Notes on the Greek New Testament Week 106 Romans 15:22-16:27

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Week 106 Romans 15:22-16:27"

Transcript

1 Notes on the Greek New Testament Week 106 Romans 15:22-16:27 Day 526: Romans 15:22-29 Verse 22 ιὸ καὶ ἐνεκοπτόµην τὰ πολλὰ τοῦ ἐλθεῖν πρὸς ὑµᾶς διο therefore, for this reason It is because Paul has been 'fully proclaiming' the gospel all the way from Jerusalem to Illiricum (vv.18-19), that he has been hindered thus far from coming to Rome. ἐνεκοπτόµην Verb, imperf pass indic, 1 s ἐγκοπτω prevent, hinder, detain ἐλθεῖν Verb, aor act infin ἐρχοµαι Cf. 1:23. Verse 23 νυνὶ δὲ µηκέτι τόπον ἔχων ἐν τοῖς κλίµασι τούτοις, ἐπιποθίαν δὲ ἔχων τοῦ ἐλθεῖν πρὸς ὑµᾶς ἀπὸ πολλῶν ἐτῶν, νυνι now Since his work in other regions is finished he is now able to come to them. µηκετι no longer τοπος, ου m place κλιµα, τος n region, district "His aims for the eastern Mediterranean have been fulfilled; he no longer has any room for new work. This sounds extraordinary, given the tiny numbers of Christians we must envisage compared to the population in general; but Paul thinks of himself as a churchplanter, and once he has established churches in the major centres of population and culture he has to rely on them to do for themselves the work of continued evangelism in their neighbourhoods. So, with Ephesus, Philippi, Thessalonica, Athens possibly, and Corinth established not without difficulties and anxieties! he quite genuinely concludes that it is time to move on." Wright. ἐπιποθια, ας f longing, desire ἐτος, ους n year Verse 24 ὡς ἂν πορεύωµαι εἰς τὴν Σπανίαν ἐλπίζω γὰρ διαπορευόµενος θεάσασθαι ὑµᾶς καὶ ὑφ ὑµῶν προπεµφθῆναι ἐκεῖ ἐὰν ὑµῶν πρῶτον ἀπὸ µέρους ἐµπλησθω πορευοµαι go, proceed, travel ὡς ἀν πορευωµαι So that I might go... "Parts of Spain had been occupied by the Romans since about 200 BC. But the Romans had fully organised the area as a province only in Paul's lifetime. There may have been a significant Jewish community there, although the matter is debated. Obviously Paul thinks it a good place to embark in a fresh churchplanting ministry." Moo. ἐλπιζω hope, expect διαπορευοµαι go through, travel through θεαοµαι see, look at, observe προπεµφθῆναι Verb, aor pass infin προπεµπω send on one's way, help on one's way Used regularly in the NT in the context of missionary support (Acts 15:3; 20:38; 21:5; 1 Cor 16:6,11; 2 Cor 1:16; Titus 3:13; 3 John 6). ἐκει there, in that place, to that place πρωτον adv. first, in the first place µερος, ους n part, piece, in part, partly ἐµπλησθω Verb, aor pass subj, 1 s ἐµπι(µ)πληµι and ἐµπιπλαω fill, enjoy ὑµων πρωτον ἀπο µερους ἐµπλησθω 'I have first enjoyed your [company] for a while' Verse 25 νυνὶ δὲ πορεύοµαι εἰς Ἰερουσαλὴµ διακονῶν τοῖς ἁγίοις. διακονεω serve, care for Words from this root refer to the collection also in 2 Cor 8:4,19,20; 9:1,12,13. Verse 26 εὐδόκησαν γὰρ Μακεδονία καὶ Ἀχαΐα κοινωνίαν τινὰ ποιήσασθαι εἰς τοὺς πτωχοὺς τῶν ἁγίων τῶν ἐν Ἰερουσαλήµ. εὐδοκεω be pleased, take pleasure in κοινωνια, ας f fellowship, sharing in, contribution ποιήσασθαι Verb, aor midd infin ποιεω πτωχος, η, ον poor Cf. 1 Cor 16:1-4 and 2 Cor 8 and 9. Verse 27 εὐδόκησαν γάρ, καὶ ὀφειλέται εἰσὶν αὐτῶν εἰ γὰρ τοῖς πνευµατικοῖς αὐτῶν ἐκοινωνησαν τὰ ἔθνη, ὀφείλουσιν καὶ ἐν τοῖς σαρκικοῖς λειτουργῆσαι αὐτοῖς. ὀφειλετης, ου m debtor, one indebted πνευµατικος, η, ον spiritual, pertaining to the spirit Week 106: Page 1

