Notes on the Greek New Testament Day 151 May 31 st John 19:17-42
|
|
- Σίβύλλα Κρεστενίτης
- 7 χρόνια πριν
- Προβολές:
Transcript
1 Notes on the Greek New Testament Day 151 May 31 st John 19:17-42 Works frequently referenced in these notes on John Barrett, CK The Gospel According to John, London, SPCK, 1967 Beasley-Murray, GR John, Word Bible Commentary, vol 36, Word Books, 1987 Carson, DA The Gospel According to John, Leicester, IVP (Apollos), 1991 Verses Carson comments, "In main outline, John's account of Jesus' death parallels that of Mark rather closely. Nevertheless, he omits some details, and introduces several features not reported elsewhere, including the controversy caused by the inscription on the cross (vv ), several fulfilment quotations (vv. 24, 28-29, 36-37), the care of Jesus for his mother (vv ) and the last cry before his death (v. 30)." Added to the above is the piercing of Jesus' side (vv ). Beasley-Murray comments, "It is evident that, as in his account of the ministry of Jesus, the Evangelist has been very selective in his story of the death of Jesus. As he made choice of seven signs, and made much of their significance, so he has concentrated on a few features in the tradition that he received of Jesus death which appeared to him most significant. The controlling motif in his account is that which dominated his narration of the arrest and trial of Jesus, namely, the kingship of Jesus. The anticipations in the Gospel of Jesus being 'lifted up' are here fulfilled, so that the crucifixion is seen as the enthronement of Jesus." Verse 17 καὶ βαστάζων αὑτῷ τὸν σταυρὸν ἐξῆλθεν εἰς τὸν λεγόμενον Κρανίου Τόπον, ὃ λέγεται Ἑβραϊστὶ Γολγοθα, βασταζω carry, bear σταυρος, ου m cross "It was customary for a criminal not to bear the whole cross but the cross-beam." Barrett. Beasley-Murray comments, "The usual procedure was for the condemned person to have his outstretched arms nailed to the crossbeam as he lay on the ground; it was then lifted up with his body on it and affixed to the vertical post which was already in the ground; at Golgotha such posts will presumably have been standing permanently." Beasley-Murray also adds, "The significance of Isaac carrying the wood for his sacrifice was much in the minds of the Church Fathers, and not alone in theirs but in the minds of the rabbis also... It was said that Isaac carried the wood 'as one bears the cross on one s shoulder' (Gen. Rab. 56.4, on Gen 22:6). It would be no wonder if our Evangelist paralleled Jesus setting out for Golgotha and Isaac setting out for the mount with his Father. Christians have also very understandably linked Jesus bearing his cross to Golgotha with his call to take up the cross and follow him (note esp. the closeness of Luke s language in Luke 14:27 with John 19:17)." κρανιον, ου n skull τοπος, ου m place Ἑβραϊστι see v.13 Beasley-Murray comments, "Luke 23:33 does not cite the Semitic name but simply reads, 'they came to the place that is called Skull.' John 19:17 could be translated in the same way, the gen. then being regarded as one of apposition. Presumably the name was given by reason of the shape of the ground (hence the tradition that it was a hill ). The hillock behind the bus station in Jerusalem, Gordon s Calvary, is undoubtedly reminiscent of a skull in shape, but the traditional site of Golgotha in the Church of the Holy Sepulchre is favoured by recent archaeologists." Verse 18 ὅπου αὐτὸν ἐσταύρωσαν, καὶ μετʼ αὐτοῦ ἄλλους δύο ἐντεῦθεν καὶ ἐντεῦθεν, μέσον δὲ τὸν Ἰησοῦν. ὁπου adv. where σταυροω crucify
