Notes on the Greek New Testament Day 298 October 25 th 2 Timothy 4:1-22. Works frequently referenced in these notes on 2 Timothy

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Day 298 October 25 th 2 Timothy 4:1-22. Works frequently referenced in these notes on 2 Timothy"

Transcript

1 Notes on the Greek New Testament Day 298 October 25 th 2 Timothy 4:1-22 Works frequently referenced in these notes on 2 Timothy Mounce, Willian D Word Biblical Commentary Vol 46: Pastoral Epistles, Nashville, Thomas Nelson, 2000 Stott, John R W Guard the Gospel: The message of 2 Timothy, London, IVP, Timothy 4:1 Διαμαρτύρομαι ἐνώπιον τοῦ θεοῦ καὶ Χριστοῦ Ἰησοῦ, τοῦ μέλλοντος κρίνειν ζῶντας καὶ νεκρούς, καὶ τὴν ἐπιφάνειαν αὐτοῦ καὶ τὴν βασιλείαν αὐτοῦ διαμαρτυρομαι declare solemnly and emphatically, charge Cf. 1 Tim 5:21. ἐνωπιον prep with gen before, in the presence of μελλω (before an infin) be going, be about κρινω judge, pass judgement on ζῶντας Verb, aor act ptc, m acc pl ζαω live, be alive νεκρος, α, ον dead For the phrase 'the living and the dead' cf. Acts 10:42; 1 Pet 4:5. ἐπιφανεια, ας f appearing, coming In place of καὶ τὴν ἐπιφάνειαν many MSS read κατα τὴν ἐπιφάνειαν. Metzger argues that this arose from a desire to smooth the awkward grammar of the verse. Verse 2 κήρυξον τὸν λόγον, ἐπίστηθι εὐκαίρως ἀκαίρως, ἔλεγξον, ἐπιτίμησον, παρακάλεσον, ἐν πάσῃ μακροθυμίᾳ καὶ διδαχῇ. κήρυξον Verb, aor act imperat, 2 s κηρυσσω preach, proclaim τον λογον is the message of the gospel, cf. 3:14. ἐπίστηθι Verb, 2 aor act imperat, 2 s ἐφιστημι approach; stand by; here perhaps be insistent or be busy in one's job εὐκαιρως when the time is right; when convenient ἀκαιρως when the time is not right Hendriksen thinks that the verb ἐφιστημι should carry its normal meaning here. He understands this injunction to mean, "'Be on hand in season, out of season.' Welcome or not welcome, Timothy must ever be on the spot with the message from God." Hendriksen therefore understand εὐκαιρως to refer to the recipients of the message, though it could be referred to Timothy, the messenger. Mounce sums up the phrase saying, "Timothy is always to be prepared to preach and perform his ministry, in season and out of season. It can possibly be a military metaphor, 'the Christian minister must always be on duty' (Guthrie)." ἔλεγξον Verb, aor act imperat, 2 s ἐλεγχω show (someone his) fault, convict ἐπιτιμαω command, rebuke παρακάλεσον Verb, aor act imperat, 2 s παρακαλεω exhort, encourage, urge "The four main imperatives ('Preach! Confront! Rebuke! Exhort!') loosely parallel the four propositional phrases in 3:16('profitable for teaching, reproof [ἐλεγμον; cf. variant spelling ἐλεγχον], correcting [ἐπανορθωσιν], training in righteousness'), especially if 'exhort' is encouragement to live out the gospel (i.e., 'righteousness')." μακροθυμια, ας f longsuffering, patience διδαχη, ης f teaching, what is taught Verse 3 ἔσται γὰρ καιρὸς ὅτε τῆς ὑγιαινούσης διδασκαλίας οὐκ ἀνέξονται, ἀλλὰ κατὰ τὰς ἰδίας ἐπιθυμίας ἑαυτοῖς ἐπισωρεύσουσιν διδασκάλους κνηθόμενοι τὴν ἀκοήν, ἔσται Verb, fut indic, 2 s εἰμι καιρος, ου m time, season, age ὁτε conj when, at which time ὑγιαινω be sound, be in good health διδασκαλια, ας f teaching, doctrine I.e. the gospel, cf. 1 Tim 1:10. ἀνεχομαι endure, be patient with ἰδιος, α, ον one's own ἐπιθυμια, ας f desire, lust, passion ἑαυτος, ἑαυτη, ἑαυτον him/her/itself ἐπισωρευω accumulate, collect Here only in the NT.