2 κοινωνεω share, take part ἔθνη Noun, nom & acc pl ἐθνος, ους n nation, people; τα ἐ. Gentiles ὀφειλω owe, ought, be bound or obligated σαρκικος, η, ον belonging to this world λειτουργεω serve, worship K. F. Nickle (The Collection: A Study in Paul's Strategy) views this collection which Paul, along with representatives of the Gentile churches, was bringing to Jerusalem, against the background of Romans He describes it as, "An eschatological pilgrimage of Gentile Christians to Jerusalem by which Jews were to be confronted with the undeniable reality of the divine gift of saving grace to the Gentiles and therefore they would be moved to seek Christ." Wright does not favour this interpretation commenting rather, "For Gentiles to give money to Jewish Christians was a sign that the Gentiles regarded them as members of the same family; for Jewish Christians to accept it would be a sign that they in turn accepted the Gentiles as part of their family." Verse 28 τοῦτο οὖν ἐπιτελέσας, καὶ σφραγισάµενος αὐτοῖς τὸν καρπὸν τοῦτον, ἀπελεύσοµαι δι ὑµῶν εἰς Σπανίαν ἐπιτελεω complete, accomplish σφραγιζω seal, secure with a seal καρπος, ου m fruit, harvest i.e. 'When I have safely delivered to them the sum that has been raised' "The idea of 'sealing' (σφραγιζω, affix a seal) often connotes an official affirmation of authenticity (see, e.g. Est 8:8,10; John 3:33; cf. also Paul's references to believers being sealed by the Holy Spirit in 2 Cor 1:22; Eph 1:13; 4:30). Paul, as the apostle to the Gentiles, must accompany the gift to Jerusalem in order to authenticate its purpose as a healing gesture." Moo. ἀπελεύσοµαι Verb, fut midd dep indic, 1 s ἀπερχοµαι Verse 29 οἶδα δὲ ὅτι ἐρχόµενος πρὸς ὑµᾶς ἐν πληρωµατι εὐλογίας Χριστοῦ ἐλεύσοµαι. οἰδα know πληρωµα, τος n fulness, completeness, fulfilment εὐλογια, ας f blessing, praise Paul probably meant that both he and his hosts would share this fulness of blessing, cf. 1: Some MSS, followed by the TR, read του εὐαγγελιου του Χριστοῦ rather than simply Χριστοῦ. The shorter reading has good, early support. ἐλεύσοµαι Verb, fut midd dep indic, 1 s ἐρχοµαι Day 527: Romans 15:30-16:2 Verse 30 Παρακαλῶ δὲ ὑµᾶς[, ἀδελφοί,] διὰ τοῦ κυρίου ἡµῶν Ἰησοῦ Χριστοῦ καὶ διὰ τῆς ἀγάπης τοῦ πνεύµατος, συναγωνίσασθαί µοι ἐν ταῖς προσευχαῖς ὑπὲρ ἐµοῦ πρὸς τὸν θεόν, παρακαλεω exhort, encourage, urge 'love of the Spirit' Barrett and Moo understand this to be the love of which the Holy Spirit is the author while Murray thinks it to be a reference to the love which the Holy Spirit has for believers. συναγωνίσασθαί Verb, aor midd dep infin συναγωνιζοµαι help, join with The verb used suggests intensity 'wrestle with me in prayer.' Verse 31 ἵνα ῥυσθῶ ἀπὸ τῶν ἀπειθούντων ἐν τῇ Ἰουδαίᾳ καὶ ἡ διακονία µου ἡ εἰς Ἰερουσαλὴµ εὐπρόσδεκτος τοῖς ἁγίοις γένηται, ῥυσθῶ Verb, aor pass subj, 1 s ῥυοµαι save, rescue ἀπειθεω disobey, be an unbeliever διακονια, ας f ministry, service εὐπροσδεκτος, ον acceptable γένηται Verb, aor subj, 3 s γινοµαι Verse 32 ἵνα ἐν χαρᾷ ἐλθων πρὸς ὑµᾶς διὰ θελήµατος θεοῦ συναναπαύσωµαι ὑµῖν. θεληµα, ατος n will, wish, desire συναναπαύσωµαι Verb, aor midd dep subj, 1 s συναναπαυοµαι have a time of rest with, enjoy a refreshing visit with This verse exhibits a number of variant readings. Some MSS read θεληµατος Ἰησου Χριστου rather than θεληµατος θεου; some omit συναναπαύσωµαι ὑµῖν. There are then various combinations of these variants. Week 106: Page 2

