πρόσωπον, εὐπροσωπέω, προσωπολημψία, προσωπολήμπτης, προσωπολημπτέω, ἀποσωπολήμπτως πρόσωπον * A. Greek Usage.

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "πρόσωπον, εὐπροσωπέω, προσωπολημψία, προσωπολήμπτης, προσωπολημπτέω, ἀποσωπολήμπτως πρόσωπον * A. Greek Usage."

Transcript

1 πρόσωπον, εὐπροσωπέω, προσωπολημψία, προσωπολήμπτης, προσωπολημπτέω, ἀποσωπολήμπτως πρόσωπον * Contents: A. Greek Usage: 1. Face; 2. Mask; 3. Person. B. Septuagint and Later Jewish Usage: I. Septuagint: 1. Face; 2. Front Side; 3. God s Countenance; II. Later Judaism: 1. Philo and Josephus; 2. Pseudepigrapha and Rabbinic Writings. C. New Testament Usage: 1. Face; 2. Front Side; 3. God s Countenance; 4. Person. D. Early Church Usage: 1. πρόσωπον in the Post-Apostolic Fathers; 2. πρόσωπον in the Christology Teaching of the Early Church. A. Greek Usage. The basic meaning of the word πρόσωπον is face, countenance. Cf. the def. in Aristot. Hist. An., I, 8, p. 491b, 9: τὸ δʼ ὑπὸ τὸ κρανίον ὀνομάζεται πρόσωπον before the heading of an article indicates that all the New Testament passages are mentioned in it. * πρόσωπον. On A.: Preisigke Wört., If, 421 f.; Liddell-Scott, s.v..; Pr.-Bauer 5, s.v.; K. Praechter, Πρόσωπον, Philol., 63 (1904), 155f.; S. Schlossmann, Persona u. ΠΡΟΣΩΠΟΝ im Recht u. im chr. Dogma (1906); A. Trendelenburg, Zur Gesch. des Wortes Person, Kantstudien, 13 (1908); R. Hirzel, Die Person, Begriff u. Name derselben im Altertum, S. A. Münch, 1914, 10 (1914); H. Rheinfelder, Das Wort Persona, Gesch. seiner Bdtg. mit besonderer Berücksichtigung d. französischen u. italienischen Mittelalters, Beih. zur Zschr. f. Romanische Philologie, 77 (1928); F. Altheim, Persona, ARW, 27 (1929), 35 52; M. Nédoncelle, Prosopon et persona dans l antiquité class., Revue des Sciences Religieuses, 22 (1948), ; L. Malten, Die Sprache des menschlichen Antlitzes in d. Antike, Forschungen u. Fortschritte. 27 (1953), On B.: J. Boehmer, Gottes Angesicht, BFTh, 12 (1908), ; W. W. Graf Baudissin, Gott schauen in d. at.lichen Religion, ARW, 18 (1915), ; E. G. Gulin, Das Antlitz Jahwes im AT, Annales Academiae Scientiarum Fennicae, 17, 3 (1923); F. Nötscher, Das Angesicht Gottes schauen, nach bibl. u. babyl. Auffassung (1924); J. Morgenstern, Moses with the Shining Face, Hebrew Union Coll. Ann., 2 (1925), 1 28; Johannessohn Präpos.; H. Middendorf, Gott sieht, eine terminologische Studie über d. Schauen Gottes im AT, Diss. Freiburg (1935); A. R. Johnson, The Vitality of the Individual in the Thought of Ancient Israel (1949), On C.: S. Antoniadis, Neotestamentica, I, Neophilologus, 14 (1929), On D.: Schlossmann; A. Grillmeier, Das Konzil v. Chalkedon, I (1951), def. Definition, definition. Aristot. Aristotle, of Stageiros (c B.C.), with his teacher Plato the greatest of the Greek philosophers and the founder of the peripatetic school, quoted in each case from the comprehensive edition of the Academia Regia Borussica, 1831 ff.

2 προσώπου δὲ τὸ μὲν ὑπὸ τὸ βρέγμα (front of the head) μεταξὺ τῶν ὀμμάτων μέτωπον. 1 Understanding of the other uses rests on this basic sense. V 6, p Face. The word πρόσωπον occurs first in Hom. and here it is almost always used in the plur, to denote the face or countenance of man: γρῆυς δὶ κατέσχετο χερσὶ πρόσωπα, Od., 19, 361; σπόγγῳ δʼ ἀμφὶ πρόσωπα ἀπομόργνυ, Il., 18, 414; also Od., 20, 352; Il., 7, 212, though also sing.: χαρίεν δʼ ᾔσχυνε πρόσωπον Il., 18, 24. The plur. is also found occasionally in the tragedians: Electra says to Orestes: μή μʼ ἀποστερήσῃς τῶν σῶν προσώπων ἁδονὰν μεθέσθαι, Soph. El., 1277, cf. also Oed. Col., 314; Aesch. Ag., 794. The plural use shows that not the organ of the eye is alone or predominantly felt to be that which controls expression but the part about the mouth. For the Greeks the part about the eyes is dominant in the whole oval of the front side of the human head. 2 Already from an early period, however, there is a use in the sing. which later becomes the rule, Hes. Hist. An. Historia Animalium. 1 One cannot accept the old explanation Thes. Steph., VI, 2048: πρόσωπον == quod est circa oculos; Pars, quae est circa oculos; τὸ πρὸς τοῖς ὠψὶ μέρος. For hypostatisation from προς (earlier *προτϳ ) -ωπ is certain, but the underlying idea is hard to fix; it is certainly not circa oculos (πρός does not mean circa; the basic sense is over against ). New attempts: what is directed to the eyes (of another), Schwyzer, II, 517, n. 1; πρόσωπα the part of the head which is toward the eyes, F. Sommer, Zur Gesch. d. gr. Nominalkomposita, A. A. Münch, NF, 27 (1948), 115, n. 1 (though this fits only men and not animals). [Debrunner] Hom. Homer, of Chios (?), the classical Greek epic poet, around whose name were grouped the older epics of the Ionians in the 9th and 8th centuries B.C., ed. G. Monro and T. W. Allen, 1908 ff. Od. Odyssey. Il. Iliad. Od. Odyssey. Il. Iliad. sing. singular. Il. Iliad. plur. plural. Soph. Sophocles, of Athens ( B.C.), the real poet of the Athens of Pericles, ed. A. C. Pearson, El. Electra. Oed. Col. Oedipus Coloneus. Aesch. Aeschylus, of Eleusis near Athens ( B.C.), the first of the three great Attic dramatists, ed. U. v. Wilamowitz, 1915; Fragments, ed. A. Nauck in Tragicorum Graecorum Fragmenta, Ag. Agamemnon. 2 Malten, 24 f. sing. singular.

3 Op., 594; Aesch. Ag., 639; Soph. Oed. Tyr., 448; Eur. Hipp., 280, 720; Aristoph. Av., 1321; Simonides, 3 37, 12; Plat. Euthyd., 275e; Leg., IX, 854d; Xenoph. Cyrop., II, 2, 29; Demosth. Or., 18, 283; for the Hell. period cf. Wilcken Ptol., 70, 5; BGU, III, 909, 12; καὶ πολλὰ ἀσελγήματα λέγων εἰς πρόσωπόν μου, P. Oxy., VI, 903, 21. Normally the Gk. uses the term only for the face of men, though sometimes also for the face of gods (Eur. Ion, 1550), but not for that of animals: 4 τὸ δʼ ὑπὸ τὸ κρανίον ὀνομάζεται πρόσωπον ἐπὶ μόνου τῶν Hes. Hesiodus, of Ascra in Boetia (c. 700 B.C.), the oldest Greek poet to emerge as a tangible figure. In his Pastoral Calendar ἔργα καὶ ἡμέραι he proclaims the pastoral ideal of life. His Theogony is a speculative work on the origin and descent of the gods, ed. A. Rzach, Op. Opera et Dies. Aesch. Aeschylus, of Eleusis near Athens ( B.C.), the first of the three great Attic dramatists, ed. U. v. Wilamowitz, 1915; Fragments, ed. A. Nauck in Tragicorum Graecorum Fragmenta, Ag. Agamemnon. Soph. Sophocles, of Athens ( B.C.), the real poet of the Athens of Pericles, ed. A. C. Pearson, Oed. Tyr. Oedipus Tyrannus. Eur. Euripides, of Salamis nr. Athens ( B.C.), tragic dramatist and philosopher of the stage, ed. G. Murray, 1901 ff. Hipp. Hippolytus. Aristoph. Aristophanes, of Athens (c B.C.), the main representative of the older Attic comedy, who reached his height during the Peloponnesian War, ed. V. Coulon and H. van Daele, 1923 ff. Av. Aves. 3 ed. T. Bergk, Poetae Lyrici Graeci, III (1882). Plat. Plato, of Athens (428/7 348/7 B.C.), ed. J. Burnet, Euthyd. Euthydemus. [Plato, of Athens] Leg. Leges. [Plato, of Athens] Xenoph. Xenophon, of Athens (c B.C.), pupil of Socrates, author of various historical, philosophical and scholarly works, ed. E. C. Marchant, 1900 ff. Cyrop. Cyropaedia. Demosth. Demosthenes, of Athens ( B.C.), ed. F. Blass, 1903 ff. Or. Orati(ones). Wilcken Ptol. U. Wilcken, Urkunden der Ptolemäerzeit, 1922 ff. BGU Ägyptische Urkunden aus den Kgl. Museen zu Berlin, 1895 ff. P. Oxy. The Oxyrhynchus Papyri, ed. B. Grenfell and A. Hunt, 1898 ff. Gk. Greek. Eur. Euripides, of Salamis nr. Athens ( B.C.), tragic dramatist and philosopher of the stage, ed. G. Murray, 1901 ff. 4 Hirzel, 47.