2 διδασκαλος, ου m teacher "The passage emphasises once again the hypocrisy of the Ephesian church. They chose not to put up with correct teaching. The false teachers are chosen in accordance with their own evil desires. Rather than hearing one correct teacher, they build a wall of teachers as if the sheer number of teachers will make them right. What they really want is to have their itching ears tickled with the latest doctrinal fad. Paul's critique finds application during every stage of the church in the last days." κνηθομαι feel an itching Here only in the NT. ἀκοη, ης f hearing, the ear The word means an act of hearing or listening and hence, as here, the ear. In the following verse the word means 'hearing' or 'listening.' "They have ears that are itching (from a verb which in the active means to tickle, and thus to itch, fig. 'to have an irritating desire'). Their craving is for teachers to suit their fancies or perverted tastes (see on 2 Tim 2:22). So great is their hankering that they pile up teacher upon teacher. This reminds one of Jer. 5:31, 'The prophets prophesy falsely... and my people love to have it so.' and of Ezek 33:32, 'And lo, thou art unto them as a very lovely song of one who has a pleasant voice and can play well on an instrument; for they hear thy words, but they do them not.' The people here pictured are more interested in something different, something sensational, than they are in sober truth. And when sober truth is presented (as it surely was with Ezekiel) they are not interested in the truth itself, but only in the way in which it is presented, the preacher's 'style,' 'oratory,'... the preacher himself, his voice, bearing, looks, mannerisms. Here in 2 Tim 4:3,4 the emphasis is on the craving for fascinating stories and philosophical speculations." Hendriksen. Verse 4 καὶ ἀπὸ μὲν τῆς ἀληθείας τὴν ἀκοὴν ἀποστρέψουσιν, ἐπὶ δὲ τοὺς μύθους ἐκτραπήσονται. ἀληθεια, ας f truth, reality ἀκοη, ης f see v.3. ἀποστρεφω turn away μυθος, ου m myth, fanciful story ἐκτρεπομαι wander, go astray, stray after Verse 5 σὺ δὲ νῆφε ἐν πᾶσιν, κακοπάθησον, ἔργον ποίησον εὐαγγελιστοῦ, τὴν διακονίαν σου πληροφόρησον. νηφω be sober, be self-controlled A call to be clear minded, cf. 1 Thess 5:6,8. κακοπάθησον Verb, aor act imperat, 2 s κακοπαθεω undergo hardship; endure hardship patiently Cf. 1:8. εὐαγγελιστης, ου m one who preaches the good news, evangelist "The emphasis of the word is on the task of one so gifted; it does not describe a church office." διακονια, ας f ministry, service πληροφόρησον Verb, aor act imperat, 2 s πληροφορεω accomplish, complete Verse 6 Ἐγὼ γὰρ ἤδη σπένδομαι, καὶ ὁ καιρὸς τῆς ἀναλύσεώς μου ἐφέστηκεν. ἠδη adv now, already σπενδομαι be poured out as a drinkoffering (of one's life), give one's life in sacrifice "The present tense here stresses that the process has begun, and the passive voice that God, not Rome, is still in control, despite appearances." Paul uses similar imagery in Phil 2:17, but there the reference is to his life of ministry rather than his death. καιρος, ου m see v.3 ἀναλυσις, εως f departure, death "ἀναλυσις occurs only here in the NT but is used of soldiers breaking camp or sailors loosing a ship from its moorings and is a known euphemism for death... Its verbal cognate, ἀναλυειν, 'to depart,' occurs in Phil 1:23 also as a euphemism, emphasising the passage from life through death to be with Christ." Mounce ἐφέστηκεν Verb, perf act indic, 3 s ἐφιστημι see v.2 Here in the sense of be imminent. Verse 7 τὸν καλὸν ἀγῶνα ἠγώνισμαι, τὸν δρόμον τετέλεκα, τὴν πίστιν τετήρηκα "In view of his impending death Paul recites his spiritual legacy, not in a self-serving way but in a way that shows his perseverance as an encouragement to Timothy." Mounce καλος, η, ον good, right, proper ἀγων, ωνος m struggle, fight, opposition