2 "One element in John s account, shared incidentally by the three synoptic Gospels, is the brevity of his description of the actual crucifixion: it is contained in a sub-clause consisting of three words (v 18: ὅπου αὐτὸν ἐσταύρωσαν, 'where they crucified him'). This is in marked contrast to the tendency of Christian devotion through the ages to meditate on the sufferings of Jesus on the cross." Beasley-Murray. ἀλλος, η, ο another, other δυο gen & acc δυο dat δυσιν two ἐντευθεν from here, on this side The construction ἐντεῦθεν καὶ ἐντεῦθεν meaning 'one on this side and one on that' suggests a Semitic mind. μεσος, η, ον middle 'and Jesus as the middle one' Verse 19 ἔγραψεν δὲ καὶ τίτλον ὁ Πιλᾶτος καὶ ἔθηκεν ἐπὶ τοῦ σταυροῦ ἦν δὲ γεγραμμένον Ἰησοῦς ὁ Ναζωραῖος ὁ βασιλεὺς τῶν Ἰουδαίων. γραφω write τιτλος, ου m notice, inscription ἔθηκεν Verb, aor act indic, 3 s τιθημι place, set "It was customary for one doomed to be crucified to have a tablet or placard stating the cause for his execution hung about him, or carried by another before him, and then affixed to his cross." Beasley-Murray. γεγραμμένον Verb, perf pass ptc, m acc & n nom/acc s γραφω Ναζωραιος, ου m inhabitant of Nazareth, Nazarene Verse 20 τοῦτον οὖν τὸν τίτλον πολλοὶ ἀνέγνωσαν τῶν Ἰουδαίων, ὅτι ἐγγὺς ἦν ὁ τόπος τῆς πόλεως ὅπου ἐσταυρώθη ὁ Ἰησοῦς καὶ ἦν γεγραμμένον Ἑβραϊστί, Ῥωμαϊστί, Ἑλληνιστί. ἀνέγνωσαν Verb, aor act indic, 3 pl ἀναγινωσκω read ἐγγυς adv near τοπος, ου m see v.17 πολις, εως f city, town Ἑβραϊστι see v.13 Ῥωμαϊστι in the Latin language Ἑλληνιστι adv in the Greek language The order of languages, 'Hebrew, Latin, Greek' has strong attestation א) a B L N X it e, ff.2 syr pal cop sa,boh arm eth etc) and indicates the national language, the official language, and the common language. Many later MSS (including most minuscules and MSS of the Lat. tradition) read 'Hebrew, Greek, Latin,' viewing the languages as spoken in order from East to West (Metzger). Verse 21 ἔλεγον οὖν τῷ Πιλάτῳ οἱ ἀρχιερεῖς τῶν Ἰουδαίων Μὴ γράφε Ὁ βασιλεὺς τῶν Ἰουδαίων, ἀλλʼ ὅτι ἐκεῖνος εἶπεν Βασιλεὺς τῶν Ἰουδαίων εἰμί. ἐκεινος, η, ο demonstrative adj. that (one), he "The Jews' objection to the titulus was natural. In the first place, they had just declared that they had no king but Caesar, and the titulus, if they accepted it, was tantamount to an admission of sedition; and in the second place, to suggest that a powerless, condemned and dying outcast was the king of their nation was a studied insult." Barrett. Beasley-Murray adds, "For the Evangelist the action of Pilate was the climax of the whole series of events that culminated in the crucifixion of Jesus: Pilate, the judge and representative of the dominion that ruled the world, hereby declares that Jesus on his cross is King of his people. It was written in Hebrew that the Jews might understand it; in Latin that the Romans might know it; in Greek, the lingua franca of the world, that all nations might learn of it. 'Thus did Pilate tell it out among the nations that the Lord is king' wrote Hoskyns, in the words of Ps 96:10. Here the irony of John reaches its apex: the two men who were most responsible for the death of Jesus became the unwitting prophets of the death of Jesus: the one declaring it as the means of redemption for Israel and the nations (11:49 50) the other proclaiming it the occasion of his exaltation to be King of Israel and Lord of all." Verse 22 ἀπεκρίθη ὁ Πιλᾶτος Ὃ γέγραφα γέγραφα. ἀπεκρίθη Verb, aor midd dep indic, 3 s ἀποκρινομαι answer, reply γέγραφα Verb, perf act indic, 1 s γραφω "Pilate, no doubt anxious to avenge himself upon the Jews who had forced him to act against his will, refused to alter what he had written. Accordingly Jesus went to his death under a title unintentionally but profoundly true." Barrett.
3 Verse 23 οἱ οὖν στρατιῶται ὅτε ἐσταύρωσαν τὸν Ἰησοῦν ἔλαβον τὰ ἱμάτια αὐτοῦ καὶ ἐποίησαν τέσσαρα μέρη, ἑκάστῳ στρατιώτῃ μέρος, καὶ τὸν χιτῶνα. ἦν δὲ ὁ χιτὼν ἄραφος, ἐκ τῶν ἄνωθεν ὑφαντὸς διʼ ὅλου στρατιωτης, ου m soldier ὁτε conj when ἱματιον, ου n garment, clothing τεσσαρες neut τεσσαρα gen τεσσαρων four μερος, ους n part ἑκαστος, η, ον each, every "The clothes of an executed criminal were a recognised perquisite of the executioners." Barrett. χιτων, ωνος m tunic, shirt (generally of garment worn next to the skin) ἀραφος, ον seamless ἀνωθεν from above ὑφαντος, η, ον woven (ἐκ των ἀνωθεν ὑ. δι ὁλου woven in one piece throughout) ὁλος, η, ον whole, all, complete A detail peculiar to John. Josephus describes the tunic of the high priest in similar terms. Verse 24 εἶπαν οὖν πρὸς ἀλλήλους Μὴ σχίσωμεν αὐτόν, ἀλλὰ λάχωμεν περὶ αὐτοῦ τίνος ἔσται ἵνα ἡ γραφὴ πληρωθῇ ἡ λέγουσα Διεμερίσαντο τὰ ἱμάτιά μου ἑαυτοῖς καὶ ἐπὶ τὸν ἱματισμόν