3 συναναπαύσωµαι ὑµῖν almost as if, after the troubles he foresees in Jerusalem, his time ar Rome will be a time of rest and recouperation a time of holiday! Verse 33 ὁ δὲ θεὸς τῆς εἰρήνης µετὰ πάντων ὑµῶν ἀµήν. εἰρηνη, ης f peace Chapter 15 Postscript "One of the most important lessons of Romans 15 might be put thus: God allowed Paul to dream of Spain in order that he might write Romans. No matter that Paul probably never reached Spain. What mattered was that he wrote this letter, which has been far more powerful and influential than any missionary visit, even by Paul himself, could ever have been. Perhaps... half of our great plans, the dreams we dream for our churches and for our world, and even for ourselves, are dreams God allows us to dream in order that, on the way there, we may accomplish, almost without realising it, the crucial thing God intends us to do." Wright. Chapter 16 The number of greetings in this closing chapter is extraordinary. Paul asks the Romans to greet 26 individuals, two families and three house churches. All the more extraordinary since Paul had never visited Rome. Some scholars suggest that Romans 16 was never sent to Rome but was part of another letter, perhaps one sent to Ephesus (so T. W. Manson). However, no significant MSS of Romans omit this chapter. Moo comments, "Many of these Roman Christians (like Priscilla and Aquila, v.3) had spent years in exile away from Rome, where they had opportunity to get to know Paul. Perhaps, indeed, the relatively small number of Christians Paul knows in Rome enables him to send greetings to virtually everyone he is aware of in the city." Wright comments, "In five cases, Paul mentions, along with a name or pair of names, the Christians within the household (16:5a, 10-11, 14-15). He may or may not have wanted to mention all the individual Christians he knew in the city, but he was certainly keen to mention all the household churches he knew: we can only guess which ones might have been 'weak' and which 'strong,' but we can be reasonably sure he was careful to greet them all with equal enthusiasm. All sorts of things can be read into accidental ommisions. Paul did not want to arrive at Rome and find that he had caused fresh divisions by appearing to favour one group over another." Verse 1 Συνίστηµι δὲ ὑµῖν Φοίβην τὴν ἀδελφὴν ἡµῶν, οὖσαν [καὶ] διάκονον τῆς ἐκκλησίας τῆς ἐν Κεγχρεαῖς, συνιστηµι recommend, commend ἀδελφη, ης f sister, female believer Phoebe may have been the bearer of this letter. Probably a businesswoman who is able to travel independently. διακονος, ου m & f servant, helper, deacon Was Phoebe a deacon in the formal sense of this term? Moo thinks that the phrase διάκονον τῆς ἐκκλησίας τῆς ἐν Κεγχρεαῖς "makes it more likely that Phoebe holds an official position in the church there. Phoebe is probably a 'deacon,' serving the church by ministering to the financial and material needs of the believers (see esp. 1 Tim 3:8-12; cf also Phil 1:1)." So also Wright who says, "Attempts to make διάκονος something else [other than a deacon in the church] fail." ἐκκλησια, ας f congregation, church Cenchrea was one of the ports of Corinth. Verse 2 ἵνα αὐτὴν προσδέξησθε ἐν κυρίῳ ἀξίως τῶν ἁγίων, καὶ παραστῆτε αὐτῇ ἐν ᾧ ἂν ὑµῶν χρῄζῃ πράγµατι, καὶ γὰρ αὐτὴ προστάτις πολλῶν ἐγενήθη καὶ ἐµοῦ αὐτοῦ. προσδέξησθε Verb, aor midd dep subj, 2 pl προσδεχοµαι receive, welcome, accept ἀξιως adv (from ἀξιος) worthily παραστῆτε Verb, aor act subj, 2 pl παριστηµι and παριστανω provide χρῃζω need, have need of πραγµα, τος n matter, thing προστατις, ιδος f helper, good friend Week 106: Page 3