3 ἠγωνισμαι Verb, perf midd/pass dep indic, 1 s ἀγωνιζομαι struggle, fight, compete The picture now shifts from that of a wrestling match to a race. Cf. 1 Cor 9: δρομος, ου m course (of life) τετέλεκα Verb, perf act indic, 1 s τελεω complete, finish, fulfill, carry out "δρομος can mean 'course' in general... but most believe it is specifically an athletic course, a race. Acts uses the word of John the Baptist finishing his ministry (Acts 13:25) and of Paul's desire to finish his ministry (Acts 20:24). On the basis of this statement, most conclude that Paul knows his life will soon end (also 2 Tim 1:15-18; 4:16-18) and date this epistle as the last of Paul's writings. Paul has persevered and has brought his ministry to its intended end, its goal, its full completion, that all the Gentiles might hear the good news of the gospel." πιστις, εως f faith, trust τετήρηκα Verb, perf act indic, 1 s τηρεω keep, observe, maintain The definite article before πιστις suggests the objective sense, 'the Christian faith.' "In this case Paul would be saying that he has safely guarded the deposit of the gospel (cf. 2 Tim 1:14), preserving it from attack ('kept the faith')." Mounce Lock comments on what appears to be Paul's self-commendation, "With St Paul there is always Χριστος behind the ἐγω (Gal 2:20), always the thought of the grace which enables him who can do nothing by himself to do all things in his strength (1 Cor 15:10; Phil 4:13; 1 Tim 1:12); and to one who so recognises the power which enables him to be what he is, there is a true self-confidence, a legitimate self-praise; especially when, as here, the purpose is to give confidence to a younger man to follow." Verse 8 λοιπὸν ἀπόκειταί μοι ὁ τῆς δικαιοσύνης στέφανος, ὃν ἀποδώσει μοι ὁ κύριος ἐν ἐκείνῃ τῇ ἡμέρᾳ, ὁ δίκαιος κριτής, οὐ μόνον δὲ ἐμοὶ ἀλλὰ καὶ πᾶσιν τοῖς ἠγαπηκόσι τὴν ἐπιφάνειαν αὐτοῦ. λοιπος, η, ον rest, remaining: (το) λοιπον adv. finally, henceforth, from now on ἀποκειμαι be stored away δικαιοσυνη, ης f righteousness στεφανος, ου m wreath, crown, prize The victor's wreath, cf. 2 Tim 2:5. "Despite the imagery of God giving Paul a crown, there is no suggestion that Paul is thinking of a specific reward beyond that of life with Christ." ἀποδιδωμι give, pay, render ἐκεινος, η, ο demonstrative adj. that (one) δικαιος, α, ον righteous, just κριτης, ου m judge μονος, η, ον i) adj only, alone; ii) adv μονον only, alone ἐμοὶ Pronoun, dat s ἐγω ἠγαπηκόσι Verb, perf act ptc, m dat pl ἀγαπαω love, show love for I.e. 'long for.' ἐπιφανεια, ας f see v.1 The Christian life is to have a continual eschatological focus: we live towards the hope of Christ's coming. Verse 9 Σπούδασον ἐλθεῖν πρός με ταχέως σπούδασον Verb, aor act imperat, 2 s σπουδαζω do one's best, work hard at ἐλθεῖν Verb, aor act infin ἐρχομαι ταχεως adv. quickly, at once, soon Paul is concerned that Timothy come before winter impedes his journey, cf. v 21. Verse 10 Δημᾶς γάρ με ἐγκατέλιπεν ἀγαπήσας τὸν νῦν αἰῶνα, καὶ ἐπορεύθη εἰς Θεσσαλονίκην, Κρήσκης εἰς Γαλατίαν, Τίτος εἰς Δαλματίαν The urgency comes in part from Paul's loneliness and a desire for friends and helpers to be with him. ἐγκατέλιπεν Verb, aor act indic, 3 s ἐγκαταλειπω forsake, abandon ἀγαπήσας Verb, aor act ptc, m nom s ἀγαπαω love, show love for Note the contrast with πᾶσι τοῖς ἠγαπηκόσι τὴν ἐπιφάνειαν αὐτοῦ of v 8. αἰων, αἰωνος m age, world order "Demas had at one time been Paul's assistant in gospel-ministry (Philemon 24). During his first Roman imprisonment Demas too, had been in Rome. Twice the apostle had mentioned him in one breath with Luke the beloved physician Col 4:14; Philemon 25)." Hendriksen. Demas has now abandoned Paul and, it would seem, abandoned gospel work. ἐπορεύθη Verb, aor pass dep indic, 3 s πορευομαι go, proceed, travel