μου ἔβαλον κλῆρον. Οἱ μὲν οὖν στρατιῶται ταῦτα ἐποίησαν. ἀλληλων, οις, ους reciprocal pronoun one another σχίσωμεν Verb, aor act subj, 1 pl σχιζω split, tear, separate, disunite λάχωμεν Verb, aor act subj, 1 pl λαγχανω receive; fall to one's lot; cast lots ἔσται Verb, fut indic, 2 s εἰμι γραφη, ης f writing, Scripture πληρωθῇ Verb, aor pass subj, 3 s πληροω fill, fulfill διεμερίσαντο Verb, aor midd indic, 3 pl διαμεριζω divide, distribute ἑαυτος, ἑαυτη, ἑαυτον him/herself, itself κληρος, ου m lot (of something thrown or drawn to reach a decision) The quotation follows exactly the LXX of Ps 22(21):18. Verse 25 Εἱστήκεισαν δὲ παρὰ τῷ σταυρῷ τοῦ Ἰησοῦ ἡ μήτηρ αὐτοῦ καὶ ἡ ἀδελφὴ τῆς μητρὸς αὐτοῦ, Μαρία ἡ τοῦ Κλωπᾶ καὶ Μαρία ἡ Μαγδαληνή. εἱστήκεισαν Verb, pluperfect act indic, 3 pl ἱστημι stand σταυρος, ου m see v.17 ἀδελφη, ης f sister Μαγδαληνη, ης f woman of Magdala "It is possible that only two women are referred to (Jesus' mother = Mary the daughter (or sister) of Clopas, and her sister, Mary Magdalene), or three (Jesus' mother, her sister = Mary the daughter (or sister, or wife) of Clopas, and Mary Magdalene); but more probable that John intended his readers to think of four. Identifications are easy to conjecture but impossible to ascertain... It is possible that this Clopas should be identified with the Κλεοπας of Luke 24:18." Barrett. Beasley-Murray, having argued that the reference is best understood of four women, continues, "The relationship of the women mentioned by the Fourth Evangelist to those in the synoptics is more difficult to determine. Traditionally it has been assumed that the same persons appear in John as in Mark and Matthew. The mother of Jesus is excepted, since she is in John s list only. Mary Magdalene appears in all the lists. So that leaves two mentioned by John to be accounted for. The easiest solution is to identify Mary (wife?) of Clopas with Mary mother of James and Joses (Joseph). The unnamed sister of Jesus mother could be Salome, mentioned by Mark alone; she could also be the unnamed mother of the sons of Zebedee, who is included in Matt 27:56. This last suggestion greatly attracts a number of expositors, since it makes James and John, the sons of Zebedee, the cousins of Jesus. The traditional identification of John the son of Zebedee with the Beloved Disciple helps to explain his close relationship with Jesus in the ministry. Moreover, it makes more comprehensible the immediately following scene, in which Jesus commits his mother to the Beloved Disciple." In The Easter Enigma, Appendix II, pp , John Wenham provides detailed argument for believing that (contra Barrett and I. H. Marshall) Mary Magdalene (of Luke 8) is to be identified with the sinner of Luke 7. This sinner, he argues (see the summary given at the beginning of John 12) is the same as Mary the sister of Martha. On this argument Mary Magdalene is sister to Martha and Lazarus. Verse 26 Ἰησοῦς οὖν ἰδὼν τὴν μητέρα καὶ τὸν μαθητὴν παρεστῶτα ὃν ἠγάπα λέγει τῇ μητρί Γύναι, ἴδε ὁ υἱός σου ἰδων Verb, aor act ptc, m nom s ὁραω see, observe μαθητης, ου m disciple
4 παρεστῶτα Verb, perf act ptc, f nom s παριστημι stand by/beside γύναι Noun, voc s γυνη, αικος f woman Beasley-Murray comments, "His brief words to his mother and the disciple are not just a commendation or suggestion; they are more like a testamentary disposition, in language reminiscent of adoption." Verse 27 εἶτα λέγει τῷ μαθητῇ Ἴδε ἡ μήτηρ σου. καὶ ἀπʼ ἐκείνης τῆς ὥρας ἔλαβεν ὁ μαθητὴς αὐτὴν εἰς τὰ ἴδια. εἰτα adv. then ἐκεινος, η, ο demonstrative adj. that ὡρα, ας f hour, moment ἔλαβεν Verb, aor act indic, 3 s λαμβανω ἰδιος, α, ον one's own; τα ἰδια home It is quite unnecessary to seek allegorical meanings for what is narrated here. In the agony of his death, Jesus' concerns are not for himself but for his family and for his disciples. Verse 28 Μετὰ τοῦτο εἰδὼς ὁ Ἰησοῦς ὅτι ἤδη πάντα τετέλεσται ἵνα τελειωθῇ ἡ γραφὴ λέγει Διψῶ. εἰδως Verb, perf act ptc, m nom s οἰδα know "From first to last in this passion narrative Jesus is in control of all that takes place. The whole train of events is set in motion by him, and at the appropriate