4 ἄλλων ζῴων ἀνθρώπου ἰχθύος γὰρ καὶ βοὸς οὐ λέγεται πρόσωπον, Aristot. Hist. An., I, 8, p. 491b, 9. Yet there are occasional exceptions to this rule: of the ibis Hdt., II, 76; πρόσωπα (ἐλάφων), Aristot. Hist. An., VI, 29, p. 579a, 2; πρόσωπον τῆς ἵππου, ibid., IX, 47, p. 631a, 5. Since the face controls the whole appearance πρόσωπον can sometimes be used for form or figure : εὐφυὲς πρόσωπον Eur. Med., The fixed combination κατὰ πρόσωπον serves to denote personal presence : τὴν κατὰ πρόσωπον ἔντευξιν oral, personal converse, Plut. Caesar, 17 (I, 716a); κατὰ πρόσωπον λόγους ἐποιήσαντο, Inscr. Magn., 93b, 11; καὶ ἐπερωτηθεὶς παρʼ αὐτοῦ κατὰ πρόσωπον αὐτοῦ ὡμολόγησεν, and asked by him he told him eye to eye, Preisigke Sammelb., I, 5174, 15. Cf. also Inschr. Priene, 41, 6; Ditt. Or., II, 441, 66; P. Oxy., VII, 1071, 1. Fig. πρόσωπον is often used for front esp. in military contexts: τὴν κατὰ πρόσωπον τῆς φάλαγγος τάξιν, Xenoph. Cyrop., VI, 3, 35; ἐν τῇ κατὰ πρόσωπον πλευρᾷ, Polyb., Aristot. Aristotle, of Stageiros (c B.C.), with his teacher Plato the greatest of the Greek philosophers and the founder of the peripatetic school, quoted in each case from the comprehensive edition of the Academia Regia Borussica, 1831 ff. Hist. An. Historia Animalium. Hdt. Herodotus, of Halicarnassus (c B.C.), the first real Greek historian, described as early as Cicero as the father of history. His work deals with the conflicts between the Greeks and the barbarians from earliest times to the Persian Wars, ed. H. Kallenberg, 1926 ff. Aristot. Aristotle, of Stageiros (c B.C.), with his teacher Plato the greatest of the Greek philosophers and the founder of the peripatetic school, quoted in each case from the comprehensive edition of the Academia Regia Borussica, 1831 ff. Hist. An. Historia Animalium. Eur. Euripides, of Salamis nr. Athens ( B.C.), tragic dramatist and philosopher of the stage, ed. G. Murray, 1901 ff. Med. Medea. Plut. Plutus. Inscr. Magn. Inscriptions of Magnesia on the Meander, ed. O. Kern, Preisigke Sammelb. F. Preisigke, Sammelbuch griechischer Urkunden aus Ägypten, 1915 ff. Inschr. Priene Priene Inscriptions, ed. F. Hiller v. Gärtringen, Ditt. Or. W. Dittenberger, Orientis Graecae Inscriptiones, 1902 ff. P. Oxy. The Oxyrhynchus Papyri, ed. B. Grenfell and A. Hunt, 1898 ff. esp. especially. Xenoph. Xenophon, of Athens (c B.C.), pupil of Socrates, author of various historical, philosophical and scholarly works, ed. E. C. Marchant, 1900 ff. Cyrop. Cyropaedia. Polyb. Polybius, of Megalopolis, in Arcadia (c B.C.), hostage of Rome in 167, general and statesman, and the greatest historian of Hellenism. In 40 books he depicts in essentials the rise of Roman world dominion in the period B.C., ed. T. Büttner-Wobst, 1905.

5 11, 23, 3; also Thuc., I, 106; Xenoph. Cyrop., I, 6, 43; Polyb., 11, 14, 6. Of the front of a building: κατὰ πρόσωπον τοῦ ἱεροῦ, P. Petr., III, 1 col. II, Mask. The mask worn by actors resembles a human face and is thus called πρόσωπον: 5 τὰ τραγικὰ πρόσωπα, Aristot. Probl., 31, 7, p. 958a, 17; ἄνευ προσώπου κωμάζει Demosth. Or., 19, 287; τὰ πρόσωπα τῶν θεῶν (sc. those who appear in the play), Luc. Jup. Trag., 41; πρόσωπον ὑπάργυρον κατάχρυσον, IG, I 2, 276, 6. 6 Later we also find προσωπεῖον (e.g., Jos. Bell., 4, 156) which is used exclusively for the actor s mask, though πρόσωπον is still found for this: ὥσπερ δὲ οἱ ἐν τοῖς θεάτροις δραμάτων τινῶν ὑποκριταὶ οὐχ ὅπερ λέγουσίν εἰσιν, οὐδʼ ὅπερ βλέπονται καθʼ ὃ περίκεινται πρόσωπον τοῦτο τυγχάνουσιν, Orig. Orat., 20, 2. Thuc. Thucydides, of Athens (c B.C.), the classic historian of the Greeks, who as a contemporary wrote a history of the Peloponnesian War, ed. C. Hude, 1898 ff. Xenoph. Xenophon, of Athens (c B.C.), pupil of Socrates, author of various historical, philosophical and scholarly works, ed. E. C. Marchant, 1900 ff. Cyrop. Cyropaedia. Polyb. Polybius, of Megalopolis, in Arcadia (c B.C.), hostage of Rome in 167, general and statesman, and the greatest historian of Hellenism. In 40 books he depicts in essentials the rise of Roman world dominion in the period B.C., ed. T. Büttner-Wobst, P. Petr. The Flinders Petrie Papyri, ed. J. P. Mahaffy and J. G. Smyly, 1891 ff. col. column. 5 Schlossmann, 37; Hirzel, 40 f. Aristot. Aristotle, of Stageiros (c B.C.), with his teacher Plato the greatest of the Greek philosophers and the founder of the peripatetic school, quoted in each case from the comprehensive edition of the Academia Regia Borussica, 1831 ff. Probl. Problemata. Demosth. Demosthenes, of Athens ( B.C.), ed. F. Blass, 1903 ff. Or. Orati(ones). Luc. Lucianus, of Samosata in Syria ( A.D.), best-known, though renegade, representative of the Second Sophistic School, rhetorician and lively satirist of his epoch, ed. C. Jacobitz, 1836; W. Dindorf, Jup. Trag. Juppiter Tragicus. 6 Editio minor, ed. F. Hiller v. Gärtringen (1924). Jos. Flavius Josephus, Jewish author (c A.D.) in Palestine and later Rome, author in Greek of the Jewish War and Jewish Archaeology, which treat of the period from creation to Nero, ed. B. Niese, 1887 ff. Bell. Bellum Judaicum. Orig. Origen, of Alexandria ( A.D.), pupil of Clement of Alexandria, and most learned and fruitful representative of ancient Christian scholarship and culture, ed.

