοντα forty δυο gen & acc δυο dat δυσιν two "The temporal designation of forty-two months (11:2; 13:5) is also given in Revelation as 1260 days (11:3; 12:6) and 'a time, and times, and half a time' (12:14). Its primary reference is to the period of Jewish suffering under the Syrian despot Antiochus Epiphanes in BC. It became a conventional symbol for a limited period of time during which evil would be allowed free rein. In Luke 21:24 it is called 'the times of the Gentiles'." Mounce. Witherington comments, "The reference to forty-two months comes from Daniel and is just another way of rendering the period of three and a half years, that final penultimate period before the end of history."

2 Verse 3 καὶ δώσω τοῖς δυσὶν μάρτυσίν μου, καὶ προφητεύσουσιν ἡμέρας χιλίας διακοσίας ἑξήκοντα, περιβεβλημένοι σάκκους. δωσω Verb, fut act indic, 1 s διδωμι δυο gen & acc δυο dat δυσιν two μαρτυς, μαρτυρος dat pl μαρτυσιν m witness The two witnesses are modelled upon Moses and Elijah (cf. 2 Kings 1:10ff; 1 Kings 17:1; Ex 7:14-18; 8:12). They are a symbol of the witnessing church. Witherington thinks that the reference may be to two specific churches that are undergoing persecution and even martyrdoms for instance, Smyrna and Philadelphia. χιλίας Noun, nom s or Adjective, f acc pl χιλιας, αδος f a thousand διακοσιοι, αι, α two hundred ἑξηκοντα sixty περιβεβλημένοι Verb, perf pass ptc, m nom pl περιβαλλω put on, clothe, dress σακκος, ου m sackcloth, mourning dress Cf. Zech 13:4. Their message is a call to repentance and is reflected in their dress. Verse 4 Οὗτοί εἰσιν αἱ δύο ἐλαῖαι καὶ αἱ δύο λυχνίαι αἱ ἐνώπιον τοῦ κυρίου τῆς γῆς ἑστῶτες. ἐλαια, ας f olive tree λυχνια, ας f lampstand A symbol of the church in chapter 1. Witherington adds, "The witnesses are called olive trees for they carry in them the fuel by which the candlestick could be lit." ἐνωπιον prep with gen before ἑστῶτες Verb, perf act ptc, m nom pl ἱστημι Cf. Zech 4. "By these two metaphors John is emphasizing a truth concerning the church which has always been true but is especially appropriate in times of persecution that the power and authority for effective witness lie in the Spirit of God." Mounce. Cf. Zech 4:6. Verse 5 καὶ εἴ τις αὐτοὺς θέλει ἀδικῆσαι, πῦρ ἐκπορεύεται ἐκ τοῦ στόματος αὐτῶν καὶ κατεσθίει τοὺς ἐχθροὺς αὐτῶν καὶ εἴ τις θελήσῃ αὐτοὺς ἀδικῆσαι, οὕτως δεῖ αὐτὸν ἀποκτανθῆναι. θελω wish, will ἀδικεω wrong, harm πυρ, ος n fire ἐκπορευομαι go or come out στομα, τος n mouth κατεσθιω eat up, devour Cf. 2 Kings 1. ἐχθρος, α, ον enemy οὑτως adv. thus, in this way δει impersonal verb it is necessary ἀποκτεινω kill, put to death Verse 6 οὗτοι ἔχουσιν τὴν ἐξουσίαν κλεῖσαι τὸν οὐρανόν, ἵνα μὴ ὑετὸς βρέχῃ τὰς ἡμέρας τῆς προφητείας αὐτῶν, καὶ ἐξουσίαν ἔχουσιν ἐπὶ τῶν ὑδάτων στρέφειν αὐτὰ εἰς αἷμα καὶ πατάξαι τὴν γῆν ἐν πάσῃ πληγῇ ὁσάκις ἐὰν θελήσωσιν. ἐξουσια, ας f authority, power κλειω shut, shut up, lock ὑετος, ου m rain βρεχω rain, send rain, wet Cf 1 Kings 17:1; Jas 5: στρεφω turn αἱμα, ατος f blood Cf. Ex 7:20. πατασσω strike πληγη, ης f plague, misfortune Cf. Ex 8:12. ὁσακις adv. as often as; ὁσακις ἐαν whenever "God's servants in the new dispensation have just as great resources as did Moses and Elijah in the old." Morris. Verse 7 Καὶ ὅταν τελέσωσιν τὴν μαρτυρίαν αὐτῶν, τὸ θηρίον τὸ ἀναβαῖνον ἐκ τῆς ἀβύσσου ποιήσει μετʼ αὐτῶν πόλεμον καὶ νικήσει αὐτοὺς καὶ ἀποκτενεῖ αὐτούς. ὁταν when τελεω complete, finish μαρτυρια, ας f testimony, witness θηριον, ου n animal, beast ἀναβαινω come up, ascend Mounce says this is "the major antagonist of the church in the last days the Antichrist." πολεμος, ου m war, battle Supports the view that the witnesses are not individuals but a picture of a large group. νικαω conquer, overcome ἀποκτενεῖ Verb, fut act indic, 3 s ἀποκτεινω kill, put to death Verse 8 καὶ τὸ πτῶμα αὐτῶν ἐπὶ τῆς πλατείας τῆς πόλεως τῆς μεγάλης, ἥτις καλεῖται πνευματικῶς Σόδομα καὶ Αἴγυπτος, ὅπου καὶ ὁ κύριος αὐτῶν ἐσταυρώθη. πτωμα, τος n body, corpse πλατεια, ας f wide street πολις, εως f city, town