4 Moo suggests that the word may have the meaning here it often bears in secular Greek, namely 'patron, benefactor.' "Phoebe was probably a wealthy businesswoman, who used her wealth to support the church and its missionaries (like Paul). Her ministry in the church and beneficence to the church's workers make her worthy of a Christian greeting and any assistance the Roman church can give her." ἐγενήθη Verb, aor indic, 3 s γινοµαι Day 528: Romans 16:3-16 Verse 3 Ἀσπάσασθε Πρίσκαν καὶ Ἀκύλαν τοὺς συνεργούς µου ἐν Χριστῷ Ἰησοῦ, ἀσπαζοµαι greet συνεργος, ου m fellow-worker Cf. Acts 18:2,18-19,26; 1 Cor 16:19; 2 Tim 4:19. Verse 4 οἵτινες ὑπὲρ τῆς ψυχῆς µου τὸν ἑαυτῶν τράχηλον ὑπέθηκαν, οἷς οὐκ ἐγω µόνος εὐχαριστῶ ἀλλὰ καὶ πᾶσαι αἱ ἐκκλησίαι τῶν ἐθνῶν, οἵτινες Pronoun, m nom pl ὁστις, ἡτις, ὁ τι who, which ψυχη, ης f self, life, 'soul' ἑαυτος, ἑαυτη, ἑαυτον him/her/itself τραχηλος, ου m neck ὑπέθηκαν Verb, aor act indic, 3 pl ὑποτιθηµι risk τὸν ἑαυτῶν τράχηλον ὑπέθηκαν 'risked their necks.' We have no other information on this incident. It may have been at the time of the riot in Ephesus (Acts 19). µονος, η, ον only, alone εὐχαριστεω thank, give thanks ἐθνος, ους n nation, people; τα ἐ. Gentiles Verse 5 καὶ τὴν κατ οἶκον αὐτῶν ἐκκλησίαν. ἀσπάσασθε Ἐπαίνετον τὸν ἀγαπητόν µου, ὅς ἐστιν ἀπαρχὴ τῆς Ἀσίας εἰς Χριστόν. οἰκος, ου m house, home For churches which met in homes see also 1 Cor 16:19; Col 4:15; Philem 2. Aquila and Priscilla must have been fairly wealthy. ἀγαπητος, η, ον beloved ἀπαρχη, ης f firstfruit, first portion (set apart to God) Cf. 1 Cor 16:15 where Stephanus has the same honour in Achaea. Verse 6 ἀσπάσασθε Μαρίαν, ἥτις πολλὰ ἐκοπίασεν εἰς ὑµᾶς. κοπιαω work, work hard, labour Verse 7 ἀσπάσασθε Ἀνδρόνικον καὶ Ἰουνιᾶν τοὺς συγγενεῖς µου καὶ συναιχµαλωτους µου, οἵτινές εἰσιν ἐπίσηµοι ἐν τοῖς ἀποστόλοις, οἳ καὶ πρὸ ἐµοῦ γέγοναν ἐν Χριστῷ. Ἰουνιᾶν NIV (along with RSV, NASB, TEV and NJB) assumes that this is a contraction of the masculine name Junianus. But the Greek form could reflect the female name Junia (AV, NRSV, REB). The latter seems more likely since it is a common Greek name whereas the contracted form of Ἰουνιανος is apparently unknown. They were probably husband and wife. (Some MSS read Ἰουλιαν). This is the subject of much controversy, particularly since it seems that they may be termed 'apostles.' συγγενης, ους m kinsman, fellowcountryman συναιχµαλωτος, ου m fellow-prisoner ἐπισηµος, ον well known, outstanding Either: i) These were apostles (cf. 2 Cor 8:23; Phil 2:25) and well known as such; or ii) They were well known to the apostles. Moo thinks the former more likely but, along with Cranfield and Dunn, thinks that the sense is 'commissioned missionary.' Wright also thinks the former is meant, though he draws attention to Paul's use of the term 'apostle' to mean one whi is 'a witness to the resurrection' (cf. 1 Cor 9:1). γέγοναν Verb, perf act indic, 3 pl γινοµαι Verse 8 ἀσπάσασθε Ἀµπλιᾶτον τὸν ἀγαπητόν µου ἐν κυρίῳ. Verse 9 ἀσπάσασθε Οὐρβανὸν τὸν συνεργὸν ἡµῶν ἐν Χριστῷ καὶ Στάχυν τὸν ἀγαπητόν µου. συνεργος, ου v.3 Week 106: Page 4