moment he will terminate it." Barrett. ἠδη adv now, already τετέλεσται Verb, perf pass indic, 3 s τελεω complete, finish, fulfill τελειωθῇ Verb, aor pass subj, 3 s τελειοω complete, accomplish γραφη, ης f writing, Scripture διψαω be thirsty, thirst Ps 69(68):21. See also Mk 15:36; Matt 27:48 and Lk 23:36. Beasley-Murray comments, "The saying is part of the lengthy description of the desolation, isolation, and scorn experienced by the Righteous Sufferer, and in the psalm the giving of the drink appears to be part of the torment inflicted upon the sufferer. If Mark cites the event as linked with the cry of desolation from the cross (Ps 22:11), John underscores the reality of the desolation by his specific citation of the scripture, for the thought of Ps 69 is closely parallel to that of Ps 22. Dodd indeed thought that the cry 'I thirst' was a symbolical equivalent of the cry of desolation." Verse 29 σκεῦος ἔκειτο ὄξους μεστόν σπόγγον οὖν μεστὸν τοῦ ὄξους ὑσσώπῳ περιθέντες προσήνεγκαν αὐτοῦ τῷ στόματι. σκευος, ους n object, vessel κειμαι lie, be laid; be, exist ὀξος, ους n sour wine μεστος, η, ον full σπογγος, ου m sponge ὑσσωπος, ου m & f hyssop (a small bush with aromatic leaves used for ritual purification) Two minuscules, 476* and 1242, read ὑσσῳ, 'a javelin'. Hyssop would not be suitable to offer up a sponge to a crucified man (cf Mk 15:36 which has καλαμῳ, 'a rod'). Some, such as Dodd, think that a primitive error may have occurred and that the original was ὑσσῳ (so also Moffatt, Goodspeed, Phillips, Rieu, Williams, NEB). Barrett and Sanders suggest that John mentions hyssop because of its use in the Passover celebration (cf. Ex. 12:13). On the other hand, "although a branch of hyssop would not support a sodden sponge, a stalk of hyssop could. Indeed, the branches of the hyssop at the end of a stalk could form a little 'nest' to cradle the sponge. Roman crosses were not very high; the soldiers needed to raise the sponge barely above their own heads." Carson. περιθέντες Verb, aor act ptc, m nom pl περιτιθημι put around, put on προσήνεγκαν Verb, aor act indic, 3 pl προσφερω offer, present στομα, τος n mouth Beasley-Murray comments, "The action was certainly unusual for a member of a Roman execution squad on behalf of a crucified Jew he was guarding, not least in view of the treatment meted out to Jesus by his group and he may well have been one of them who engaged in the sport! Not surprisingly, some have wondered whether there is a link here with the synoptic account of the centurion who confessed Jesus as υἱὸς θεοῦ, 'Son of God,' in Mark 15:39." Verse 30 ὅτε οὖν ἔλαβεν τὸ ὄξος ὁ Ἰησοῦς εἶπεν Τετέλεσται, καὶ κλίνας τὴν κεφαλὴν παρέδωκεν τὸ πνεῦμα. ὁτε conj when ἔλαβεν Verb, aor act indic, 3 s λαμβανω τετέλεσται see v.28
5 His work is complete. Beasley-Murray comments, "The rendering, 'It is finished!' conveys only half the meaning. For the verb τελέω fundamentally denotes 'to carry out' the will of somebody, whether of oneself or another, and so to fulfill obligations or carry out religious acts. 'It is accomplished!' renders that aspect of the word. Doubtless both meanings of the term, the temporal and the theological, are intended here. 'So the last word of Jesus interprets his suffering and dying as the crowning conclusion and high point of the work that he has performed in obedience the obedience of the Son finds here its most radical expression and enables the believing eye to see the glorifying of the Son through the Father' (Dauer)." κλινω lay, bow κεφαλη, ης f head παραδιδωμι hand over, deliver up Cf. Mk 15:37; Lk 23:46; Matt 27:50. "The term παρέδωκεν, however, is stronger than the verbs used in the synoptic Gospels, and it is possible that it reflects the thought in 10:18, 'I have authority to lay down (my life). ' The death of Jesus is then 'a conscious act a selfoffering to the Father' (Schnackenburg)" Beasley-Murray. Verse 31 Οἱ οὖν Ἰουδαῖοι, ἐπεὶ παρασκευὴ ἦν, ἵνα μὴ μείνῃ ἐπὶ τοῦ σταυροῦ τὰ σώματα ἐν τῷ σαββάτῳ, ἦν γὰρ μεγάλη ἡ ἡμέρα ἐκείνου τοῦ σαββάτου, ἠρώτησαν τὸν Πιλᾶτον ἵνα κατεαγῶσιν αὐτῶν τὰ σκέλη καὶ ἀρθῶσιν. ἐπει since, because παρασκευη, ης f