3 ὁστις, ἡτις, ὁ τι who, which πνευματικως spiritually, symbolically Σοδομα, ων n Sodom ὁπου adv. where σταυροω crucify Mounce says that the reference is to Rome. "The witnesses meet their death at the hands of the Antichrist, whose universal dominion was in John's day epitomised by the power of Rome. The inclusion of a reference to the crucifixion is not to identify a geographical location but to illustrate the response of paganism to righteousness." Witherington, however, writes, "We must see the reference to Sodom and Egypt as a statement about the spiritual status of Jerusalem. It was a city occupied and, in fact, trampled underfoot in AD 95 by Gentiles. 'Sodom' was a prophetic title for Jerusalem that implied its judgment (Is 1:9-10; Jer 23:14; Lam 4:6). In other words it is a place of oppression, slavery and gross immorality." Morris thinks that the great city is "every city and no city. It is civilized man in organized community." Verse 9 καὶ βλέπουσιν ἐκ τῶν λαῶν καὶ φυλῶν καὶ γλωσσῶν καὶ ἐθνῶν τὸ πτῶμα αὐτῶν ἡμέρας τρεῖς καὶ ἥμισυ, καὶ τὰ πτώματα αὐτῶν οὐκ ἀφίουσιν τεθῆναι εἰς μνῆμα. βλεπω see, look λαος, ου m people φυλη, ης f tribe, nation γλωσσα, ης f tongue, language ἐθνος, ους n nation τρεις, τρια gen τριων dat τρισιν three ἡμισυς, εια, υ gen ἡμισους half The three and a half days of their public exposure corresponds to the three and a half years of their ministry. πτωμα, τος n body, corpse ἀφίουσιν Verb, fut act indic, 3 pl ἀφιημι allow τεθῆναι Verb, aor pass infin τιθημι place μνημα, τος f tomb, grave Witherington comments, "That the bodies of the witnesses were not allowed to be buried was considered in the ancient near east the ultimate way to disgrace or shame someone (see Isa 5:25; Ps Sol 2:30 ff.)." Verse 10 καὶ οἱ κατοικοῦντες ἐπὶ τῆς γῆς χαίρουσιν ἐπʼ αὐτοῖς καὶ εὐφραίνονται, καὶ δῶρα πέμψουσιν ἀλλήλοις, ὅτι οὗτοι οἱ δύο προφῆται ἐβασάνισαν τοὺς κατοικοῦντας ἐπὶ τῆς γῆς. κατοικεω live The unbelieving world. χαιρω rejoice, be glad εὐφραίνονται Verb, pres midd/pass indic, 3 pl εὐφραινω make glad; pass be glad δωρον, ου n gift πεμπω send ἀλληλων, οις, ους reciprocal pronoun one another Cf. Esth 9:19,22. βασανιζω torment, disturb "The world has always shown its hostility to the message of God a truth which ought to give some concern to the contemporary church existing for the most part rather comfortably in a world of increasing wickedness." Mounce Verse 11 Καὶ μετὰ τὰς τρεῖς ἡμέρας καὶ ἥμισυ πνεῦμα ζωῆς ἐκ τοῦ θεοῦ εἰσῆλθεν ἐν αὐτοῖς, καὶ ἔστησαν ἐπὶ τοὺς πόδας αὐτῶν, καὶ φόβος μέγας ἐπέπεσεν ἐπὶ τοὺς θεωροῦντας αὐτούς ζωη, ης f life εἰσῆλθεν Verb, aor act indic, 3 s εἰσερχομαι enter Cf. Ezek 37. ἔστησαν Verb, aor act indic, 3 pl ἱστημι stand πόδας Noun, acc pl πους, ποδος m foot φοβος, ου m fear ἐπέπεσεν Verb, aor act indic, 3 s ἐπιπιπτω fall upon, come upon θεωρεω see, watch, observe "Since murder is the last resort of man, what can be done about those who rise from the dead! The resurrection of the church is a sure indication that God possesses the ultimate authority over life and death." Mounce. Verse 12 καὶ ἤκουσαν φωνῆς μεγάλης ἐκ τοῦ οὐρανοῦ λεγούσης αὐτοῖς Ἀνάβατε ὧδε, καὶ ἀνέβησαν εἰς τὸν οὐρανὸν ἐν τῇ νεφέλῃ, καὶ ἐθεώρησαν αὐτοὺς οἱ ἐχθροὶ αὐτῶν. ἀνάβατε Verb, aor act imperat, 2 pl ἀναβαινω come up, ascend ὡδε adv here νεφελη, ης f cloud Echoes of what is said of Elijah in 2 Kings 2:11. A sign of God's vindication of his witnesses. ἐχθρος, α, ον enemy