5 Verse 10 ἀσπάσασθε Ἀπελλῆν τὸν δόκιµον ἐν Χριστῷ. ἀσπάσασθε τοὺς ἐκ τῶν Ἀριστοβούλου. δοκιµος, ον approved, genuine, valued τοὺς ἐκ τῶν Ἀριστοβούλου 'those who belong to the household of Aristobulus.' "It is quite likely that Aristobulus was the grandson of Herod the Great and brother of Agrippa I. He himself was not greeted by Paul, possibly because he himself was not a Christian, but members of his family were sent warm greetings as fellow-believers." Derek Tidball, An Introduction to the Sociology of the New Testament. "The reference is probably mainly to the slaves who work for Aristobulus." Moo. Verse 11 ἀσπάσασθε Ἡρῳδίωνα τὸν συγγενῆ µου. ἀσπάσασθε τοὺς ἐκ τῶν Ναρκίσσου τοὺς ὄντας ἐν κυρίῳ. "Probably a freed slave who took the name of the Herodian family he served." Moo. συγγενῆ Noun, acc s συγγενης, ους v.7 "Similarly it was the family of Narcissus, rather than Narcissus himself, who were greeted. It is usually thought that this Narcissus was the famous and very wealthy freedman of the emperor Claudius whom Juvenal mentions and who exercised tremendous influence over Claudius. The fact that he personally was not greeted either implies that he was already dead or that he himself had not become a Christian." Tidball. Wright comments, "If this is the same man, as most assume, Christians within his household after his death would have occupied a challenging and dangerous position." Verse 12 ἀσπάσασθε Τρύφαιναν καὶ Τρυφῶσαν τὰς κοπιωσας ἐν κυρίῳ. ἀσπάσασθε Περσίδα τὴν ἀγαπητήν, ἥτις πολλὰ ἐκοπίασεν ἐν κυρίῳ. κοπιαω v.6 Verse 13 ἀσπάσασθε Ῥοῦφον τὸν ἐκλεκτὸν ἐν κυρίῳ καὶ τὴν µητέρα αὐτοῦ καὶ ἐµοῦ. ἐκλεκτος, η, ον chosen Perhaps the same person as is mentioned in Mk 15:21 as the son of Simon, the man forced to carry Jesus' cross. Wright comments, "One of the tantalising things about this chapter is that, like watching a sequence of film clips going by too fast to take in, we catch tiny glimpses into the world of early Christianity that could be very revealing if only we could freeze the frame and ask one or two leading questions. There was clearly quite a subculture growing up, but we know very nearly nothing about it." Verse 14 ἀσπάσασθε Ἀσύγκριτον, Φλέγοντα, Ἑρµῆν, Πατροβᾶν, Ἑρµᾶν, καὶ τοὺς σὺν αὐτοῖς ἀδελφούς. The last is probably a reference to Christians who met in Hermas's house for worship. Verse 15 ἀσπάσασθε Φιλόλογον καὶ Ἰουλίαν, Νηρέα καὶ τὴν ἀδελφὴν αὐτοῦ, καὶ Ολυµπᾶν, καὶ τοὺς σὺν αὐτοῖς πάντας ἁγίους. ἀδελφη, ης f sister, female believer "Some have speculated that Philologus and Julia were husband and wife, with Nereus and his sister being their children. They, with Olympas, play host to another house church." Wright. Verse 16 Ἀσπάσασθε ἀλλήλους ἐν φιλήµατι ἁγίῳ. Ἀσπάζονται ὑµᾶς αἱ ἐκκλησίαι πᾶσαι τοῦ Χριστοῦ. ἀλληλων, οις, ους reciprocal pronoun one another φιληµα, τος n kiss Cf. 1 Cor 16:20; 2 Cor 13:12; 1 Thess 5:26; 1 Peter 5:14. Conclusions from this list of greetings Moo draws the following conclusions: "Social composition of the church... The historian Peter Lampe has done a thorough study of the names in Romans 16. He concludes that most of the people whom Paul mentions are Gentiles or freedmen or are descendants of slaves and freedmen (freedman is the term given the class of freed slaves in the Roman empire). Note too that Paul specifically mentions at least two groups of slaves: the household (servants) of Aristobulus (v.10) and those of Narcissus (v.11)... What little evidence we have suggests that most of the early Christians came from the 'lower' classes." Week 106: Page 5

6 "Organisation of the early church. What 16:1-16 reveals about the organisation of the church is that it was apparently loose. Paul refers to at least three, and perhaps five, house churches (vv. 5,14,15 are clear; the 'households' mentioned in vv.10 and 11 may also represent house churches). The Christian community reflects the loose organisation of the Jewish community, which was apparently also broken up into many independent synagogues. It was probably the case, for instance, that certain house churches were composed of believers 'weak in faith' and others of believers 'strong in faith' (see comments on 14:1-15:13). Paul's plea for acceptance of one another, then, is seeking reconciliation among various 'churches' in Rome." "Women in the early church. Of the twentyseven Christians Paul greets or commends in verses 1-15, ten (more than one-third) are women. Six of them (Phoebe [vv. 1-2], Priscilla [v.3], Junias [v.7], Tryphena [v.12], Tryphosa [v.12], and Persis [v.12]) are commended for their labour 'in the Lord.' Junia is a 'commissioned missionary (ἀποστολος; see comments on v.7), and Phoebe is a benefactor and deacon of the church. What conclusions can we draw...? (1) women made up a significant part of the early Christian church...; (2) women were given the same access to God that men enjoyed (e.g., Gal 3:28; 1 Peter 3:7); and (3) women engaged in significant ministry." And Wright concludes, "What we... have, then, is a small, vulnerable church, needing to know and trust one another across various boundaries; a church many of whose members were not native to Rome, living most likely in immigrant communities within particular areas; a church in which men and women alike took leadership roles; a church where families and households formed the basis of worshiping communities. There is something both attractive and frightening about this picture: enormous potential, huge risks, a community both lively and vulnerable. This is the community that will now be the first to hear one of the greatest letters in the history of the world." Day 529: Romans 16:17-23 Verses "Paul does not elsewhere launch into a warning about false teachers in the conclusion of a letter. But he does issue exhortations and warnings that may presume their presence (e.g. 1 Cor 16:13-14; 2 Cor 13:11; Col 4:17). It is a greater mystery why he waits until the very end of Romans to issue such a warning. Possibly he waits until now because the false teachers have not yet arrived on the scene, or because he only hears about the threat as he is finishing the letter." Moo. Verse 17 Παρακαλῶ δὲ ὑµᾶς, ἀδελφοί, σκοπεῖν τοὺς τὰς διχοστασίας καὶ τὰ σκάνδαλα παρὰ τὴν διδαχὴν ἣν ὑµεῖς ἐµάθετε ποιοῦντας, καὶ ἐκκλίνετε ἀπ αὐτῶν παρακαλεω exhort, encourage, urge σκοπεω pay attention to, watch out (for) διχοστασια, ας f division, dissension A word found only here and in Gal 5:20. σκανδαλον, ου n that which causes sin/ offence, obstacle παρα preposition with acc beside, rather than, contrary to διδαχη, ης f teaching, what is taught ἐµάθετε Verb, aor act indic, 2 pl µανθανω learn, find out ἐκκλίνετε Verb, pres act imperat, 2 pl ἐκκλινω turn away, turn aside Verse 18 οἱ γὰρ τοιοῦτοι τῷ κυρίῳ ἡµῶν Χριστῷ οὐ δουλεύουσιν ἀλλὰ τῇ ἑαυτῶν κοιλίᾳ, καὶ διὰ τῆς χρηστολογίας καὶ εὐλογίας ἐξαπατῶσιν τὰς καρδίας τῶν ἀκάκων. τοιουτος, αυτη, ουτον such, of such kind ἑαυτος v.4 κοιλια, ας f stomach Barrett believes the reference here is not to gluttony but to a preoccupation with food laws. Murray thinks it simply means preoccupation with self-service, as does Moo who thinks the term "a synecdoche for sensual appetites generally. The false teachers are interested in their own pleasure and ease, not in helping people to know God." So Wright who thinks it refers to "their appetites in general." Cf. Phil 3: χρηστολογια, ας f smooth talk, plausible talk εὐλογια, ας f blessing, praise ἐξαπαταω deceive, lead astray ἀκακος, ον innocent, unsuspecting Week 106: Page 6