day of preparation (before a sacred day) Here clearly meaning a day of preparation for the Sabbath (cf. Mk 15:42), cf. v. 14. μενω remain, stay σωμα, τος n body "Jewish law laid it down that one that is hanged (usually after execution) should not remain on a gibbet overnight, since a hanged man is accursed in God s sight and pollutes the land (Deut 21:22, 23)." Beasley-Murray. μεγας, μεγαλη, μεγα large, great I.e. not just a Sabbath but also part of a special festival. ἐκεινος, η, ο demonstrative adj. that ἐρωταω ask, request κατεαγῶσιν Verb, aor pass subj, 3 pl καταγνυμι break σκέλη Noun, nom/acc pl σκελος, ους n leg "Romans left crucified men to linger till their death, sometimes for several days, and then the vultures finished them off. If there was any reason for hastening the death of crucified men, their legs were smashed with an iron mallet, so causing great loss of blood and asphyxia It is of interest that the bones of a man crucified in this period, discovered in the area north of Jerusalem, had been broken; one leg was simply fractured, the other was smashed to pieces" Beasley-Murray. ἀρθῶσιν Verb, aor pass subj, 3 pl αἰρω take, take away Verse 32 ἦλθον οὖν οἱ στρατιῶται, καὶ τοῦ μὲν πρώτου κατέαξαν τὰ σκέλη καὶ τοῦ ἄλλου τοῦ συσταυρωθέντος αὐτῷ ἦλθον Verb, aor act ind, 1s & 3 pl ἐρχομαι στρατιωτης, ου m soldier πρωτος, η, ον first κατέαξαν Verb, aor act indic, 3 pl καταγνυμι ἀλλος, η, ο another, other συσταυρωθέντος Verb, aor pass ptc, m gen s συσταυροομαι be crucified together (with someone else) Verse 33 ἐπὶ δὲ τὸν Ἰησοῦν ἐλθόντες, ὡς εἶδον ἤδη αὐτὸν τεθνηκότα, οὐ κατέαξαν αὐτοῦ τὰ σκέλη, εἶδον Verb, aor act ind, 1s & 3pl ὁραω see ἠδη see v.28 τεθνηκότα Verb, perf act ptc, m acc s θνῃσκω die; pf be dead "So speedy a death was unusual. Victims of crucifixion sometimes lingered for days. Cf. Mark 15:44, ἐθαυμασεν εἰ ἠδη τεθνηκεν." Barrett. Verse 34 ἀλλʼ εἷς τῶν στρατιωτῶν λόγχῃ αὐτοῦ τὴν πλευρὰν ἔνυξεν, καὶ ἐξῆλθεν εὐθὺς αἷμα καὶ ὕδωρ. εἱς, μια, ἑν gen ἐνος, μιας, ἑνος one λογχη, ης f spear πλευρα, ας f side (of the body) ἔνυξεν Verb, aor act indic, 3 s νυσσω prick, stab εὐθυς adv. straightway, immediately αἱμα, ατος f blood ὑδωρ, ὑδατος n water
6 Most commentators (Dodd, Lindars, Barrett, Sanders) look for a 'spiritual' meaning in this passage and link it with earlier teaching by John on eternal life, water, Spirit and blood. Barrett, for instance, says, "It is highly probable then that in the effusion of blood and water from the pierced side of Christ John saw a symbol of the fact that from the Crucified there proceed those living streams by which men are quickened and the Church lives. Nor can it be accidental that water signifies baptism and regeneration, and the blood the eucharistic cup." It is safer, rather, to see this as evidence of the real humanity of Jesus and of the reality of his death. Verse 35 καὶ ὁ ἑωρακὼς μεμαρτύρηκεν, καὶ ἀληθινὴ αὐτοῦ ἐστιν ἡ μαρτυρία, καὶ ἐκεῖνος οἶδεν ὅτι ἀληθῆ λέγει, ἵνα καὶ ὑμεῖς πιστεύητε. ἑωρακως Verb, perf act ptc, m nom s ὁραω μαρτυρεω bear witness, testify These two words are characteristic of John, cf. 1:34; 3:11. "It is generally inferred, probably rightly, that this witness is the beloved disciple (vv ), responsible for the Fourth Gospel as a whole." Carson. ἀληθινος, η, ον real, genuine, true μαρτυρια, ας f testimony ἐκεινος, η, ο demonstrative adj. that (one), he Probably Jesus, or the Father. οἰδα know, understand ἀληθης, ες true, genuine πιστεύσητε Verb, aor act subj, 2 pl πιστευω believe (in), have faith (in) "This clause is only loosely constructed with the sentence, as will appear if an attempt is made to take it closely with ἀληθινη ἐστιν, οἰδεν, or λεγει. It indicates the general aim of the veracious testimony of the witness. 