4 Verse 13 καὶ ἐν ἐκείνῃ τῇ ὥρᾳ ἐγένετο σεισμὸς μέγας, καὶ τὸ δέκατον τῆς πόλεως ἔπεσεν, καὶ ἀπεκτάνθησαν ἐν τῷ σεισμῷ ὀνόματα ἀνθρώπων χιλιάδες ἑπτά, καὶ οἱ λοιποὶ ἔμφοβοι ἐγένοντο καὶ ἔδωκαν δόξαν τῷ θεῷ τοῦ οὐρανοῦ. ἐκεινος, η, ο demonstrative adj. that ὡρα, ας f hour, moment ἐγένετο Verb, aor midd dep indic, 3 s γινομαι σεισμος, ου m earthquake Cf. Ezek 38:19-20; Zech 14:5. δεκατος, η, ον tenth ἔπεσεν Verb, aor act indic, 3 s πιπτω fall, fall down ἀπεκτάνθησαν Verb, aor pass indic, 3 pl ἀποκτεινω see v.7 ὀνομα, τος n name, person χιλιας, αδος f a thousand ἑπτα seven λοιπος, η, ον rest, remaining, other ἐμφοβος, ον full of fear ἔδωκαν Verb, aor act indic, 3pl διδωμι δοξα, ης f glory Some think that this is repentance and even conversion. Mounce says, "Kiddle is correct in his view that in that day 'the great mass of mankind will have committed the unpardonable crime of deifying evil.' They give glory to God 'when they are compelled by overriding terror to recognize that the true Lord is Christ and not Antichrist'." On the other hand, Fiorenza writes, "It is crucial to recognise that Revelation's rhetoric of judgment expresses hope for the conversion of nine-tenths of the nations in response to Christian witness and preaching. Otherwise, one will not understand that the author advocates a theology of justice rather than a theology of hate and resentment." Similarly, Koester points out the contrast when one compares 1 Kings 19:18 to Rev 11:13. In the former, all but 7,000 embrace idolatry, in the latter all but 7,000 glorify God. "The conversion of the nations, rather than their destruction is God's will for the world." Verse 14 Ἡ οὐαὶ ἡ δευτέρα ἀπῆλθεν ἰδοὺ ἡ οὐαὶ ἡ τρίτη ἔρχεται ταχύ. οὐαι woe! δευτερος, α, ον second τριτος, η, ον third ταχυ adv quickly, without delay, soon Verses The remainder of chapter 11 is a "summary of all that is still to come" Barclay. Verse 15 Καὶ ὁ ἕβδομος ἄγγελος ἐσάλπισεν καὶ ἐγένοντο φωναὶ μεγάλαι ἐν τῷ οὐρανῷ λέγοντες Ἐγένετο ἡ βασιλεία τοῦ κόσμου τοῦ κυρίου ἡμῶν καὶ τοῦ χριστοῦ αὐτοῦ, καὶ βασιλεύσει εἰς τοὺς αἰῶνας τῶν αἰώνων. ἑβδομος, η, ον seventh σαλπιζω sound a trumpet κοσμος, ου m world βασιλευω rule, reign "Glasson refers to the common saying, 'It's all over bar the shouting,' and remarks that the only difference is that the shout of victory has already begun... During his earthly ministry Jesus had resisted the tempting offer of Satan to hand over the kingdoms of this world in exchange for worship (Mt 4:8-9). Now this sovereignty passes to him as a rightful possession in view of the successful completion of his messianic ministry." Mounce. Verse 16 Καὶ οἱ εἴκοσι τέσσαρες πρεσβύτεροι οἱ ἐνώπιον τοῦ θεοῦ καθήμενοι ἐπὶ τοὺς θρόνους αὐτῶν ἔπεσαν ἐπὶ τὰ πρόσωπα αὐτῶν καὶ προσεκύνησαν τῷ θεῷ, εἰκοσι twenty τεσσαρες neut τεσσαρα gen τεσσαρων four ἐνωπιον prep with gen before καθημαι sit, sit down θρονος, ου m throne ἔπεσαν Verb, aor act indic, 3 pl πιπτω fall, fall down προσωπον, ου n face προσκυνεω worship Cf. 4:10; 5:8,14; 19:4. Verse 17 λέγοντες Εὐχαριστοῦμέν σοι, κύριε, ὁ θεός, ὁ παντοκράτωρ, ὁ ὢν καὶ ὁ ἦν, ὅτι εἴληφας τὴν δύναμίν σου τὴν μεγάλην καὶ ἐβασίλευσας. εὐχαριστεω thank, give thanks παντοκρατωρ, ορος m Almighty Cf. 1:8; 4:8. "In the same two passages, as well as in 1:4, he is the one who is, who was, and who is to come. In the present verse (and in 16:5) the third member is omitted because his coming is no longer seen as future. Already he has come and entered upon his reign." Mounce. εἴληφας Verb, perf act indic, 2 s λαμβανω The perfect indicates a permanent taking of power. δυναμις, εως f power βασιλευω see v.15.