4 "Titus had gone to Dalmatia. Perhaps he wintered in Nicopolis on his return from Crete and then headed north... Dalmatia was the southwestern part of Illyricum on the eastern shore of the Adriatic Sea (modern day Yugoslavia, currently Croatia, Bosnia, and Hertzegovina...). Paul had gone as far as Illyricum in his journeys (Rom 15:19), so Titus may have been following up on Paul's missionary endeavours as he may have done in Crete." Mounce Verse 11 Λουκᾶς ἐστιν μόνος μετʼ ἐμοῦ. Μᾶρκον ἀναλαβὼν ἄγε μετὰ σεαυτοῦ, ἔστιν γάρ μοι εὔχρηστος εἰς διακονίαν, μονος, η, ον adj only, alone "There may be more here than an expression of loneliness... the apostle also wishes to stress the fact that he is short on help." Hendriksen. The greetings of v 21 suggest there are others with Paul or able to contact him. Hence the meaning here may be that Luke alone of Paul's inner circle is left with him. Luke was probably the amanuensis of this epistle. ἀναλαβων Verb, aor act ptc, m nom s ἀναλαμβανω take up, take σεαυτου, ης reflexive pronoun yourself εὐχρηστος, ον useful, beneficial "John Mark was the son of Mary of Jerusalem and the cousin of Barnabas. He accompanied Paul and Barnabas on the first missionary journey as far as Pamphylia but then returned to Jerusalem (Acts 12:12, 25; 13:13). The circumstances were such that Paul did not want to take him on the second missionary journey, so Barnabas and Mark went to Cyprus and Paul took Silas (Acts 15:37, 39). Evidently there was a reconciliation because Mark was with Paul in his first Roman imprisonment and was called Paul's fellow worker (Col 4:10-11; Phlm 24; cf. 1 Pet 5:13). " Tim 4:11 is often seen as an acknowledgement that the reconciliation was complete, although this can be assumed from Paul's prior use of the title fellow worker." διακονια, ας f ministry, service, help Hendriksen argues that Paul means that Mark would be useful for necessary kingdom-work in Rome not simply as a personal servant. Verse 12 Τυχικὸν δὲ ἀπέστειλα εἰς Ἔφεσον. ἀποστειλα Verb, aor act indic, 1 s ἀποστελλω send, send out May be an epistolatory aorist. Tychicus could have been the bearer of this letter. "He had already carried Paul's letters to the Ephesian (and Colossian) church and remained to tell them how Paul was doing (Acts 20:4; Eph 6:21; Col 4:7; Titus 3:12). Paul calls him a beloved brother, a faithful servant (Eph 6:21), and a fellow slave in the Lord (Col 4:7)." Verse 13 τὸν φαιλόνην, ὃν ἀπέλιπον ἐν Τρῳάδι παρὰ Κάρπῳ, ἐρχόμενος φέρε, καὶ τὰ βιβλία, μάλιστα τὰς μεμβράνας. φαιλονης, ου m cloak Some commentators think that the word here means a satchel in which books/documents might be kept and transported. Hendriksen argues that it is a form of cloak: "A kind of blanket of course wool that was used as an outer garment to protect against the cold and the rain. It had a hole in the middle for the head to pass through. There were no sleeves." Mounce comments, "It is assumed that he asks for the cloak because he is cold or in anticipation of the coming winter (v 21)." ἀπελιπον Verb, aor act indic, 1 s & 3 pl ἀπολειπω leave behind Τρῳας, αδος f Troas παρα with φερω bring, carry, bear, lead βιβλιον, ου n book, scroll Probably scrolls of Scripture μαλιστα especially μεμβρανα, ης f parchment Maybe writing materials so that Paul could continue his correspondence. Verse 14 Ἀλέξανδρος ὁ χαλκεὺς πολλά μοι κακὰ ἐνεδείξατο ἀποδώσει αὐτῷ ὁ κύριος κατὰ τὰ ἔργα αὐτοῦ χαλκευς, εως m coppersmith, metal worker πολυς, πολλη, πολυ gen πολλου, ης, ου i) much, many ii) πολλα many things κακος, η, ον evil, bad, wrong Alexander may have acted as a witness against Paul at the legal hearing mentioned in v. 16. He may have been instrumental in Paul's arrest. Most think he was the same person excommunicated in 1 Tim 1:20. ἐνεδείξατο Verb, aor midd indic, 3 s ἐνδεικνυμαι show, do Can be used in the legal sense of 'inform against.'