6 Fig. πρόσωπον can then mean the part played by the actor: τριῶν δʼ ὄντων προσώπων καθάπερ ἐν ταῖς κωμῳδίαις τοῦ διαβάλλοντος καὶ τοῦ διαβαλλομένου καὶ τοῦ πρὸς ὃν ἡ διαβολὴ γίνεται Luc. Calumniae, 6; πρόσελθε ἐν προσώπῳ V 6, p 770 τοιούτῳ, Epict. Diss., I, 29, 45; τοῦτό μοι τὸ πρόσωπον ἀνάλαβε, I, 29, Acc. to Epict. it is every man s business to play well in life the role assigned specifically to him: τὸ δοθὲν ὑποκρίνεσθαι πρόσωπον καλῶς, Ench., 17. In the dialogues of the diatribe there was often presented the view of an anonymous opponent who was called κωφὸν πρόσωπον; the point was to present one s own view the more clearly in contrast: κωφὸν ὡς ἐπὶ σκηνῆς προσωπεῖον, Philo Flacc., 20; cf. also Plut. An Seni Sit Gerenda Res Publica, 15 (II, 791e) Person. In the Hell. period πρόσωπον takes on the sense of person to denote man in his position in human society. 9 The face, the eye is so distinctive for gods and men that a person by different scholars in Die griech, christl. Schriftsteller der ersten 3 Jahrhunderte, 1899 ff. Orat. De Oratione. Luc. Lucianus, of Samosata in Syria ( A.D.), best-known, though renegade, representative of the Second Sophistic School, rhetorician and lively satirist of his epoch, ed. C. Jacobitz, 1836; W. Dindorf, Epict. Epictetus, Phrygian slave of Hierapolis in the days of Nero ( A.D.), freed at the imperial palace, Stoic of the younger school and preacher of ethics tinged with religion. From his lectures his pupil Arrian collected 8 books of diatribes which have been preserved, ed. H. Schenkl 2, Diss. Dissertation. 7 The Gk. πρόσωπον is closely related to the Lat. persona, which can mean mask, role, person, also prominent personage, whereas the legal use of πρόσωπον, as will be shown, developed only later. Cf. Hirzel, 47 f. It is still a matter of debate whether or not the Lat. persona ( mask, person ) was borrowed from the Gk. πρόσωπον; if so, it could only be circuitously; cf. Walde-Hofmann, 291 f. [Debrunner]. Epict. Epictetus, Phrygian slave of Hierapolis in the days of Nero ( A.D.), freed at the imperial palace, Stoic of the younger school and preacher of ethics tinged with religion. From his lectures his pupil Arrian collected 8 books of diatribes which have been preserved, ed. H. Schenkl 2, Ench. Enchiridion. Philo Philo, of Alexandria (c. 20 B.C. 50 A.D.), ed. L. Cohn and P. Wendland. Flacc. In Flaccum. Plut. Plutus. 8 Cf. Dib. Jk. on 2:18. 9 Rheinfelder, 6 17 derives the use of πρόσωπον for person from the speech of the theatre: in the actor who plays Oedipus we see Oedipus. Thus persona as the husk becomes the kernel of the matter, 8. But this is too restricted a derivation.

7 is perceived in it. 10 πρόσωπον thus replaces other terms like σῶμα which had previously been used in the sense of person. 11 Whether πρόσωπον already means person in Polyb. is debated and cannot be proved beyond dispute. For ἐζήτουν ἡγεμόνα καὶ πρόσωπον in Polyb., 5, 107, 3 means they sought a leader and a man of esteem, while τὸ τῆς Ἑλλάδος ὄνομα καὶ πρόσωπον in 8, 13, 5 means the name and face of Greece. Again, the ref. of τὸ τοῦ Ὀδυσσέως πρόσωπον in 12, 27, 10 is more to his dramatic role, 769, 43 ff. 12 On the other hand, πρόσωπον certainly means person in the following passages: ξένοις προσώποις, foreign persons, P. Oxy., XIV, 1672, 4 (37 41 A.D.); μὴ κρῖνε πρόσωπον, Ps.-Phokylides, 10 (Diehl 3, II, 92); ὁ φθόνος ἅπτεται μάλιστα τῶν χρηστῶν καὶ αὐξομένων πρὸς ἀρετὴν καὶ δόξαν καὶ ἠθῶν καὶ πρόσωπων, Plut. De Invidia et Odio, 6 (II, 537 f.); ἐξ Αἰγυπτιακῶν προσώπων, P. Oxy., II, 237 col. VII, 34; cf. also Dion. Hal. De Thucydide, 34; Epict. Diss., I, 2, 7; Plut. De Garrulitate, 13 (II, 509b); P. Ryl., 28, 8. Grammarians then used πρόσωπον for grammatical person, Dion. Thr. Art. Gramm., 638b, 4; Apollon. Dyscol. De Pronominis Appellationibus, 1 10 Malten, Hirzel, In early times the term σῶμα could be used with no derogatory nuance. Only later did its stock decline so that it could be used for the slave with no sense of person. Polyb. Polybius, of Megalopolis, in Arcadia (c B.C.), hostage of Rome in 167, general and statesman, and the greatest historian of Hellenism. In 40 books he depicts in essentials the rise of Roman world dominion in the period B.C., ed. T. Büttner-Wobst, Polyb. Polybius, of Megalopolis, in Arcadia (c B.C.), hostage of Rome in 167, general and statesman, and the greatest historian of Hellenism. In 40 books he depicts in essentials the rise of Roman world dominion in the period B.C., ed. T. Büttner-Wobst, On the disputed ref. in Polyb. cf. Hirzel, 44 f. P. Oxy. The Oxyrhynchus Papyri, ed. B. Grenfell and A. Hunt, 1898 ff. Ps. Pseudo, often grouped under the names of the supposed authors, e.g., Ps.- or Pseud.-Plat. under Plato. Plut. Plutus. P. Oxy. The Oxyrhynchus Papyri, ed. B. Grenfell and A. Hunt, 1898 ff. col. column. Dion. Hal. Dionysius of Halicarnassus, from 30 B.C. a teacher of rhetoric in Rome, Atticist and historian, author of an old Roman history, ed. C. Jacoby, Epict. Epictetus, Phrygian slave of Hierapolis in the days of Nero ( A.D.), freed at the imperial palace, Stoic of the younger school and preacher of ethics tinged with religion. From his lectures his pupil Arrian collected 8 books of diatribes which have been preserved, ed. H. Schenkl 2, Diss. Dissertation. Plut. Plutus. P. Ryl. Catalogue of the Greek Papyri in the John Rylands Library at Manchester, ed. A. Hunt and others, Dion. Thr. Dionysius Thrax, Greek grammarian and rhetorician in Rhodes ( B.C.), ed. G. Uhlig, 1883.

8 c. 13 A technical use whereby πρόσωπον means a person legally is still not found in the first cent. A.D 14 In the 2nd cent. Phrynichos 15 complains that orators often spoke of πρόσωπα in court and in so doing offended against correct Gk. But only later, probably under the influence of the Lat. persona n. 7, did the word take on the technical sense which is then common in legal documents: οἱ τὸ σὸν πρόσωπον πληροῦντες, the representatives of thy person, Preisigke Sammelb., I, 6000, II, line 13 (6th cent.): τὴν ὠνὴν τὴν γενομένην εἰς πρόσωπον τοῦ σοῦ εἰρημένου ἀδελφοῦ ( in the name of thy brother ), ibid., line 25; ἀναπληροῦντες τὸ πρόσωπον τοῦ ἁγίο[υ μοναστηρίου], ibid., I, 5114, 49 (7th cent.). One may not assume that the word had this sense in the NT period or the age of the early Church. V 6, p 771 B. Septuagint and Later Jewish Usage. I. Septuagint. πρόσωπον occurs in the LXX over 850 times, in by far the greatest no. of instances for Heb. נ ים.פ It is also the rendering of א ף in Gn. 2:7; מ ר א ה in 1 Βασ. 16:7 A; ע ינ י ם in 1 Βασ. 16:7; Am. 9:4 A; פ ה in ψ 54:22 and א נ ף in Da. 3:19 LXX פ נ ים Θ; 16 is connected with the verb to turn and means the side turned to the fore, the face of man, the front of an inanimate obj. 17 The meaning of πρόσωπον in the LXX corresponds to this broad sense Art. Gramm. De Arte Grammatica. Apollon. Dyscol. Apollonius Dyscolus, important Greek grammarian of the Hadrian- Antoninus period in Alexandria, ed. R. Schneider and G. Uhlig in Grammatici Graeci, II ff. 13 Ed. R. Schneider-G. Uhlig in Grammatici Graeci, II, 1 (1878), 3, line On the question of the legal use of πρόσωπον cf. Schlossmann. 15 Ed. C. A. Lobeck (1820), 379. Gk. Greek. Lat. Latin, latin. 7 The Gk. πρόσωπον is closely related to the Lat. persona, which can mean mask, role, person, also prominent personage, whereas the legal use of πρόσωπον, as will be shown, developed only later. Cf. Hirzel, 47 f. It is still a matter of debate whether or not the Lat. persona ( mask, person ) was borrowed from the Gk. πρόσωπον; if so, it could only be circuitously; cf. Walde-Hofmann, 291 f. [Debrunner]. Preisigke Sammelb. F. Preisigke, Sammelbuch griechischer Urkunden aus Ägypten, 1915 ff. NT New Testament. no. number. Heb. Hebrew. 16 Prepositional combinations (ἀπὸ προσώπου etc.) and their Heb. originals are not counted. obj. object.