5 Verse 18 καὶ τὰ ἔθνη ὠργίσθησαν, καὶ ἦλθεν ἡ ὀργή σου καὶ ὁ καιρὸς τῶν νεκρῶν κριθῆναι καὶ δοῦναι τὸν μισθὸν τοῖς δούλοις σου τοῖς προφήταις καὶ τοῖς ἁγίοις καὶ τοῖς φοβουμένοις τὸ ὄνομά σου, τοὺς μικροὺς καὶ τοὺς μεγάλους, καὶ διαφθεῖραι τοὺς διαφθείροντας τὴν γῆν. ἔθνη Noun, nom & acc pl ἐθνος, ους n nation, people; τα ἐ. Gentiles ὠργίσθησαν Verb, aor pass indic, 3 pl ὀργιζομαι be furious, be angry ὀργη, ης f wrath, anger Cf. Ps 2:2,5,12. καιρος, ου m time, appointed time νεκρος, α, ον dead κριθῆναι Verb, pres pass infin κρινω judge The triumph of God's wrath is proclaimed in 14:10-11; 16:15-21 and 20:8-9. δοῦναι verb, aor act infin διδωμι μισθος, ου m pay, wages, reward δουλος, ου m slave, servant ἁγιος, α, ον holy φοβεομαι fear, reverence "A reasonable translation would be, 'To thy servants the prophets, and to the saints those who fear thy name, both small and great.' There are two groups (prophets and saints), who are further described as fearing the name of God. This arrangement holds intact the expression 'thy servants the prophets' (which occurs again at 10:7) and joins to it a second group (the saints) as in 16:6 ('the blood of the saints and prophets'), 18:24 (order reversed), and 22:9 ('the prophets and... them that keep the words of this book' that is, saints)." Mounce. μικρος, α, ον little, small, insignificant διαφθεῖραι Verb, aor act infin διαφθειρω destroy, ruin Cf. 2 Thess 1:6-7. A reference here to the Roman empire of John's day. "The wrathful ones will receive wrath, and the destroyers will be destroyed." Witherington. Verse 19 Καὶ ἠνοίγη ὁ ναὸς τοῦ θεοῦ ὁ ἐν τῷ οὐρανῷ, καὶ ὤφθη ἡ κιβωτὸς τῆς διαθήκης αὐτοῦ ἐν τῷ ναῷ αὐτοῦ καὶ ἐγένοντο ἀστραπαὶ καὶ φωναὶ καὶ βρονταὶ καὶ σεισμὸς καὶ χάλαζα μεγάλη. "Verse 19 is a response to the hymn of praise in verses 17 and 18. The ark of the covenant corresponds to the rewarding of the faithful, and the cosmic disturbances to the outpouring of God's wrath." Mounce. Witherington adds, "The ark was the locus of God's Word and his presence, and, in apocalyptic vision, it is quite proper to stress the heavenly nature of these things. It is accompanied by the usual signs of theophany and of God coming down, which is the ultimate event." ἠνοίγη Verb, aor pass indic, 3 s ἀνοιγω open ναος, ου m temple, sanctuary ὤφθη Verb, aor pass indic, 3 s ὁραω trans see; pass. appear κιβωτος, ου f ark, box διαθηκη, ης covenant Both the blessing of his people and the judgement of rebels proceed from the covenant faithfulness of God (cf. 16:1). "This vision promises God will be faithful to his Word and maintain fellowship with his covenant people." Witherington. ἀστραπη, ης f lightning, ray βροντη, ης f thunder σεισμος, ου m earthquake χαλαζα, ης f hail These events recall the giving of the law at Sinai. Postscript Witherington speaks of the book of Revelation, in common with all apocalyptic literature, as 'resistance literature.' He comments that it needs to be read as such. It is a call to active but nonviolent resistance to the oppressive powers that be, a resistance that involves witness to Jesus Christ as supreme Lord, witness which leads both to the extension of his kingdom but also to persecution, even to the point of death. Prayer also plays a vital part for it is a cry to God for justice, for him to vindicate his oppressed people.