7 Verse 19 ἡ γὰρ ὑµῶν ὑπακοὴ εἰς πάντας ἀφίκετο ἐφ ὑµῖν οὖν χαίρω, θέλω δὲ ὑµᾶς σοφοὺς εἶναι εἰς τὸ ἀγαθόν, ἀκεραίους δὲ εἰς τὸ κακόν. ὑπακοη, ης f obedience ἀφίκετο Verb, aor midd dep indic, 3 s ἀφικνεοµαι reach, be known to χαιρω rejoice, be glad θελω wish, will σοφος, η, ον wise, experienced εἶναι Verb, pres infin εἰµι ἀγαθος, η, ον good, useful, fitting ἀκεραιος, ον innocent, guiltless κακος, η, ον evil, bad, wrong, harm ἀκεραίους δὲ εἰς τὸ κακόν a play on the phrase των ἀκακων at the end of the previous verse. An echo of Jesus' words recorded in Matt 10:16. Verse 20 ὁ δὲ θεὸς τῆς εἰρήνης συντρίψει τὸν Σατανᾶν ὑπὸ τοὺς πόδας ὑµῶν ἐν τάχει. ἡ χάρις τοῦ κυρίου ἡµῶν Ἰησοῦ µεθ ὑµῶν. εἰρηνη, ης f peace συντριβω break in pieces, crush, shatter, bruise Σατανας, α the Adversary, Satan πόδας Noun, acc pl πους, ποδος m foot ταχος, ους n speed; ἐν τ. speedily, quickly, without delay, soon Cf. Gen 3:15, and see also Lk 10:17-19 and behind that Ps 91:13. Cf. also Rev 12: "Paul elsewhere sees the new, young church vulnerable to enemy attack; it was part of his theology of new creation that the church was now, like Adam and Eve, open to fresh deceit (2 Cor 11:3). But his earlier exposition of the victory of God in Jesus Christ over the sin of Adam and all its entail (5:12-21) enables him here simply to promise that the victory promised in Genesis will be theirs, and that it will come soon." Wright. "Paul's grace wish in verse 20b finds a parallel in every other letter he writes. It acts as a kind of bookend with the beginning of the letter, since Paul there wishes the Romans 'grace and peace to you from God our Father and from the Lord Jesus Christ' (1:7)." Moo. Most MSS read Ἰησου Χριστου but the shorter reading Ἰησου is supported by p 46 א B 1881 and "appears to be more primitive." Metzger. The Byzantine Text, followed by the TR, repeats 'the grace' before the doxology, i.e. as 16:24. Verse 21 Ἀσπάζεται ὑµᾶς Τιµόθεος ὁ συνεργός µου, καὶ Λούκιος καὶ Ἰάσων καὶ Σωσίπατρος οἱ συγγενεῖς µου. συνεργος, ου see v.3 Λούκιος probably not Luke the Evangelist Ἰάσων cf. Acts 17:5-9. Σωσίπατρος cf. Acts 20:4. συγγενης, ους see v.7 Verse 22 ἀσπάζοµαι ὑµᾶς ἐγω Τέρτιος ὁ γράψας τὴν ἐπιστολὴν ἐν κυρίῳ. ἐπιστολη, ης f letter Paul's amanuensis "peeps for a moment out of hiding." Wright. Verse 23 ἀσπάζεται ὑµᾶς Γάϊος ὁ ξένος µου καὶ ὅλης τῆς ἐκκλησίας. ἀσπάζεται ὑµᾶς Ἔραστος ὁ οἰκονόµος τῆς πόλεως καὶ Κούαρτος ὁ ἀδελφός. Γάϊος cf. 1 Cor 1:14. ξενος, ου foreigner; host The latter sense is intended here. Gaius is Paul's host and would seem to have been owner of a house in which the church at Corinth frequently met. ὁλος, η, ον whole, all, complete, entire "An inscription has been discovered in Corinth that refers to an Erastus who was an aedile of the city. This title may be equivalent to Paul's oikonomos (NIV 'director of public works'). Even if the two are not identical, Erastus may first have served as oikonomos before being promoted to aedile." Moo. οἰκονοµος, ου m steward, manager πολις, εως f city, town Verse 24 This verse is omitted from what are considered the best MSS. It consists of a repetition of the latter half of v. 20, with some variations. Day 530: Romans 16:25-27 Verses The following verses are found moved to two other places in a variety of MSS but hardly any copies omit them altogether. The repositioning may have been to make the truncated letter (without greetings) more suitable for general church reading. Week 106: Page 7