9 of the Heb. equivalent. 1. Face. πρόσωπον is very commonly used for face in the LXX: εἶδεν Ιακωβ τὸ πρόσοπον τοῦ Λαβαν, Gn. 31:2; τὸ πρόσωπον τοῦ πατρός, Gn. 50:1; πρόσωπον τοῦ παιδαρίου, 4 Βασ. 4:29, 31; ἔπεσεν Αβραμ ἐπὶ πρόσωπον αὐτοῦ, Gn. 17:3 a frequent expression for respectful greeting or veneration; ἀπέστρεψεν ὁ βασιλεὺς τὸ πρόσωπον αὐτοῦ, 3 Βασ. 8:14. To see the face of a king is to be admitted to audience, so that οἱ ὁρῶντες τὸ πρόσωπον τοῦ βασιλέως can be a title for court officials, 4 Βασ. 25: πρόσωπον πρὸς πρόσωπον נ ים א ל פ נ ים) (פ face to face, Gn. 32:30; Ju. 6:22; 19 cf. also πρόσωπον κατὰ πρόσωπον, Dt. 34:10. Often πρόσωπον is used for the face of animals too, e.g., πρόσωπον λέοντος, Ez. 1:10; 41:19; 1 Ch. 12:9. Sometimes πρόσωπον means features, appearance : συνέπεσεν (sc. Καιν) τῷ προσώπῳ, Gn. 4:5; poor appearance: τὰ πρόσωπα ὑμῶν σκυθρωπά, Gn. 40:7; appearance of a matter: τὸ πρόσωπον τοῦ ῥήματος τούτου, 2 Βασ. 14:20. Sometimes the face of a man can be spoken of in such a way as to denote the whole man. Thus it is said of Absalom in 2 Βασ. 17:11: τὸ πρόσωπόν σου πορευόμενον ἐν μέσῳ αὐτῶν, i.e., Absalom should go forth among the Israelites in person. In this connection ref. might also be made to the Heb. of Dt. 7:10, which says that Yahweh will cause the one who hates him to undergo in his own person א ל פ נ יו) LXX κατὰ πρόσωπον) retribution by destruction. 2. Front Side. As the Heb. פ נ ים ( the side to the front ) can be used of inanimate objects, so the LXX often uses πρόσωπον in this way: τὸ πρόσωπον τῆς γῆς, the surface of the earth, Gn. 2:6; σκοπεύων πρόσωπον Δαμασκοῦ ( towards ), Cant. 7:5; πρόσωπον (sc. τοῦ σιδηρίου), the edge of iron, Qoh. 10:10. In the broad sense of the front side πρόσωπον is found in countless instances with prepositions denoting direction to or from: Instead of simple prepositions the Semitic languages love to create fuller and more vivid expressions with the help of a noun which 17 Cf. Koehler-Baumg., s.v. and Johnson, 42 46, with good material on OT usage. Johnson aptly remarks on the plur. form :פ נ ים Indeed the fact that in Hebrew the use of this Semitic noun is restricted to the plur. form is sufficient to indicate the importance which was attached to what we should call one s features, 42. Heb. Hebrew. 18 Cf. Baudissin, 191; V, 325, 20 f. 19 Cf. ὀφθαλμοὶ πρὸς ὀφθαλμούς, Is. 52:8; στόμα πρὸς στόμα, Ἰερ. 39(32):4. Heb. Hebrew. Heb. Hebrew.

10 usually denotes a part of the body. 20 Like the Heb. original נ ים,פ πρόσωπον often serves simply to strengthen the prepos. on which it depends. 21 V 6, p 772 a. ἀπὸ (τοῦ) 22 προσώπου מ פ נ י) etc.) going out from, away from : ἀπὸ προσώπου κυρίου τοῦ θεοῦ, Gn. 3:8; φύγωμεν ἀπὸ προσώπου Ισραηλ, Ex. 14:25; ἐφοβήθητε ἀπὸ προσώπου τοῦ πυρός, Dt. 5:5; also Dt. 9:5; 4 Βασ. 13:23; 1 Ch. 16:30; ψ 37:4; Jdt. 5:8 etc. The fact that with a prepos. πρόσωπον is almost always a simple expletive may be seen from the MS tradition at Job 1:12 LXX: א B ἐξῆλθεν ὁ διάβολος παρὰ τοῦ (Α ἀπὸ προσώπου) κυρίου. b. εἰς (τὸ) πρόσωπον ע ל פ נ י,ב פ נ י) etc.) in or before the face : here πρόσωπον always means face or front : οὐκέτι ὀφθήσομαί σοι εἰς πρόσωπον, Ex. 10:29; εἰς πρόσωπόν σε εὐλογήσει, Job 2:5; cf. also 3 Βασ. 8:8; 2 Ch. 5:9; Hos. 5:5. 23 c. ἐκ (τοῦ) προσώπου מ פ נ י) etc.) from : ἐὰν οὖν λάβητε καὶ τοῦτον ἐκ προσώπου μου, Gn. 44:29; ἔφυγον ἐκ προσώπου αὐτοῦ, 1 Βασ. 19:8; ἐκ προσώπου σου τὸ κρίμα μου ἐξέλθοι, ψ, 16:2; cf. also 1 Βασ. 19:10; 21:11; 25:10; 31:1; 2 Βασ. 23:11 etc. d. ἐν προσώπῳ פ נ י) (ל before : ταπεινῶσαί δε ἐν προσώπῳ δυνάστου, Prv. 25:7. e. ἐπὶ προσώπου, ἐπὶ προσώπῳ ἐπὶ (τὸ) πρόσωπον ע ל פ נ י) etc. on : ὃ ἦν ἐπὶ προσώπου πάσης τῆς γῆς, Gn. 7:23; cf. also Gn. 11:4; 41:56; Dt. 14:2; Ez. 34:6 etc. In the phrase ἐπὶ πρόσωπον the word πρόσωπον often has its true sense face : ἔπεσεν Μωυσης καὶ Ααρων ἐπὶ πρόσωπον, Nu. 14:5; cf. Nu. 16:4, 22 etc.; ἤμην πεπτωκὼς ἐπὶ πρόσωπόν μου, Da. 10:9 LXX. f. κατὰ πρόσωπον ל פ נ י) etc.) before, over against : 24 κατὰ πρόσωπον πάντων τῶν ἀδελφῶν αὐτοῦ κατοικήσει, Gn. 16:12; κατὰ πρόσωπον τῆς πόλεως, Gn. 33:18; κατὰ πρόσωπον τοῦ ἱλαστηρίου, Lv. 16:14, 15; cf. also Nu. 3:38; Dt. 9:2; 11:25; Ἰερ. 18:17; 41(34):18. This is often used to denote geographical situation, e.g., ὅς ἐστιν κατὰ πρόσωπον Μαμβρη, Gn. 23:17; ἥ ἐστιν κατὰ προσωπον Αἰγύπτου, Gn. 25:18; κατὰ 20 Johannessohn, 348. Heb. Hebrew. 21 In this use we have definite Semitisms. Gk. knows only κατὰ πρόσωπον 769, 24 ff. 22 Since these are transl. of Semitic expressions, the art. may be left out. Cf. Bl.-Debr. 259, 1. MS Maaser Scheni, Mishnah-, Tosefta-, Talmud tractate The Second Tithe (Strack, Einl., 35). 23 In a lit. rendering of the Heb. ל פ נ י Ἀ Gn. 17:1 has περιπάτει εἰς πρόσωπόν μου. Cf. P. Katz, Notes on the Septuagint, JThSt, 47 (1946), 31 f. 24 The κατὰ πρόσωπον found in Gk. lit. never takes a dependent case except in later Egypt. pap.: κατὰ πρόσωπον τοῦ ἱεροῦ, P. Petr., III, 1 col. II, 8 769, 33. Cf. κατὰ πρόσωπον τοῦ ναοῦ in Ez. 41:4. Materially cf. Johannessohn, 248, n. 2.