6 Witherington comments, "Sometimes there has been an overreaction to this particular section of Revelation, and in some quarters judgment has been banished as a topic of Christian discourse or belief. In protest against the latter H. Richard Neibuhr once wrote that the essential message of liberal protestantism was, 'A God without wrath brought me without sin into a kingdom without judgment through the ministrations of a Christ without the cross.'... It needs to be recognised that a God without judgment is also a God who does not care about justice, which is to say a God who is neither holy nor righteous nor fair. According to John and other NT writers, God's love is a holy love, and therefore it could not neglect the issues of justice and fairness. If one is a persecuted believer, one could easily say that for God to neglect justice or judgment would not be a loving thing to do. God must in the end vindicate not only his own people but the divine nature itself, or people will never recognise the full character of God, nor will God's plan for the rectification of a lost world come to fruition."

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 WEEK 21 The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 I. The Feast of Firstfruits signifies the resurrected Christ as the firstfruits for our enjoyment as

Διαβάστε περισσότερα

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son 70 The Spirit Agreement that Jesus is the Son is the Revelation of the Spirit Apostles which is the Apostolic witness Children Thus those who believe the Apostles are children Witnesses to The Love of

Διαβάστε περισσότερα

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * *

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * In the first chapter, we practiced the skill of reading Greek words. Now we want to try to understand some parts of what we read. There are a

Διαβάστε περισσότερα

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

Revelation 10. LGNT - September 7, 2019 Page 1. Book Chapter Verse. Word # Rev. Interlinear English. Numeric value. # of words. # of letters.