8 On these verses, see particularly, I. Howard Marshall, "Romans 16:25-27 An Apt Conclusion," Romans and The People of God, eds. Sven K Soderlund & NT Wright, Eerdmans, Grand Rapids, 1999, pp The doxology echoes many of the key themes of the letter. Verse 25 [Τῷ δὲ δυναµένῳ ὑµᾶς στηρίξαι κατὰ τὸ εὐαγγέλιόν µου καὶ τὸ κήρυγµα Ἰησοῦ Χριστοῦ, κατὰ ἀποκάλυψιν µυστηρίου χρόνοις αἰωνίοις σεσιγηµένου στηριζω strengthen, establish, set firm "While Paul (cf. 1:11) or others seek to establish believers in their faith, only God can ultimately do so." Moo. He is the source of all power. κηρυγµα, τος n message, proclamation ἀποκαλυψις, εως f revelation µυστηριον, ου n secret, mystery (of something formerly unknown but now revealed) χρονος, ου m time, period of time αἰωνιος, ον eternal, everlasting σεσιγηµένου Verb, perf pass ptc, m & n gen s σιγαω keep silent, keep secret Cf. 1 Cor. 2:6-7; Eph 1:9; 3:3-9; Col 1: Verse 26 φανερωθέντος δὲ νῦν διά τε γραφῶν προφητικῶν κατ ἐπιταγὴν τοῦ αἰωνίου θεοῦ εἰς ὑπακοὴν πίστεως εἰς πάντα τὰ ἔθνη γνωρισθέντος, φανερωθέντος Verb, aor pass ptc, m nom s φανεροω make known, reveal γραφη, ης f writing, Scripture προφητικος, η, ον prophetic ἐπιταγη, ης f command, authority "The fact and timing of the revelation of this mystery lay in God's plan; it was his 'command' that put the gospel into effect." Moo. αἰωνιος, ον eternal, everlasting ὑπακοη, ης f obedience πιστις, εως f faith, trust, belief Cf 1:5. γνωρισθέντος Verb, aor pass ptc, m nom s γνωριζω make known, disclose "All this is designed to explain the significance of the gospel proclamation of Jesus Christ: when this gospel is announced, it enables people of every nation to see that in Jesus the veil has been drawn back on the eternal plan of the eternal God, and to respond in grateful and obedient loyalty and trust. And it is by this gospel that God is able to strengthen the young church, not least through Paul's ministry as he comes to Rome (1:11)." Wright. Verse 27 µόνῳ σοφῷ θεῷ διὰ Ἰησοῦ Χριστοῦ ᾧ ἡ δόξα εἰς τοὺς αἰῶνας ἀµήν.] µονος, η, ον only, alone σοφος, η, ον wise, experienced Some MSS read αὐτῳ in place of ᾡ, some few (including B) omit either. Metzger writes "Despite the difficulty of construing the sentence when ᾡ is read, the committee felt constrained to include the word on the strength of early and diversified external evidence. The other readings have an appearance of being correctives introduced by various copyists in order to avoid anacoluthon and to complete the sentence." δοξα, ης f glory αἰῶνας Noun, acc pl αἰων, αἰωνος m age, eternity "The concluding description of God (16:27) reminds us especially that he has instituted a 'wise' and wonderful plan for the redemption of his creation (cf. 11:33-36). Surely our response should echo Paul, as we give glory to him through Jesus Christ!" Moo. Week 106: Page 8

Notes on the Greek New Testament Day 215 August 3 rd Romans 16:3-24

Notes on the Greek New Testament Day 215 August 3 rd Romans 16:3-24 Notes on the Greek New Testament Day 215 August 3 rd Romans 16:3-24 Works frequently referenced in these notes on Romans Barrett, CK A Commentary on the Epistle to the Romans, San Francisco, Harper & Row,

Διαβάστε περισσότερα

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

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

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

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

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

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

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

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

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

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

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής

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

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

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

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

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

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

1999 MODERN GREEK 2 UNIT Z

1999 MODERN GREEK 2 UNIT Z STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student

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

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

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

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

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

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

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

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

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

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

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

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 3: Phrases to use in business letters and e-mails Το περιεχόμενο του μαθήματος διατίθεται

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

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

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

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

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α.  Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:. ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,

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

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

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

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

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

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

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can.