11 πρόσωπον τῆς Ἀραβίας, Jdt. 2:25. g. μετὰ τοῦ προσώπου ת פ נ ים) :(א πληρώσεις με εὐφροσύνης μετὰ τοῦ προσώπου σου ( with thee ), ψ 15:11. h. πρὸ προσώπου מ ל פ נ י,ל פ נ י) etc.) before : 25 ἀποστέλλω τὸν ἄγγελόν μου πρὸ προσώπου σου, Ex. 23:20; cf. also Ex. 32:34; Nu. 14:42; Dt. 3:18; 30:1; Ἰερ. 21:8; Mal. 3:1; Jdt. 10:13; 2 Βασ. 6:14 Ἀ etc. 3. God s Countenance. In many places in the LXX πρόσωπον, like the Heb. נ ים,פ is used to denote God s countenance, i.e., the side He turns to man. a. Sometimes the manner of speech is anthropomorphic. When God lifts His countenance over man He has pity and gives peace: ἐπάραι κύριος τὸ πρόσωπον αὐτοῦ ἐπὶ σέ, Nu. 6:26. Prayer is made that He will cause His face to shine on the Israelites: ἐπιφάναι κύριος τὸ πρόσωπον αὐτοῦ ἐπὶ σέ, Nu. 6:25. When He hides His face He withdraws His grace: ἀποστρέψω τὸ πρόσωπόν μου, V 6, p 773 Dt. 32:20; cf. Mi. 3:4. Anxious prayer is made: ἕως πότε ἀποστρέψεις τὸ πρόσωπόν σου ἀπʼ ἐμοῦ; ψ 12:2; cf. 29:8; 43:25. If God has not turned away His countenance, grateful confession is made: οὐδὲ ἀπέστρεψεν τὸ πρόσωπον αὐτοῦ ἀπʼ ἐμοῦ, ψ 21:25. Prayer is also made to God μὴ ἀποστρέψῃς τὸ πρόσωπόν σου ἀπʼ ἐμοῦ, ψ 101:3; 142:7. In penal wrath God turns His face against those who do evil: πρόσωπον δὲ κυρίου ἐπὶ ποιοῦντας κακά, ψ 33:17. His wrathful glance smites transgressors of the Law: ἐπιστήσω τὸ πρόσωπόν μου ἐπὶ τὴν ψυχὴν τὴν ἔσθουσαν τὸ αἷμα καὶ ἀπολῶ αὐτὴν ἐκ τοῦ λαοῦ αὐτῆς, Lv. 17:10, cf. Lv. 20:3, 6; 26:17; Ez. 14:8; 15:7. It is often said that men have seen the face of God: εἷδον γὰρ θεὸν πρόσωπον πρὸς πρόσωπον, Gn. 32:30; cf. Ju. 6:22. Because he had seen God face to face Jacob called the place of meeting נ יא ל,פ Gn. 32:30 f. LXX == εἶδος θεοῦ. 26 Seeing God involves the greatest peril, for man necessarily perishes before God s holiness. The OT does not dispute the fact that man may see God s face in certain circumstances, yet in general he 25 πρὸ προσώπου does not occur in Gn.; instead we find ἐναντίον, ἔμπροσθεν and ἐνώπιον. Johannessohn, 190. Heb. Hebrew. 26 The place-name θεοῦ πρόσωπον (== א ל (?פ נ י is used for the mountain ra s shak k a which juts out into the Mediterranean on the Lebanese coast, Strabo, 16, 754; Ps.- Skylax, Periplus, 104 (ed. C. Müller, Geographi Graeci Minores, I [1855], 78). Cf. on this K. Galling, Die syrisch-palästinische Küste nach Ps.-Skylax, ZDPV, 61 (1938), 74 f.

12 may not do so, since the consuming holiness of God destroys man. 27 Thus Moses is warned οὐ δυνήσῃ ἰδεῖν μου τὸ πρόσωπον οὐ γὰρ μὴ ἴδῃ ἄνθρωπος τὸ πρόσωπόν μου καὶ ζήσεται, Ex. 33:20. Moses can see only from behind when the glory of God passes by: ὄψῃ τὰ ὀπίσω μου, τὸ δὲ πρόσωπόν μου οὐκ ὀφθήσεταί σοι, Ex. 33:23. In distinction from the religion of the Greeks, according to which the gods can reveal themselves to the eye of man, the OT insists that God reveals Himself through the Word, not through seeing His face, I, 217, 26 ff. b. Alongside this use of God s countenance there is a second series of instances in which πρόσωπον (θεοῦ) is employed cultically. To see God s face is to visit the cultic site. This expression was probably taken over from non-israelite cults which had an idol in the temple for the veneration of worshippers. It then passed into OT usage in a transferred sense. 28 The yearning question is asked in prayer: πότε ἥξω καὶ ὀφθήσομαι τῷ προσώπῳ τοῦ θεοῦ; ψ 41:3; 94:2. Believers seek the face of the Lord and find it when they attend the temple: ἐκζητῆσαι τὸ πρόσωπον κυρίου, Zech. 8:21 f. 29 There is often reference to δεηθῆναι τοῦ προσώπου (God s), ψ 118:58; 4 Βασ. 13:4; Bar. 2:8; Zech. 8:21 Cf. ἐξιλάσκεσθε τὸ πρόσωπον τοῦ θεοῦ ὑμῶν, Mal. 1:9. In these expressions the accent is not on seeing. To see the face of God is to be certain of His presence and grace. Hence ψ 104:4 can say with reference to the everyday life of the righteous: ζητήσατε τὸ πρόσωπον αὐτοῦ (sc. God s) διὰ παντός. Here the expression breaks away from the cultic world and stresses the need to keep up a daily relation with God. When the Psalmist says: τὸ πρόσωπόν σου, κύριε, V 6, p 774 ζητήσω (ψ 26:8), he means that he wants to make Yahweh s grace and help a matter of supreme concern. 30 It may be mentioned in conclusion that the shewbread is called ἄρτοι τοῦ προσώπου in 1 Βασ. 21:7 because it is kept in the holy place, the place of God s presence. II. Later Judaism. 1. Philo and Josephus. 27 Cf. Baudissin, 184 f.; E. Fascher, Deus invisibilis, Marburger Theol. Studien. I (1931), 41 77; R. Bultmann, Untersuchungen zum Joh.-Ev., B. θεὸν οὐδεὶς ἑώρακεν πώποτε, ZNW, 29 (1930), and what is said about seeing God in the art. ὁράω V, 325, 7 f.), 331, 1 ff. 28 Baudissin, : Gulin, 5 7; Nötscher, 88 95; G. Kittel, Religionsgeschichte u. Urchr. (1932), The cultic phrase to see God s face was avoided later. Thus ל ר א ות פ נ י in Is. 1:12 was read as א ות פ נ י,ל ר which was transl. ὀφθήναί μοι in the LXX [J. Fichtner]. 30 Cf. Nötscher, 136.

13 a. Philo describes τὸ πρόσωπον as σώματος ἡγεμονικόν, Leg. All., I, 39; cf. Fug., 182. At creation God blew into man πνοὴν ζωῆς εἰς τὸ τοῦ σώματος ἡγεμονικώτατον, τὸ πρόσωπον, Spec. Leg., IV, 123. Acc. to the will of God, then, the face is the most important part of the human body, Poster. C., 127; Leg. All., I, 28; for ἐν προσώπῳ τὰς αἰσθήσες ἐδημιούργει, Leg. All., I, 39. Cf. Op. Mund., 139: τὸ πρόσωπον, ἔνθα τῶν αἰσθήσεων ὁ τόπος. It is worth noting that the face is controlled by the significant number seven: τό τε ἡγεμονικώτατον τοῦ ζῴου πρόσωπον ἑπταχῆ κατατέτρηται, δυσὶν ὀφθαλμοῖς καὶ ὠσὶ δυσίν, ἴσοις μυκτῆρσιν, ἑβδόμῳ στόματι, Leg. All., I, 12. Ref. is often made to God s face: Cain must withdraw ἐκ προσώπου τοῦ θεοῦ, Poster. C., 12, 22 etc. God s Word goes forth ἐκ προσώπου θεοῦ, Deus Imm., 109; Plant., 63; Conf. Ling., 168; Mut. Nom., 39 etc. In Mut. Nom., 13 Philo speaks of a λόγιον ἐκ προσώπου θεσπισθὲν τοῦ τῶν ὅλων ἡγεμόνος. In harmony with the OT Philo also says that God s face is hidden from man. He takes the story in Ex. 33:12 23 to mean that the works of God may be seen but not His essential being, Poster. C., Cf. also Fug., 165: αὔταρκες γάρ ἐστι σοφῷ τὰ ἀκόλουθα καὶ ἑπόμενα καὶ ὅσα μετὰ τὸν θεὸν γνῶναι, τὴν δʼ ἡγεμονικὴν οὐσίαν ὁ βουλόμενος καταθεάσασθαι τῷ περιαυγεῖ τῶν ἀκτίνων πρὶν ἰδεῖν πηρὸς ἔσται. In Spec. Leg., I, Philo explains that Moses based his request that God would show Himself to him on the ground that only God Himself could reveal His essential being. When God could not accede to this request because man is incapable of such vision, Moses prayed that at least God would reveal His δόξα, the δυνάμεις which encircle Him in service. But even this petition was denied because the δυνάμεις are invisible and can be perceived only by God who is invisible. Sometimes it would seem that πρόσωπον is used for person : τί δεῖ τὰς τῶν προσώπων ἀμυθήτους ἰδέας καταλέγεσθαι; Poster. C., 110; τὰ πράγματα καὶ τὰ Leg. All. Legum Allegoriae. Fug. De Fuga et Inventione. Spec. Leg. De Specialibus Legibus. Poster. C. De Posteritate Caini. Leg. All. Legum Allegoriae. Leg. All. Legum Allegoriae. Op. Mund. De Opificio Mundi. Leg. All. Legum Allegoriae. Poster. C. De Posteritate Caini. Deus Imm. Quod Deus sit Immutabilis. Plant. De Plantatione. Conf. Ling. De Confusione Linguarum. Mut. Nom. De Mutatione Nominum. Mut. Nom. De Mutatione Nominum. Poster. C. De Posteritate Caini. 31 I owe this ref. to G. Bertram. Fug. De Fuga et Inventione. Spec. Leg. De Specialibus Legibus. 32 Cf. on this M. Pohlenz, Pls. u. die Stoa, ZNW, 42 (1949), 71 f. Poster. C. De Posteritate Caini.