'You' (the readers of the gospel) 'are not merely to believe that blood and water did in fact issue from the side of the Crucified, but to believe in the full Christian sense' (cf. 20:31 for the aim of the gospel as a whole)." Barrett. Verse 36 ἐγένετο γὰρ ταῦτα ἵνα ἡ γραφὴ πληρωθῇ Ὀστοῦν οὐ συντριβήσεται αὐτοῦ. ἐγένετο Verb, aor midd dep indic, 3 s γινομαι πληρωθῇ Verb, aor pass subj, 3 s πληροω fill, fulfill ὀστεον, ου and ὀστουν, ου n bone συντριβήσεται Verb, fut pass indic, 3 s συντριβω break in pieces, shatter "It is difficult to give the source of this quotation. Three or four Old Testament passages come under consideration: Ex 12:10 (cf. v.46), Num 9:12; Ps 34(33):20. The Pentateuchal passages refer to the passover sacrifice, of which no bone may be broken; that in the Psalter refers to God's care of the faithful (κυριος θυλασσει παντα τα οστα αὐτων)." Barrett. Lindars thinks the Evangelist had both typologies in mind. Carson thinks the Pentateuchal references more likely. Verse 37 καὶ πάλιν ἑτέρα γραφὴ λέγει Ὄψονται εἰς ὃν ἐξεκέντησαν. παλιν again ἑτερος, α, ον other, another, different ὄψονται Verb, fut midd dep indic, 3 pl ὁραω see ἐκκεντεω pierce Accurately follows the Hebrew of Zech 12:10. Beasley-Murray comments, "Zech 12:10 was an important testimony in the primitive Church, as its use in Matt 24:30; Rev 1:7, and this passage shows In Matthew and Revelation the lamentation takes place at the coming of the Son of Man, and it is unclear whether it is through remorse or in repentance. The application in John 19:37 is not to be restricted to the end of the age; in statements in the Gospel concerning 'seeing' the Son of Man lifted up, the primary emphasis is on salvation. The link between this citation and that concerning the Lamb who brings deliverance at the second Exodus (or the Righteous Man whose sufferings bring salvation) suggests that the salvation aspect is to the fore here also. Naturally the obverse of judgment for those who persist in looking on the Redeemer in unbelief is not excluded." Carson adds, "But if there is uncertainty in the referent of They, and debate as to when all will see the one they have pierced, there is little doubt about John's Christological purpose. John's first readers, familiar with their Bibles, would remember the references in Zechariah to God's promised shepherd, and remember that Jesus said, 'I am the good shepherd. The good shepherd lays down his life for the sheep' (10:11). They might also remember that the next chapter of Zechariah begins with the words, 'On that day a fountain will be opened to the house of David and the inhabitants of Jerusalem, to cleanse them from sin and impurity.' And it would be hard for them not to reflect on the flow of blood and water from Jesus' side, the promise of the Spirit (7:37-39) and the cleansing and life that issue from these new covenant promises."
7 Verse 38 Μετὰ δὲ ταῦτα ἠρώτησεν τὸν Πιλᾶτον Ἰωσὴφ ἀπὸ Ἁριμαθαίας, ὢν μαθητὴς τοῦ Ἰησοῦ κεκρυμμένος δὲ διὰ τὸν φόβον τῶν Ἰουδαίων, ἵνα ἄρῃ τὸ σῶμα τοῦ Ἰησοῦ καὶ ἐπέτρεψεν ὁ Πιλᾶτος. ἦλθεν οὖν καὶ ἦρεν τὸ σῶμα αὐτοῦ. ἐρωταω see v.31 "All four Gospels tell of Joseph of Arimathea s going to Pilate and requesting that he might remove the body of Jesus. The synoptic Gospels yield information not in John: that Joseph was a member of the Sanhedrin (Mark 15:43 par.), and so a resident of Jerusalem; that he was one who looked for the kingdom of God (Mark 15:43; Luke 23:51); that he was rich (Matt 27:57); and that he dissented from the policy and actions of the Sanhedrin regarding Jesus (Luke 23:50 51). Matthew also speaks of him as a disciple of Jesus (27:57); John alone adds, 'but a secret one through fear of the Jews'." Beasley-Murray. κεκρυμμένος Verb, perf pass ptc, m nom s κρυπτω hide φοβος, ου m fear ἄρῃ Verb, aor act subj, 3 s αἰρω take (away) σωμα, τος n body ἐπιτρεπω let, allow, permit ἦρεν Verb, aor act indic, 3 s αἰρω "Commonly the crucified were left to vultures. Exceptions could be made only as an act of grace by the authorities, and that gesture to relatives who so petitioned. Usually the body was granted, but never when the offense was lèse-majesté. The Jews could not bring themselves to deny those they executed a burial, but neither did they allow such to be buried in family tombs, for fear of the executed contaminating those already buried in them. Accordingly they provided a burial place for executed criminals away from the city It was therefore an uncommonly courageous act for Joseph to dissociate himself from the