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can. BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN Name GRADE Science Teacher A. What do I think about School? bit I try hard to do well in school. I look forward to coming to school.

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

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΜΑΘΗΜΑΤΑ ΥΠΕΥΘΥΝΟΤΗΤΑΣ/ LESSONS ABOUT RESPONSIBILITY Μάθημα 1: Νιώθω υπερήφανος όταν.../ I feel proud when.

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

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

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

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ Π Τ Υ Χ Ι Α Κ Η Ε Ρ Γ Α Σ Ι Α: Ο ΡΟΛΟΣ ΤΗΣ ΣΥΝΑΙΣΘΗΜΑΤΙΚΗΣ ΝΟΗΜΟΣΥΝΗΣ ΣΤΗΝ ΑΠΟΤΕΛΕΣΜΑΤΙΚΗ ΗΓΕΣΙΑ ΕΠΙΜΕΛΕΙΑ

Διαβάστε περισσότερα

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ» I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

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

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 7: More about gerunds Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

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

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

2 Thessalonians 3. Greek

2 Thessalonians 3. Greek Book Chapter Verse Interlinear English Word # in 2 Thess Greek # of letters # of words Numeric value 140301 00548 ΤΟ 2 370 140301 finally 00549 ΛΟΙΠΟΝ 6 310 140301 pray 00550 ΠΡΟΣΕΥΧΕΣΘΕ 11 1674 140301

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

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

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

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

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 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

13:31 38 Intro to farewell discourse. Jesus is going

13:31 38 Intro to farewell discourse. Jesus is going South Central Gospel Partnership Day Conference THESE THINGS I HAVE SAID TO YOU John 14-16 If running a discipleship group/course, what topics would you want to cover? Purpose clauses in John 14-16 ταῦτα

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

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

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

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

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

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

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

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

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

Notes are available 1

Notes are available 1 Notes are available 1 Galatians 2:15 4.12 2 3:15, 3:19 interpretational contradiction LAW cannot be and was added Promise 3 Gal.3:19 4 Mt 6:27 Which of you by taking thought can add one cubit unto

Διαβάστε περισσότερα

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ Πρόγραμμα Μεταπτυχιακών Σπουδών «Επιστήμη και Τεχνολογία Τροφίμων και Διατροφή του Ανθρώπου» Κατεύθυνση: «Διατροφή, Δημόσια

Διαβάστε περισσότερα

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Τμήμα Δημοσίων Σχέσεων & Επικοινωνίας Τεχνολογικό Εκπαιδευτικό Ίδρυμα Ιονίων

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

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

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

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

SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ

SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ WELCOME TO ST. CATHERINE S GREEK SCHOOL! WEEKDAY GREEK SCHOOL - REGISTRATION FORM SCHOOL YEAR 2016-2017 ΑΙΤΗΣΗ ΕΓΓΡΑΦΗΣ ΣΧΟΛΙΚΗ ΧΡΟΝΙΑ

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

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 3β: Types of Speeches & Strong Language Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative

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

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

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT 2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, 26-6-2016 Can anyone hear me? The participation of juveniles in juvenile justice. EVALUATION REPORT 80 professionals

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

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 2: A Business Letter Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά.

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Διαστημικό εστιατόριο του (Μ)ΑστροΈκτορα Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Μόλις μια παρέα πελατών κάτσει σε ένα

Διαβάστε περισσότερα

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get)

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Νόμος περί Αναπηριών 2006 (Disability Act 2006) Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Greek Νόμος περί Αναπηριών

Διαβάστε περισσότερα

Block Ciphers Modes. Ramki Thurimella

Block Ciphers Modes. Ramki Thurimella Block Ciphers Modes Ramki Thurimella Only Encryption I.e. messages could be modified Should not assume that nonsensical messages do no harm Always must be combined with authentication 2 Padding Must be

Διαβάστε περισσότερα

Objectives-Στόχοι: -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» 6/2/2014

Objectives-Στόχοι: -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» 6/2/2014 -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» Dr Caroline Linse Queens University, Belfast, Northern Ireland Objectives-Στόχοι:

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

Policy Coherence. JEL Classification : J12, J13, J21 Key words :

Policy Coherence. JEL Classification : J12, J13, J21 Key words : ** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji

Διαβάστε περισσότερα

(C) 2010 Pearson Education, Inc. All rights reserved.

(C) 2010 Pearson Education, Inc. All rights reserved. Connectionless transmission with datagrams. Connection-oriented transmission is like the telephone system You dial and are given a connection to the telephone of fthe person with whom you wish to communicate.

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