14 πρόσωπα, ibid., 111; ἐπὶ τιμῇ προσώπων Spec. Leg., I, 245. b. In Joseph. πρόσωπον means face : πεσὼν (Hezekiah) ἐπὶ πρόσωπον τὸν θεὸν ἱκέτευσε, Ant., 10, 11. Cf. also Ant., 6, 285; 7, 95 and 114; 9, 11 and 269; 10, 211 for this expression. When the brother of a dead man refuses Levirate marriage, the rejected woman is to πτύειν εἰς πρόσωπον (cf. Dt. 25:8 f.), Ant., 4, 256; 5, 335. In Bell., 2, 29 πρόσωπον denotes the features : ἐπισχηματίζων τὸ πρόσωπον εἰς λύπην. The outside of the temple is called τὸ ἔξωθεν αὐτοῦ πρόσωπον in Bell., 5, 222. The sense role is found in Bell., I, 517. The common LXX combination κατὰ πρόσωπον with dependent case is also common in Jos.: κατὰ πρόσωπον τῆς τραπέζης, Ant., 3, 144; κατὰ πρόσωπον τοῦ ναοῦ, 9, 8; κατὰ πρόσωπον αὐτοῦ (of the king), 11, 235. Jos. refers to God s face only in explanation of the OT word Peniel: ἡσθεὶς δὲ τούτοις (sc. the encounter with God) Ἰάκωβος Φανούηλον ὀνομάζει τὸν τόπον ὃ σημαίνει θεοῦ πρόσωπον, Ant., 1, 334. πρόσωπον means person in Bell., 1, 263: προλαβὼν Ἡρώδης μετὰ τῶν οἰκειοτάτων προσώπων. ( with the persons most intimate with him, i.e., his closest relatives) νύκτωρ ἐπὶ Ἰδουμαίας ἐχώρει λάθρα τῶν πολεμίων. V 6, p Pseudepigrapha and Rabbinic Writings. It is not our task to give all the many examples of פ נ ים in Jewish literature. One still finds the OT senses ( 771, 1 ff.) forward side : face, front, surface, and also the combination with various prepos. 771, 33 ff. Apart from this the pseudepigr. speak of the face of the perfected righteous shining like the sun in the future world, since God will cause His light to shine on the face of the saints and the elect righteous, Eth. En. 38:4; cf. Da. 12:3; Eth. En. 39:7; 104:2. This means, however, that they will be changed from beauty to splendour and from light to the Spec. Leg. De Specialibus Legibus. Joseph. Flavius Josephus, Jewish author (c A.D.) in Palestine and later Rome, author in Greek of the Jewish War and Jewish Archaeology, which treat of the period from creation to Nero, ed. B. Niese, 1887 ff. Ant. Antiquitates. Ant. Antiquitates. Ant. Antiquitates. Bell. Bellum Judaicum. Bell. Bellum Judaicum. Bell. Bellum Judaicum. Ant. Antiquitates. Ant. Antiquitates. Bell. Bellum Judaicum. pseudepigr. pseudepigraphical. Eth. En. Ethiopian Enoch, ed. A. Dillmann, 1851; R. Charles, Eth. En. Ethiopian Enoch, ed. A. Dillmann, 1851; R. Charles, 1906.

15 radiance of glory, S. Bar. 51:10. Immediate proximity to God will be the lot of the righteous, S. Bar. 51:3. In 4 Esr. 7:97 the sixth joy granted to those who have kept the ways of the Most High is that it will be shown to them how their face will one day shine as the sun. The seventh joy is that they exultantly press on to see the face of Him whom they have served in life and from whom they will receive praise and reward, 7: In the hour of death so say the Rabbis all men must see the face of God. Hence R. Jochanan b. Zakkai dies full of fears ( II, 527, 23 ff.), Ab RNat, 25; cf. b. Ber., 28b. The ungodly will see God s face to receive their punishment, Midr. Ps (99a). 34 But in the world to come the righteous will see the face of the shekinah as a reward for their deeds, b. Men., 43b; b. Sota, 42a. 35 He who gives alms or does meritorious works will be made worthy thereby to greet the face of the shekinah, b. BB, 10a. In the form to see or to greet the face of the shekinah the Rabb. use the OT cultic formula to see the face of God not only for attending the temple but later for taking part in the worship of the synagogue as well, Dt. r., 7 (204a), 36 since this is the place where God draws near. It is also said of those who pray or study that they greet God s face, for God is near to those who pray and who apply themselves to the Torah, b. Sanh., 42a. 37 S. Bar. Syrian Apocalypse of Baruch, originally Hebrew and strongly dependent on 4 Esdras (c. 100 A.D.), ed. R. Charles, S. Bar. Syrian Apocalypse of Baruch, originally Hebrew and strongly dependent on 4 Esdras (c. 100 A.D.), ed. R. Charles, On the vision of God in the pseudepig. and Rabb. writings cf. Str.-B., I, ; V, 339, 12 ff. R. Rabbi. b. ben, when between the personal and family names of rabbis. Ab RNat Abot of Rabbi Nathan an extracanonical Rabbinic tractate (Strack, Einl., 72). b. Babylonian Talmud when before tractates from the Mishnah. Ber. Berakhot, Mishnah-, Tosefta-, Talmud tractate Benedictions. Midr. Ps. Midrash on Psalms (Strack, Einl., 215). 34 Cf. Str.-B., I, 209. b. Babylonian Talmud when before tractates from the Mishnah. Men. Menachot, Mishnah-, Tosefta-, Talmud tractate Meat Offerings (Strack, Einl., 55 f.). b. Babylonian Talmud when before tractates from the Mishnah. Sota Sota, Mishnah-, Tosefta-, Talmud tractate Suspected Adultress. 35 For further examples cf. Str.-B., I, b. Babylonian Talmud when before tractates from the Mishnah. BB Baba Batra, Mishnah-, Tosefta-, Talmud tractate Last Gate (Legal Questions, Immovables) (Strack, Einl., 51). Rabb. Rabbis, Dt. r. Deuteronomium rabba (Debarim rabba), Homiletic Midrash on Deuteronomy (Strack, Einl., 206). 36 Ibid., 207. b. Babylonian Talmud when before tractates from the Mishnah.

16 πρόσωπον also came into Rabb. usage as a loan word and is of frequent occurrence: דומות זה לזה 2: Ber., 7, 38 Thus one reads in T..פרצופא Aram. or פרסופ/פרצוף Heb. another. 39 their (men s) faces are not like one == אין פרוצופותיהין C. New Testament Usage. The use of πρόσωπον in the NT follows closely that of the LXX ( 771, 1 ff.) and the word has the same range of meaning as in the OT 771, 3 ff. 1. Face. πρόσωπον is often used in the sense ( 769, 1 ff., 771, 9 ff.) face (Mt. 6:16 f.; Ac. 6:15; Rev. 4:7; 9:7; Mk. 14:65; Mt. 26:67), εἰς πρόσωπον δέρειν, to hit in the face, 2 C. 11: Inclining (Lk. 24:5) or falling on one s face 41 (Mt. 17:6; V 6, p :39; Rev. 7:11; 11:16; without αὐτοῦ Lk. 5:12; 17:16; 1 C. 14:25) expresses respect and veneration, cf. the OT πίπτειν ἐπὶ (τὸ) πρόσωπον αὐτοῦ, 771, 12 ff. Mention of the face of the angel (Rev. 10:1; cf. Ac. 6:15) or the face of Jesus (Mt. 17:2; Lk. 9:29) shining like the sun is a feature in the description of epiphanies. On the basis of Ex. 34:29 35 Paul in a Christian midrash (2 C. 3:7 18) 42 refers to the radiant πρόσωπον of Moses which the Israelites could not look on because of its δόξα, v. 7. But the δόξα on the face of Moses was transitory, so that Moses had to cover his Sanh. Sanhedrim Mishnah-, Tosefta-, Talmud tractate On the court of justice and its procedure (Strack, Einl., 51 f.). 37 Ibid., 206 f. Rabb. Rabbis, Heb. Hebrew. Aram. Aramaic. 38 Cf. S. Krauss, Griech. u. lat. Lehnwörter im Talmud, Midrasch u. Targum, II (1899), 495. T. Tosefta (Strack, Einl., 74 ff.), ed. G. Kittel-H. Rengstorf, 1933 ff. Ber. Berakhot, Mishnah-, Tosefta-, Talmud tractate Benedictions. 39 πρόσωπον in the sense of person is also a loan word in Syr.: O. Sol. 31:5 (ed. W. Bauer, Kl. T., 64 [1933]) פרצופה == his person ; cf. also O. Sol. 17:4. NT New Testament. 40 To be taken fig. here, perhaps proverbially of bad treatment; cf. Ltzm. K., ad loc. 41 The art. may be left out in the phrase ἐπὶ πρόσωπον πίπτειν, cf. Bl.-Debr. 255, Cf. Wnd. 2 K., 112; Ltzm. K., ad loc. In exposition I, 454, 10 ff.; II, 251, 4 ff.; IV, 869, 10 ff.; S. Schulz, Die Decke des Moses, ZNW, 49 (1958), v. verse.