5 ἀποδωσει Verb, fut act indic, 3 s ἀποδιδωμι give, pay, render, repay Cf. the contrasting use of this verb in v 8. Verse 15 ὃν καὶ σὺ φυλάσσου, λίαν γὰρ ἀντέστη τοῖς ἡμετέροις λόγοις. φυλασσω keep, guard; midd guard against, avoid If Alexander had been instrumental in Paul's arrest, Paul wants Timothy to watch lest a similar thing should happen to him. λιαν adv exceedingly, greatly ἀντέστη Verb, perf act indic, 3 s ἀνθιστημι resist, oppose, withstand ἡμετερος, α, ον our Verse 16 Ἐν τῇ πρώτῃ μου ἀπολογίᾳ οὐδείς μοι παρεγένετο, ἀλλὰ πάντες με ἐγκατέλιπον μὴ αὐτοῖς λογισθείη πρωτος, η, ον first, earlier ἀπολογια, ας f verbal defence, defence "Most modern writers see this first defence as the Roman prima actio, a public, preliminary hearing designed to gather basic information, which, if necessary, would be followed by a trial." οὐδεις, οὐδεμια, οὐδεν no one, nothing παραγινομαι come, arrive, appear It may have been fear that prevented any standing by Paul to speak in his defence. πάντες Adjective, m nom pl πας ἐγκατέλιπον Verb, aor act indic, 1 s & 3 pl ἐγκαταλειπω see v.10 λογιζομαι reckon, count, credit Verse 17 ὁ δὲ κύριός μοι παρέστη καὶ ἐνεδυνάμωσέν με, ἵνα διʼ ἐμοῦ τὸ κήρυγμα πληροφορηθῇ καὶ ἀκούσωσιν πάντα τὰ ἔθνη, καὶ ἐρρύσθην ἐκ στόματος λέοντος. παρέστη Verb, 2 aor act indic, 3 s παριστημι and παριστανω stand before/by; provide ἐνδυναμοω strengthen, make strong κηρυγμα, τος n what is preached, message, proclamation πληροφορηθῇ Verb, aor pass subj, 3 s πληροφορεω accomplish, proclaim fully ἔθνη Noun, nom & acc pl ἐθνος, ους n nation, people; τα ἐ. Gentiles Hendriksen links these words with his view that, after Paul's first imprisonment and the hearing spoken of in these verses, he was released for a while and was able to preach the Gospel in Gentile areas to the west of Rome even as far as Spain (cf. Rom 15:24,28). Mounce thinks that the defence mentioned was not Paul's previous imprisonment and trial (see above). Hence he argues that Paul is seeing the whole of his ministry brought to its designed conclusion in the declaration of the gospel before the authorities in Rome (cf. Acts 9:15; 23:11). ἐρρύσθην Verb, aor pass indic, 1 s ῥυομαι save, rescue στομα, τος n mouth λεων, οντος m lion Hendriksen suggests that this may be an idiomatic expression for escaping from the jaws of death rather than implying that Paul was literally in danger of being thrown to lions. Mounce suggests the situation referred to is as follows: "Paul made his defence at a preliminary hearing and instead of being condemned to immediate death was given a temporary reprieve, allowing sufficient time for Timothy to travel to Rome. It was also a victory in that Paul proclaimed the gospel in the Roman courts and received a somewhat positive hearing. It is this event that Paul terms a rescue from the lion's mouth. This does not mean that Paul believes he will be freed. He knows he is going to die (vv 6-8), and the temporary rescue (ἐρρυσθην, 'was rescued') enjoyed now looks forward to the rescue (ῥυσεται, 'will rescue' [v 18]) that will take him into God's heavenly kingdom. Paul does not envisage a rescue to freedom and extended earthly ministry." Verse 18 ῥύσεταί με ὁ κύριος ἀπὸ παντὸς ἔργου πονηροῦ καὶ σώσει εἰς τὴν βασιλείαν αὐτοῦ τὴν ἐπουράνιον ᾧ ἡ δόξα εἰς τοὺς αἰῶνας τῶν αἰώνων, ἀμήν. ῥύσεταί Verb, fut midd dep indic, 3 s ῥυομαι save, rescue, deliver πονηρος, α, ον evil, bad, wicked Cf. v 14. σωζω save, rescue, heal ἐπουρανιος, ον heavenly, celestial