Revelation 10. LGNT - September 7, 2019 Page 1. Book Chapter Verse. Word # Rev. Interlinear English. Numeric value. # of words. # of letters. Book Chapter Verse Interlinear English Word # Rev Greek # of letters # of words Numeric value 271001 and 03876 ΚΑΙ 3 31 271001 I saw 03877 ΕΙΔΟΝ 5 139 271001 another 03878 ΑΛΛΟΝ 5 181 271001 [mighty] angel

Διαβάστε περισσότερα

Notes on the Greek New Testament Week 242 Revelation 9:20-11:14

Notes on the Greek New Testament Week 242 Revelation 9:20-11:14 Notes on the Greek New Testament Week 242 Revelation 9:20-11:14 Day 1206: Revelation 9:20-21 Verse 20 Καὶ οἱ λοιποὶ τῶν ἀνθρωπων, οἳ οὐκ ἀπεκτάνθησαν ἐν ταῖς πληγαῖς ταύταις, οὐδὲ µετενόησαν ἐκ τῶν ἔργων

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live. Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ Ενότητα 1β: Principles of PS Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης

Διαβάστε περισσότερα

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015 Adjectives Describing the Qualities of Things A lesson for the Paideia web-app Ian W. Scott, 2015 Getting Started with Adjectives It's hard to say much using only nouns and pronouns Simon is a father.

Διαβάστε περισσότερα

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013 LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English.

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English. Book Chapter Verse Interlinear English Word # 1 John Greek # of letters # of words Numeric value 230501 everyone 01709 ΠΑΣ 3 281 230501 01710 Ο 1 70 230501 believing 01711 ΠΙΣΤΕΥΩΝ 8 1845 230501 that 01712

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

I haven t fully accepted the idea of growing older

I haven t fully accepted the idea of growing older I haven t fully accepted the idea of growing older 1 Peter Authorship Questions Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας 1 Peter Authorship

Διαβάστε περισσότερα

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS ΟΜΗΡΟΥ ΙΛΙΑΔΑ ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS www.scooltime.gr [- 2 -] The Project Gutenberg EBook of Iliad, by Homer This ebook is for the use of anyone anywhere at no cost and with almost no restrictions

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple A/ Ονόματα και ένα παράδειγμα 1 Present Simple 7 Present PERFECT Simple 2 Present Continuous 8 Present PERFECT Continuous 3 Past Simple (+ used to) 9 Past PERFECT Simple she eats she is eating she ate

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 4: English a Language of Economy Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΝΟΜΙΚΗ ΣΧΟΛΗ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΤΟΜΕΑΣ ΙΣΤΟΡΙΑΣ ΦΙΛΟΣΟΦΙΑΣ ΚΑΙ ΚΟΙΝΩΝΙΟΛΟΓΙΑΣ ΤΟΥ ΔΙΚΑΙΟΥ Διπλωματική εργασία στο μάθημα «ΚΟΙΝΩΝΙΟΛΟΓΙΑ ΤΟΥ ΔΙΚΑΙΟΥ»

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Συστήματα Διαχείρισης Βάσεων Δεδομένων

Συστήματα Διαχείρισης Βάσεων Δεδομένων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Συστήματα Διαχείρισης Βάσεων Δεδομένων Φροντιστήριο 9: Transactions - part 1 Δημήτρης Πλεξουσάκης Τμήμα Επιστήμης Υπολογιστών Tutorial on Undo, Redo and Undo/Redo

Διαβάστε περισσότερα

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 Conditional Relative Clauses relative clauses referring to an indefinite person or thing (whoever, whatever, anyone,

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

Every set of first-order formulas is equivalent to an independent set

Every set of first-order formulas is equivalent to an independent set Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

Διαβάστε περισσότερα

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014 LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV 4 February 2014 Somewhere κάπου (kapoo) Nowhere πουθενά (poothena) Elsewhere αλλού (aloo) Drawer το συρτάρι (sirtari) Page η σελίδα (selida) News τα νέα (nea)

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η προβολή επιστημονικών θεμάτων από τα ελληνικά ΜΜΕ : Η κάλυψή τους στον ελληνικό ημερήσιο τύπο Σαραλιώτου

Διαβάστε περισσότερα

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

Διαβάστε περισσότερα

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς We review side by side a model of stems ending in ι: πόλις, πόλεως, ἡ = city-state and a masculine model of stems ending in υ: πρέσβυς,

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case A Target for the Action A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case So far we've seen three noun cases Nominative Genitive Vocative We need one more case

Διαβάστε περισσότερα

Living and Nonliving Created by: Maria Okraska

Living and Nonliving Created by: Maria Okraska Living and Nonliving Created by: Maria Okraska http://enchantingclassroom.blogspot.com Living Living things grow, change, and reproduce. They need air, water, food, and a place to live in order to survive.