17 face lest the children of Israel should see it fade, v. 13. Paul abruptly adds a new thought. He speaks now, not of the cover on the face of Moses. but of that on the hearts of the Jews in virtue of which the OT is concealed from them and its true sense is closed to them, vv. 14ff. 43 Christians, on the other hand, can see with uncovered face the δόξα κυρίου and experience the change ἀπὸ δόξης εἰς δόξαν which proceeds from the Lord of the Spirit, v This line of thought is adopted again in 2 C. 4:6 where we are told that the δόξα of God shines for us in the face of Christ. In a series of verses πρόσωπον denotes personal presence ( 769, 24 ff.; 771, 14 ff.): ὁρᾶν τὸ πρόσωπόν τινος, to see someone again (Ac. 20:25, 38; Col. 2:1; 1 Th. 2:17b; 3:10 Hebraism, cf. Gn. 32:21; 43:3, 5); ἀπορφανισθέντες ἀφʼ ὑμῶν προσώπῳ οὐ καρδίᾳ, 1 Th. 2:17a; ἀγνοούμενος τῷ προσώπῳ, unknown personally, Gl. 1:22. When Lk. 9:51 says of Jesus αὐτὸς τὸ πρόσωπον (αὐτοῦ) ἐστήρισεν τοῦ πορεύεσθαι εἰς Ἰερουσαλήμ, an OT form of expression is adopted (στηρίζειν τὸ πρόσωπον ==.(ש ים פ נ ים 45 To turn one s face in a particular direction is to declare the firm intention of following this course without deviation. 46 The Hebraicising expression shows how significant to salvation history is the section which begins with the journey of Jesus from Galilee to Samaria and then on to Jerusalem 50, 11 ff. With the τὸ πρόσωπον αὐτοῦ ἦν πορευόμενον εἰς Ἰερουσαλήμ of Lk. 9:53 one may compare the τὸ πρόσωπόν σου (Absalom s) πορευόμενον ἐν μέσῳ αὐτῶν of the OT model in 2 Βασ. 17:11, 771, 22 ff. τὸ πρόσωπον here denotes the whole man: He journeyed towards Jerusalem. 47 v. verse. 43 On the train of thought III, 560 f.; V, 883, 5 ff. v. verse. 44 In exposition of the v. cf. J. Dupont, Le Chrétien miroir de la gloire divine d après II Cor. III 18, Rev. Bibl., 56 (1949) Ἰερ. 3:12; 21:10 [24:6]; Ez. 6:2; 13:17; 14:8. Cf. also 4 ἔταξεν Αζαηλ τὸ προσωπον αὐτοῦ ἀναβῆναι ἐπὶ Ἰερουσαλημ. Cf. A. Wifstrand, Lukas och Septuaginta, Svensk Teologisk Kvartalskrift, 16 (1940), Additional OT par.: τάξει τὸ πρόσωπον αὐτοῦ εἰσελθεῖν, Da. 11:17 Θ; ἐφίστημι τὸ πρόσωπόν μου τοῦ ἀπολέσαι, Ἰερ. 51 (44): 11f.; ἔδωκεν Ιωσαφατ τὸ πρόσωπον αὐτοῦ ἐκζητῆσαι τὸν κύριον, 2 Ch. 20:3 [P. Katz]. 46 Cf. Schl. Lk., ad loc.; also Str.-B., II, 165, ad loc.; Dalman WJ, I, Dalman WJ, I, 25: This Lucan expression is an incorrectly used Hebraism which cannot be imitated in Hebrew. Lk. 9:53 refers back to v. 51. The τὸ πρόσωπον αὐτοῦ ἐστήρισεν τοῦ πορεύεσθαι εἰς Ἰερουσαλήμ there ought properly to be repeated. The expression in v. 53 is an unskilful abbreviation of the full phrase.

18 Sometimes πρόσωπον does not denote the face but the appearance or features of a man or object. For τὸ πρόσωπον τῆς γενέσεως αὐτοῦ (sc. the man) in Jm. 1:23 one might have expected τὸ πρόσωπον αὐτοῦ; the reference is obviously V 6, p 777 to the kind of person he looks like. 48 ἡ εὐπρέπεια τοῦ προσώπου αὐτοῦ is used of the outside of the flower in Jm. 1:11, while there is reference to the appearance of the sky in Mt. 16:3 (par. Lk. 12:56). 2. The Front Side. As in the LXX ( 771, 28 ff.) πρόσωπον can also mean the front or surface : ἐπὶ πρόσωπον πάσης τῆς γῆς, Lk. 21:35; ἐπὶ παντὸς προσώπου τῆς γῆς, Ac. 17:26. πρόσωπον is also used in dependence on prepositions 49 as in the LXX ( 771, 33 ff.); here it mostly serves as a strengthening expletive. a. ἀπὸ προσώπου: ἀπὸ προσώπου τοῦ κυρίου coming forth from the Lord, Ac. 3:19; ἀπὸ προσώπου τοῦ συνεδρίου, Ac. 5:41; also Ac. 7:45; 2 Th. 1:9; Rev. 6:16 (cf. Is. 2:10, 19, 21); 12:14 (to denote distance == far from ); 20:11. b. εἰς πρόσωπον: εἰς πρόσωπον τῶν ἐκκλησιῶν, before the eyes of the (other) churches, 2 C. 8:24. c. ἐν προσώπῳ: by means of ἐν προσώπῳ Χριστοῦ in 2 C. 2:10 Paul appeals to Christ as witness to the sincerity of his forgiveness. πρὸς τοὺς ἐν προσώπῳ καυχωμένους, against those who boast of external things, 2 C. 5:12. d. κατὰ πρόσωπον: without dependent case personally present, eye to eye ( 769, 24): Ac. 25:16; 2 C. 10:1; Gl. 2:11. τὰ κατὰ πρόσωπον, what is before the eyes, 2 C. 10:7. With gen. following (as in LXX) κατὰ πρόσωπον occurs only in Luke: 50 κατὰ πρόσωπον πάντων τῶν λαῶν, 51 Lk. 2:31; κατὰ πρόσωπον Πιλάτου Ac. 3:13. e. μετὰ προσώπου: only in the quotation from ψ 15:11 in Ac. 2:28. f. πρὸ προσώπου: ἀποστέλλω τὸν ἄγγελόν μου πρὸ προσώπου σου ( before thee ) Mal. 3:1 == Mk. 1:2; Mt. 11:10; Lk. 7:27; ἀπέστειλεν ἀγγέλους πρὸ προσώπου αὐτοῦ, Lk. 9:52; cf. also Lk. 1:76 vl.; 10:1; πρὸ προσώπου τῆς εἰσόδου αὐτοῦ, before his coming, Ac. 13: God s Countenance. Following an OT mode of speech the NT often refers to God s countenance ( 772, 48 Cf. Dib. Jk., ad loc. On this difficult expression I, 682, 37 ff. par. parallel. 49 Cf. Bl.-Debr. 217, The common use of πρόσωπον in dependence on prep. in Luke is due to the fact that the author models his style on the LXX. 51 πρόσωπον in the sing. in spite of the plur. which follows. Cf. Bl.-Debr vl. varia lectio.

19 31 ff.), as in quotations from the OT: πρόσωπον δὲ κυρίου ἐπὶ ποιοῦντας κακά (ψ 33:17 == 1 Pt. 3:12; cf. also Ac. 2:28 == ψ 15:11). There is vision of the face of God only in the heavenly world: Christ has gone into the sanctuary, i.e., heaven, νῦν ἐμφανισθῆναι τῷ προσώπῳ τοῦ θεοῦ ὑπὲρ ἡμῶν, Hb. 9:24. Here the expression which the OT used for visiting the temple is transferred to the heavenly sanctuary. The guardian angels of the μικροί always see τὸ πρόσωπον τοῦ πατρός μου τοῦ ἐν οὐρανοῖς (Mt. 18:10) to whom the welfare of the smallest is especially dear. They are thus in the immediate presence of God. To see the divine countenance which is concealed from man will be granted to God s servants in the consummation, Rev. 22:4. Now we can only see through a glass obscurely ( I, 178, 10 ff.), τότε δὲ πρόσωπον πρὸς πρόσωπον, 1 C. 13:12. This V 6, p 778 means that what we see and say is now imperfect. There will be perfect vision and real knowledge only in the future consummation. 4. Person. The sense person occurs in the NT at 2 C. 1:11. The Corinthians are to join the apostle in prayer in order that thanks may be given for us by many persons (ἐκ πολλῶν προσώπων). 52 D. Early Church Usage. 1. πρόσωπον in the Post-Apostolic Fathers. The usage of the post-apost. fathers reveals no peculiarities as compared with the NT. The word is very common in OT quotations, a. The meaning face occurs in 1 Cl., 4, 3f. (Gn. 4:5 f.); 16, 3 (Is. 53:3); Barn., 5, 14 (Is. 50:6); Mart. Pol., 9, 2; 12, 1; Herm. v., 3, 10, 1. Of personal presence: ἐκζητεῖν τὰ πρόσωπα τῶν ἁγίων to appear before the saints, Barn., 19, 10; Did., 4, 2; also Ign. R., 1, 1; Pol., 1, 1; Barn., 13, 4 (Gn. 48:11). b. The meaning NT New Testament. NT New Testament. 52 Cf. Wnd. 2 K.; Ltzm. K., ad loc. NT New Testament. 1 Cl. Epistle of Clement Barn. Epistle of Barnabas. Mart. Martyrium. Pol. Polycarpi. Herm. Pastor Hermae. v. visiones. Barn. Epistle of Barnabas. Did. Didache. Ign. Ignatius.