6 "Perhaps it is intended to contrast with the earthly kingdom whose rulers will soon have Paul executed. The emperor, a 'lion,' has his kingdom and is soon to condemn Paul; God will save Paul for the true heavenly kingdom. The implicit comparison of both kings and kingdoms seems intentional." δοξα, ης f glory αἰῶνας Noun, acc pl αἰων, αἰωνος m age, world order, eternity Verse 19 Ἄσπασαι Πρίσκαν καὶ Ἀκύλαν καὶ τὸν Ὀνησιφόρου οἶκον. ἄσπασαι Verb, aor midd dep imperat, 2 s ἀσπαζομαι greet Having previously returned to Rome (Rom 16:3-4), Priscilla and Aquila had now evidently returned to Ephesus, perhaps to help Timothy. For Onesiphorus, cf. 2 Tim 1: "Some suggest Onesiphorus died after leaving Paul, and therefore he could not be greeted directly." οἰκος, ου m house, household, family Verse 22 Ὁ κύριος μετὰ τοῦ πνεύματός σου. ἡ χάρις μεθʼ ὑμῶν. Note the change from the second person singular to the plural, from personal wish to one directed at the whole Ephesian church. χαρις, ιτος f grace, unmerited favour "If the traditional historical reconstruction of the PE is correct, then these are the final recorded words written by Paul, apostle to the Gentiles. God's grace overflowed in his life with the faith and love that were in Christ Jesus (1 Tim 1:14). He lived a life characterised by the grace of God calling sinful men and women to Christ by faith. And he ends his ministry having fulfilled his calling (2 Tim 4:6-7) with χαρις, 'grace,' on his lips." Verse 20 Ἔραστος ἔμεινεν ἐν Κορίνθῳ, Τρόφιμον δὲ ἀπέλιπον ἐν Μιλήτῳ ἀσθενοῦντα. ἔμεινεν Verb, aor act indic, 3 s μενω remain, stay ἀπολειπω leave behind ἀσθενεω be sick, be ill, be weak The language suggests "that these two men had been accompanying Paul but have stopped along the way. It is not clear whether this happened before or after Paul's arrest." Verse 21 Σπούδασον πρὸ χειμῶνος ἐλθεῖν. Ἀσπάζεταί σε Εὔβουλος καὶ Πούδης καὶ Λίνος καὶ Κλαυδία καὶ οἱ ἀδελφοὶ πάντες. σπούδασον Verb, aor act imperat, 2 s σπουδαζω see v. 9 χειμων, ωνος m winter, bad weather During winter, few ships would sail on the open sea because of the bad weather. "The urgency may also be related to Paul's need for his cloak (v 13) and the timing of the trial." ἐλθεῖν Verb, aor act infin ἐρχομαι ἀσπαζομαι see v.19 σε Pronoun, acc s συ The names are probably those of leaders of the church in Rome who were known to Timothy. πάντες Adjective, m nom pl πας