Sanhedrin and to show his sympathy with Jesus, who had been so ignominiously condemned and killed. He will have been aware that he had no right to make the request, since he was unrelated to Jesus. But he was equally aware that none of the brothers of Jesus would attempt to take this step. His position and wealth naturally will have commended him to Pilate; nevertheless he should have been denied what he asked in view of the nature of Jesus offense against Caesar. That Pilate acceded to it is in line with John s whole account of the trial of Jesus. Pilate knew well that the charge against Jesus was unfounded, and so he released the body to Joseph." Beasley-Murray. Verse 39 ἦλθεν δὲ καὶ Νικόδημος, ὁ ἐλθὼν πρὸς αὐτὸν νυκτὸς τὸ πρῶτον, φέρων μίγμα σμύρνης καὶ ἀλόης ὡς λίτρας ἑκατόν. ἐλθων Verb, aor act ptc, m nom s ἐρχομαι John alone mentions the involvment of Nicodemus another sympathyser from among the Sanhedrin. νυξ, νυκτος f night πρωτον i) adv. first; ii) equivalent to prep with gen before φερω bring, carry μιγμα, τος n mixture Instead of μίγμα (= 'mixture'), attested by P 66vid א c A D supp K L X Δ Θ etc, ἔλιγμα, 'a fold, wrapping' appears in א * B W cop boms, σμῆγμα, 'ointment,' in 1242 *, and σμίγμα, a variation of μίγμα, in Ψ etc The first reading has superior attestation and probability. σμυρνα, ης f myrrh (a resinous gum used for aromatic purposes) ἀλοη, ης f aloes (aromatic tree sap used for a burial ointment) λιτρα, ας f pound (of the Roman pound weighing 11.5 oz) ἑκατον one hundred
8 The total weight was about 35 kilos (75 pounds). Beasley-Murray comments, "Selfevidently Nicodemus would not normally have on hand the amount of spices here mentioned. There must have been an urgent collaboration with Joseph while Jesus was dying, and so Joseph procured the grave clothes and Nicodemus the spices." The purpose of the spices, as used by the Jews, was not to embalm but to stifle the smell of putrefaction. Verse 40 ἔλαβον οὖν τὸ σῶμα τοῦ Ἰησοῦ καὶ ἔδησαν αὐτὸ ὀθονίοις μετὰ τῶν ἀρωμάτων, καθὼς ἔθος ἐστὶν τοῖς Ἰουδαίοις ἐνταφιάζειν. δεω bind, tie ὀθονιον, ου n linen cloth, wrapping ἀρωμα, ατος n aromatic spice or oil ἐθος, ους n custom, practice ἐνταφιαζω prepare for burial Verse 41 ἦν δὲ ἐν τῷ τόπῳ ὅπου ἐσταυρώθη κῆπος, καὶ ἐν τῷ κήπῳ μνημεῖον καινόν, ἐν ᾧ οὐδέπω οὐδεὶς ἦν τεθειμένος τοπος, ου m place Here meaning 'vicinity' ὁπου adv. where σταυροω crucify κηπος, ου m garden Cf. 18:1 μνημειον, ου n grave, tomb καινος, η, ον new οὐδεπω adv not yet οὐδεις, οὐδεμια, οὐδεν no one, nothing τεθειμένος Verb, aor pass ptc, m nom s τιθημι place, set Cf. Lk 23:55 Verse 42 ἐκεῖ οὖν διὰ τὴν παρασκευὴν τῶν Ἰουδαίων, ὅτι ἐγγὺς ἦν τὸ μνημεῖον, ἔθηκαν τὸν Ἰησοῦν. ἐκει there παρασκευὴν see v.31 ἐγγυς adv near ἔθηκαν Verb, aor act indic, 3 s τιθημι Carson comments, "John does not mention that Joseph rolled a stone across the tomb's mouth, or that Mary Magdalene and Mary the mother of Joses saw where Jesus was laid (Mk. 15:46-47 par.), but both details are assumed by the opening verses of the next chapter."
+Stative. Greek aspect. +Perfective Perfective +Imperfective +Stative +Remote Imperfect Pluperfect Aorist
The Stative Aspect and Its Discourse Function in Koine Greek Paper presented by Toshikazu S. Foley at the Biblical and Theological Seminar 10:30 A.M. 12:00, November 21, 2011, China Evangelical Seminary,
Διαβάστε περισσότεραChapter 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 περισσότεραWEEK 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 περισσότεραCHAPTER 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 περισσότεραΣυντακτικές 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 περισσότεραLESSON 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 περισσότεραAdjectives. 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 περισσότεραEE512: 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 περισσότεραNotes on the Greek New Testament Week 228 John 19:4-37
Notes on the Greek New Testament Week 228 John 19:4-37 Day 1136: John 19:4-7 Verse 4 Καὶ ἐξῆλθεν πάλιν ἔξω ὁ Πιλᾶτος καὶ λέγει αὐτοῖς, Ἴδε ἄγω ὑµῖν αὐτὸν ἔξω, ἵνα γνῶτε ὅτι οὐδεµίαν αἰτίαν εὑρίσκω ἐν αὐτῷ.