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 1: Elements of Syntactic Structure Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 9: Inversion Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons εκτός

Διαβάστε περισσότερα

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015 Present Participles Verbal Adjectives with Present Aspect A lesson for the Paideia web-app Ian W. Scott, 2015 Participles with Present Aspect Participle = a verbal adjective Allows a whole clause to tell

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Math221: HW# 1 solutions

Math221: HW# 1 solutions Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin

Διαβάστε περισσότερα

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951)

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) 1 Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) Αναγνώσματα από το βιβλίο Η Απόλαυση της Μουσικής (Machlis, Forney), για τους μαθητές που θα μελετήσουν το έργο: «Ο Σαίνμπεργκ

Διαβάστε περισσότερα

Croy Lessons Participles

Croy Lessons Participles A Croy Lessons 18-20 Participles Aorist (Act/Mid/Dep Dep) ) Participles Adjectival and Substantive Ω STEM + TENSE + THEME + PTCP CODE + ENDING PARTICIPLE CODES CASE ENDINGS ντ - masc and neut active (and

Διαβάστε περισσότερα

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect)

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) 15 Ρηματική άποψη (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) imperfective perfective Verb forms in Modern Greek are based either on the imperfective or the perfective

Διαβάστε περισσότερα

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 Name: Surname: Date: Class: 1. Write these words in the correct order. /Γράψε αυτέσ τισ λέξεισ ςτη ςωςτή ςειρά. 1) playing / his / not /

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *6301456813* GREEK 0543/03 Paper 3 Speaking Role Play Card One 1 March 30

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο

Διαβάστε περισσότερα

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017 ΦωτίστεΤονΚόσμο ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ 2017 24 Νοεμβρίου -- 25 Δεκεμβρίου 2017 ΘΕΜΑ «Καθώς ακολουθούμε το παράδειγμα του Σωτήρος και ζούμε όπως ζούσε Εκείνος και όπως δίδασκε, αυτό το φως θα καίει μέσα

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας ΤΕΙ ΚΑΒΑΛΑΣ ΠΑΡΑΡΤΗΜΑ ΔΡΑΜΑΣ ΤΜΗΜΑ ΑΡΧΙΤΕΚΤΟΝΙΚΗΤΟΠΙΟΥ Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Διαβάστε περισσότερα

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook

Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook Βήμα 1: Step 1: Βρείτε το βιβλίο που θα θέλατε να αγοράσετε και πατήστε Add to Cart, για να το προσθέσετε στο καλάθι σας. Αυτόματα θα

Διαβάστε περισσότερα

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions 2007 Classical Greek Intermediate 2 Translation Finalised Marking Instructions Scottish Qualifications Authority 2007 The information in this publication may be reproduced to support SQA qualifications

Διαβάστε περισσότερα

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ ΕΛΛΗΝΙΔΕΣ ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΚΔΟΣΗ ΤΗΣ ΣΟΡΟΠΤΙΜΙΣΤΙΚΗΣ ΕΝΩΣΗΣ ΕΛΛΑΔΟΣ - ΤΕΥΧΟΣ Νο 110 - Δ ΤΡΙΜΗΝΟ 2014 Το πρώτο βραβείο κέρδισε η Ελλάδα για την φωτογραφία Blue + Yellow = Green στον διαγωνισμό 2014 του

Διαβάστε περισσότερα

Door Hinge replacement (Rear Left Door)

Door Hinge replacement (Rear Left Door) Door Hinge replacement (Rear Left Door) We will continue the previous article by replacing the hinges of the rear left hand side door. I will use again the same procedure and means I employed during the

Διαβάστε περισσότερα

LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF : 101/011/9-BEG. 14 January 2013

LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF : 101/011/9-BEG. 14 January 2013 LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF : 101/011/9-BEG 14 January 2013 Up πάνω Down κάτω In μέσα Out/outside έξω (exo) In front μπροστά (brosta) Behind πίσω (piso) Put! Βάλε! (vale) From *** από Few λίγα (liga) Many

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Δρ. Παναγιώτης Πεντάρης - University of Greenwich - Association for the Study of Death and Society (ASDS) Περιεχόµενα Εννοιολογικές

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case.