Notes on the Greek New Testament Week Timothy 3:10-4:22

Notes on the Greek New Testament Week Timothy 3:10-4:22 Notes on the Greek New Testament Week 129 2 Timothy 3:10-4:22 Day 641: 2 Timothy 3:10-17 Verse 10 Σὺ δὲ παρηκολούθησάς µου τῇ διδασκαλίᾳ, τῇ ἀγωγῇ, τῇ προθέσει, τῇ πίστει, τῇ µακροθυµίᾳ, τῇ ἀγάπῃ, τῇ ὑποµονῇ,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ

ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ :ΤΥΠΟΙ ΑΕΡΟΣΥΜΠΙΕΣΤΩΝ ΚΑΙ ΤΡΟΠΟΙ ΛΕΙΤΟΥΡΓΙΑΣ ΣΠΟΥ ΑΣΤΡΙΑ: ΕΥΘΥΜΙΑ ΟΥ ΣΩΣΑΝΝΑ ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ : ΓΟΥΛΟΠΟΥΛΟΣ ΑΘΑΝΑΣΙΟΣ 1 ΑΚΑ

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

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

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

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

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

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

[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

6.003: Signals and Systems. Modulation

6.003: Signals and Systems. Modulation 6.003: Signals and Systems Modulation May 6, 200 Communications Systems Signals are not always well matched to the media through which we wish to transmit them. signal audio video internet applications

Διαβάστε περισσότερα

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015 Passive and Middle Voices A lesson for the Paideia web-app Ian W. Scott, 2015 The Passive Voice So far all of our Greek verbs have been in the active voice Subject performs the verbal action "Clare is

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

Final Test Grammar. Term C'

Final Test Grammar. Term C' Final Test Grammar Term C' Book: Starting Steps 1 & Extra and Friends Vocabulary and Grammar Practice Class: Junior AB Name: /43 Date: E xercise 1 L ook at the example and do the same. ( Κξίηα ηξ παοάδειγμα

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

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

Μηχανική Μάθηση Hypothesis Testing

Μηχανική Μάθηση Hypothesis Testing ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider

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

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

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ EΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΕΚΠΑΙΔΕΥΤΙΚΟ ΤΕΧΝΟΛΟΓΙΚΟ ΙΔΡΥΜΑ ΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : Λεωφ. Αντ.Τρίτση, Αργοστόλι Κεφαλληνίας Τ.Κ. 28 100 τηλ. : 26710-27311 fax : 26710-27312

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

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

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

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

Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε.

Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε. THE PASSIVE VOICE ΠΑΘΗΤΙΚΗ ΦΩΝΗ Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε. Είναι επίσης πιθανό είτε κάποιος να αγνοεί το άτομο που έκανε κάτι (το ποιητικό αίτιο agent) είτε

Διαβάστε περισσότερα

Αζεκίλα Α. Μπνπράγηεξ (Α.Μ. 261)

Αζεκίλα Α. Μπνπράγηεξ (Α.Μ. 261) ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΧΝ ΥΟΛΖ ΑΝΘΡΧΠΗΣΗΚΧΝ ΚΑΗ ΚΟΗΝΧΝΗΚΧΝ ΠΟΤΓΧΝ ΠΑΗΓΑΓΧΓΗΚΟ ΣΜΖΜΑ ΓΖΜΟΣΗΚΖ ΔΚΠΑΗΓΔΤΖ ΜΔΣΑΠΣΤΥΗΑΚΟ ΠΡΟΓΡΑΜΜΑ ΠΟΤΓΧΝ ΘΔΜΑ ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ: Ζ ΑΝΣΗΛΖΦΖ ΣΧΝ ΔΚΠΑΗΓΔΤΣΗΚΧΝ ΓΗΑ ΣΖ ΖΜΑΗΑ ΣΖ ΑΤΣΟΔΚΣΗΜΖΖ

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

LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV. 25 February 2014

LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV. 25 February 2014 LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV 25 February 2014 Often/frequently Συχνά (sihna) Seldom Σπάνια (spania) Early Νωρίς (noris) Late (adv)/slowly Αργά (arga) I am having a bath When/whenever

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

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

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

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

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

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS 1. Developing a grammar fragment...1 2. A formalism that is too strong and too weak at the same time...3 3. References...4 1. Developing a grammar fragment The

Διαβάστε περισσότερα

ΤΟ ΣΤΑΥΡΟΔΡΟΜΙ ΤΟΥ ΝΟΤΟΥ ΤΟ ΛΙΜΑΝΙ ΤΗΣ ΚΑΛΑΜΑΤΑΣ

ΤΟ ΣΤΑΥΡΟΔΡΟΜΙ ΤΟΥ ΝΟΤΟΥ ΤΟ ΛΙΜΑΝΙ ΤΗΣ ΚΑΛΑΜΑΤΑΣ ΤΟ ΣΤΑΥΡΟΔΡΟΜΙ ΤΟΥ ΝΟΤΟΥ ΤΟ ΛΙΜΑΝΙ ΤΗΣ ΚΑΛΑΜΑΤΑΣ ΖΑΡΑΒΕΛΑ Δ. 1, και ΒΡΥΩΝΗΣ Δ. 1 1 4ο Τ.Ε.Ε. Καλαμάτας, Δ/νση Δευτεροβάθμιας Εκ/σης Μεσσηνίας e-mail: dzaravela@yahoo.qr ΕΚΤΕΝΗΣ ΠΕΡΙΛΗΨΗ Από τις κύριες

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

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

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

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author.

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. 2012, Γεράσιμος Χρ. Σιάσος / Gerasimos Siasos, All rights reserved. Στοιχεία επικοινωνίας συγγραφέα / Author

Διαβάστε περισσότερα

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015 Passive and Middle Voices A lesson for the Paideia web-app Ian W. Scott, 2015 The Passive Voice So far all of our Greek verbs have been in the active voice Subject performs the verbal action "Clare is

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

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

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE «ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing

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

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

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