Διαβάστε περισσότεραLESSON 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 περισσότεραPhys460.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 περισσότεραEvery 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 περισσότεραHOMEWORK 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 περισσότεραRight 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 περισσότεραCode 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 περισσότεραthe 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 περισσότεραFinite 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 περισσότεραSection 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 περισσότερα2 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 περισσότεραdepartment 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 περισσότεραChapter 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 περισσότερα14 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 περισσότεραΟι 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 περισσότεραΑΓΓΛΙΚΗ 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 περισσότεραderivation 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 περισσότεραΤΕΧΝΟΛΟΓΙΚΟ 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 περισσότεραC.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 περισσότεραLESSON 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 περισσότεραThe 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 περισσότεραPresent 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 περισσότεραInstruction 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 περισσότεραMath 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Διαβάστε περισσότεραLESSON 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 περισσότερα1999 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 περισσότερα1 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 περισσότεραFINAL 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 περισσότεραConcrete 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 περισσότεραΕΠΙΧΕΙΡΗΣΙΑΚΗ 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 περισσότεραMath221: 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 περισσότεραWriting 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 περισσότεραSample Pages of John in Greek Σελίδες δειγμάτων John στα ελληνικά KEY WORDS AND PHRASES IN JOHN ΛΈΞΕΙΣ ΚΛΕΙΔΊ ΚΑΙ ΦΡΑΣΕΙΣ ΣΕ JOHN
Sample Pages of John in Greek Σελίδες δειγμάτων John στα ελληνικά KEY WORDS AND PHRASES IN JOHN ΛΈΞΕΙΣ ΚΛΕΙΔΊ ΚΑΙ ΦΡΑΣΕΙΣ ΣΕ JOHN BELIEVE (80 VERSES) ΘΕΩΡΗΣΤΕ (80 ΣΤΙΧΟΙ) 1:7 4:39 6:30 8:24 10:38 12:37
Διαβάστε περισσότερα7 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 περισσότεραHomework 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 περισσότερα3.4 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 περισσότεραPARTIAL 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 περισσότεραΚΥΠΡΙΑΚΗ 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 περισσότεραPotential 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 περισσότεραΠΑΝΕΠΙΣΤΗΜΙΟ 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 περισσότεραModern 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 περισσότεραLESSON 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 περισσότεραΣτην 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 περισσότεραSection 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 περισσότεραPolicy 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[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 περισσότεραΠΤΥΧΙΑΚΗ 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 περισσότεραΦΥΛΛΟ 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 περισσότεραOrdinal Arithmetic: Addition, Multiplication, Exponentiation and Limit
Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal
Διαβάστε περισσότεραGalatia 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 περισσότεραLESSON 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 περισσότερα5.4 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 περισσότεραΕΠΙΧΕΙΡΗΣΙΑΚΗ 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 περισσότεραΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
Διαβάστε περισσότεραNotes 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 περισσότεραSection 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 περισσότεραΙΠΛΩΜΑΤΙΚΗ 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 περισσότεραST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Διαβάστε περισσότεραΣυστήματα 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 περισσότεραΠώς 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 περισσότεραAdvanced 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 περισσότεραΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ - ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΕΠΛ 133: ΑΝΤΙΚΕΙΜΕΝΟΣΤΡΕΦΗΣ ΠΡΟΓΡΑΜΜΑΤΙΣΜΟΣ ΕΡΓΑΣΤΗΡΙΟ 3 Javadoc Tutorial
ΕΡΓΑΣΤΗΡΙΟ 3 Javadoc Tutorial Introduction Το Javadoc είναι ένα εργαλείο που παράγει αρχεία html (παρόμοιο με τις σελίδες στη διεύθυνση http://docs.oracle.com/javase/8/docs/api/index.html) από τα σχόλια
Διαβάστε περισσότεραNowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in
Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in : tail in X, head in A nowhere-zero Γ-flow is a Γ-circulation such that
Διαβάστε περισσότερα4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Διαβάστε περισσότεραΘΕΙΑΣ ΑΝΑΛΗΨΕΩΣ. Greek Orthodox Church. Ελληνική Ορθόδοξη Εκκλησία. Ecumenical Patriarchate Greek Orthodox Metropolis of New Jersey ASCENSION
Ecumenical Patriarchate Greek Orthodox Metropolis of New Jersey ASCENSION Greek Orthodox Church FAIRVIEW - NEW JERSEY Weekly Bulletin Sunday June 1 st, 2014 Fathers of the 1st Ecumenical Council Οικουμενικόν
Διαβάστε περισσότεραΕΠΙΧΕΙΡΗΣΙΑΚΗ 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 περισσότερα1 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 περισσότεραΕπιβλέπουσα 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 περισσότεραΕΠΙΧΕΙΡΗΣΙΑΚΗ 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 περισσότεραPractice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1
Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the
Διαβάστε περισσότεραVerklarte 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 περισσότερα6.1. 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 περισσότεραΟΙ 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 περισσότεραΑΓΓΛΙΚΑ 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 περισσότεραInverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Διαβάστε περισσότεραI 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 περισσότεραLecture 2. Soundness and completeness of propositional logic
Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness
Διαβάστε περισσότεραDoor Hinge replacement (Rear Left Door)
Door Hinge replacement (Rear Left Door) We will continue the previous article by replacing the hinges of the rear left hand side door. I will use again the same procedure and means I employed during the
Διαβάστε περισσότεραΚατανοώντας 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 περισσότεραεἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016
εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 Conditional Relative Clauses relative clauses referring to an indefinite person or thing (whoever, whatever, anyone,
Διαβάστε περισσότεραΚΥΠΡΙΑΚΟΣ 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 περισσότεραThe 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 περισσότεραANSWERSHEET (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 περισσότεραUniform Convergence of Fourier Series Michael Taylor
Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula
Διαβάστε περισσότεραDESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Διαβάστε περισσότεραExample 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 περισσότεραΑναερόβια Φυσική Κατάσταση
Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής
Διαβάστε περισσότεραOther Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Διαβάστε περισσότεραCroy 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 περισσότεραAssalamu `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