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case. A Summer Greek Lesson 3 Ω Parts of Speech NOUN- person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE- describes a noun (includes in/definite articles) PRONOUN-word

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your GP practice in Islington Σε όλα τα Ιατρεία Οικογενειακού

Διαβάστε περισσότερα

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014 LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG 4 March 2014 Family η οικογένεια a/one(fem.) μία a/one(masc.) ένας father ο πατέρας mother η μητέρα man/male/husband ο άντρας letter το γράμμα brother ο

Διαβάστε περισσότερα

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

Διαβάστε περισσότερα

Ephesians. Wayne Stewart

Ephesians. Wayne Stewart Ephesians Wayne Stewart 1 Shadows of a ministry independent of Jerusalem and the 12 Taken from CH Welch 2 Acts 28:25 25 (AV) And when they agreed not among themselves, they departed, after that Paul had

Διαβάστε περισσότερα

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

Διαβάστε περισσότερα

Conditional Sentences

Conditional Sentences Conditional Sentences It all depends! A lesson for the Paideia web-app Ian W. Scott, 2015 What is a conditional sentence? An If then sentence States that something will happen if some condition is fulfilled

Διαβάστε περισσότερα

Relationships & Reconciliation. Engaging the World Series The Lord s Prayer

Relationships & Reconciliation. Engaging the World Series The Lord s Prayer Relationships & Reconciliation Engaging the World Series The Lord s Prayer ZGM Vision Every Life for Jesus 11 Jan 2015 ZGM Mission We are a Spirit-led Community That Exalts Christ, By Equipping Disciples

Διαβάστε περισσότερα

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

Galatia SIL Keyboard Information

Galatia SIL Keyboard Information Galatia SIL Keyboard Information Keyboard ssignments The main purpose of the keyboards is to provide a wide range of keying options, so many characters can be entered in multiple ways. If you are typing

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV. 4 March 2014

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV. 4 March 2014 LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV 4 March 2014 Immediately/At once I arrive/reach αμέσως φτάνω I arrive I start/begin Present : φτάνω ξεκινάω (ξεκινώ) S.Past : έφτασα ξεκίνησα S.Future :

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

Περί γκρίζων ζωνών και άλλων καινών δαιμονίων: Η οριοθέτηση στον Κόλπο της Βεγγάλης Μαρία Γαβουνέλη

Περί γκρίζων ζωνών και άλλων καινών δαιμονίων: Η οριοθέτηση στον Κόλπο της Βεγγάλης Μαρία Γαβουνέλη Περί γκρίζων ζωνών και άλλων καινών δαιμονίων: Η οριοθέτηση στον Κόλπο της Βεγγάλης Μαρία Γαβουνέλη Επίκουρη καθηγήτρια Νομική Σχολή, Πανεπιστήμιο Αθηνών Μια συνολική ρύθμιση: q Bangladesh/Myanmar: ITLOS

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ Διπλωµατική Εργασία Της Φοιτήτριας του Τµήµατος Ηλεκτρολόγων

Διαβάστε περισσότερα

LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014

LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014 LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28 2 December 2014 Place/Seat Right (noun) I am right I am not right It matters It does not matter The same (singular) The same (Plural) Η θέση Το δίκιο Έχω

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής Ενότητα 12b: The Little Prince Τμήμα Εφαρμοσμένης Πληροφορικής Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται

Διαβάστε περισσότερα

If You Build It, They May Come Parable of the Tower Builder

If You Build It, They May Come Parable of the Tower Builder If You Build It, They May Come Parable of the Mark Vitalis Hoffman www.crossmarks.com Τίς γὰρ ἐξ ὑµῶν θέλων πύργον οἰκοδοµῆσαι οὐχὶ πρῶτον καθίσας ψηφίζει τὴν δαπάνην, εἰ ἔχει εἰς ἀπαρτισµόν; doesn't first

Διαβάστε περισσότερα

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014 LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ

Διαβάστε περισσότερα