20 front, surface occurs in the quotation of ψ 1:4 in Barn., 11, 7: ὃν ἐκρίπτει ὁ ἄνεμος ἀπὸ προσώπου τῆς γῆς. πρόσωπον is common in dependence on prepos.: ἀπὸ προσώπου, 1 Cl., 4, 8. 10; 18:11 (ψ 50:13); 28, 3 (ψ 138:7); Barn., 6, 9; εἰς πρόσωπον, Ign. Pol., 2, 2; Herm. v., 3, 6, 3; κατὰ πρόσωπον, 1 Cl., 35, 10 (ψ 49:21). On κατὰ πρόσωπον for personally present cf. Barn., 15, 1; Pol., 3, 2. In Barn., 19, 7 and Did., 4, 10 κατὰ πρόσωπον in the abs. means with partiality. πρὸ προσώπου, 1 Cl., 34, 3 (Is. 62:11); Ign. Eph., 15, 3. c. There is ref. to the face of God only in OT quotations in 1 Cl., 18, 9 (ψ 50:11); 22, 6 (ψ 33:17); 60, 3 (Nu. 6:25; ψ 66:2). d. Sometimes πρόσωπον means person : ὀλίγα πρόσωπα, 1 Cl., 1, 1; ἓν ἢ δύο πρόσωπα, 1 Cl., 47, 6; τὰ προγεγραμμένα πρόσωπα, the afore-mentioned persons, Ign. Magn., 6, 1. εὐπροσωπέω. From the adj. εὐπρόσωπος, 1 1 which derived from πρόσωπον but does not occur in the NT, there was later formed a verb εὐπροσωπέω, to have a good appearance. It is found in R. ad Romanos. Pol. Epistle of Polycarp. Barn. Epistle of Barnabas. Barn. Epistle of Barnabas. 1 Cl. Epistle of Clement Barn. Epistle of Barnabas. Ign. Ignatius. Pol. Epistle of Polycarp. Herm. Pastor Hermae. v. visiones. 1 Cl. Epistle of Clement Barn. Epistle of Barnabas. Pol. Epistle of Polycarp. Barn. Epistle of Barnabas. Did. Didache. 1 Cl. Epistle of Clement Ign. Ignatius. Eph. Epistula ad Ephesios. 1 Cl. Epistle of Clement 1 Cl. Epistle of Clement 1 Cl. Epistle of Clement Ign. Ignatius. Magn. ad Magnesios. before the heading of an article indicates that all the New Testament passages are mentioned in it. adj. adjective. 1 == with fair face, attested frequently from the 5th cent. Cf., e.g., LXX Gn. 12:11: Abraham tells the beautiful Sarah that he knows ὅτι γυνὴ εὐπρόσωπος εἶ. NT New Testament.

21 a letter of 114 B.C.: ὅπως εὐπροσωπῶμεν, P. Tebt., I, 19, In the NT εὐπροσωπέω is used only at Gl. 6:12: ὅσοι θέλουσιν εὐπροσωπῆσαι ἐν σαρκί, who want to stand well with men. προσωπολημψία, προσωπολήμπτης, προσωπολημπτέω, ἀπροσωπολήμπτως. 1. The expressions נ ש א פ נ ים == λαμβάνειν πρόσωπον or θαυμάζειν πρόσωπον and ה כ יר פ נ ים == γιγνώσκειν πρόσωπον are common in the OT. They are to be explained in terms of the respectful oriental greeting in which one humbly turns one s face to the ground or sinks to the earth. If the person greeted thus raises the face of the man, this is a sign of recognition and esteem. The translation of נ ש א פ נ ים by λαμβάνειν πρόσωπον is modelled closely on the Hebrew expression. 1 In secular Greek, of course, λαμβάνειν means only to take, to accept, never to raise up. But since can mean to take as well as to lift, λαμβάνειν was used for it in Greek. This נ ש א rendering must have been virtually unintelligible to the Greek. 2 In the phrase θαυμάζειν πρόσωπον, θαυμάζειν means to esteem, III, 30, 1 ff., 41, 12 ff. God does not respect persons: οὐ θαυμάζει πρόσωπον (Dt. 10:17; cf. 2 Ch. 19:7). Men, however; honour one another by humble greeting and lifting of the face. Thus Jacob before his meeting with Esau hopes: ἴσως γὰρ προσδέξεται τὸ πρόσωπόν μου, Gn. 32:21. But λαμβάνειν πρόσωπον may be partial when regard is hard for the person and there is unjust preference. Judges in particular are warned: οὐκ ἐπιγνώσῃ πρόσωπον ἐν κρίσει, Dt. 1:17, cf. also Lk. 19:15; Dt. 16:19. As there is no respect of persons with God, so the earthly judge must be incorruptible and return just verdicts. P. Tebt. The Tebtunis Papyri, ed. B. Grenfell, A. Hunt and others, 1920 ff. 2 Cf. also Deissmann LO, 76 f. NT New Testament. before the heading of an article indicates that all the New Testament passages are mentioned in it. before the heading of an article indicates that all the New Testament passages are mentioned in it. before the heading of an article indicates that all the New Testament passages are mentioned in it. before the heading of an article indicates that all the New Testament passages are mentioned in it. 1 The following sentences are based on a hint from Debrunner. 2 Cf. J. Leipoldt-S. Morenz, Heilige Schriften (1953), 80.

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

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

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

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

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

Concrete Mathematics Exercises from 30 September 2016

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

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

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

Διαβάστε περισσότερα

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

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

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

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

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

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

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

4.6 Autoregressive Moving Average Model ARMA(1,1)

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

Διαβάστε περισσότερα

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

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

Math 6 SL Probability Distributions Practice Test Mark Scheme

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

Διαβάστε περισσότερα

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

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

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

Διαβάστε περισσότερα

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

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

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

Διαβάστε περισσότερα

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

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

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

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

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

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

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

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

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

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

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

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

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

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

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

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

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

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

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

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

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

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

Section 7.6 Double and Half Angle Formulas

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

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

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

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

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

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

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ Neapolis University HEPHAESTUS Repository School of Health Sciences http://hephaestus.nup.ac.cy Master Degree Thesis 2015 þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ þÿ Ä Æ Á Â, Á ÃÄ Â þÿ Á̳Á±¼¼±

Διαβάστε περισσότερα

PARTIAL NOTES for 6.1 Trigonometric Identities

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

Διαβάστε περισσότερα

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

ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ. ιπλωµατική Εργασία. της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411

ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ. ιπλωµατική Εργασία. της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411 Παρακίνηση εργαζοµένων: Ο ρόλος του ηγέτη στην παρακίνηση των εργαζοµένων. ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ ιπλωµατική Εργασία της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411 ΠΑΡΑΚΙΝΗΣΗ

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

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

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

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other 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 περισσότερα

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

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

Διαβάστε περισσότερα

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

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

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

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

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

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 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 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

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

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

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

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

Διαβάστε περισσότερα

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

Πειραματικό Λύκειο Αναβρύτων, 2012

Πειραματικό Λύκειο Αναβρύτων, 2012 «Ήδη από τον 3 ο π.χ. αιώνα η μνήμη της ανθρωπότητας στη Μεσόγειο λειτουργεί στα ελληνικά» (Jean Sirinelli, Τα παιδιά του Αλεξάνδρου, μετάφρ. Σ. Μπίνη-Σωτηροπούλου, εκδ. Σ. Ι. Ζαχαρόπουλος, 2001, σ. 157.)

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

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

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

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

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

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

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

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten LESSON TEN: THE ADJECTIVE Memorization of vocabulary ten ἀγαθος good ἁγιος holy, set apart ἀλλα but (the regular contrasting particle, with δε used at times) ἀληθεια truth ἀληθινος true/genuine αὐτος he

Διαβάστε περισσότερα

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert)

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert) Herodian and the Greek language: rules of thumb for accenting Greek enclitics Stephanie Roussou (a joint project with Philomen Probert) What are enclitics? Enclitics are small words forming close-knit

Διαβάστε περισσότερα

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ Ι Ο Ν Ι Ω Ν Ν Η Σ Ω Ν ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι Κεφαλληνίας, Ελλάδα 28100,+30

Διαβάστε περισσότερα

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)

Διαβάστε περισσότερα

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ

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

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ 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 περισσότερα

Matthew Mark Luke Luke Greek Reconstruction Hebrew Reconstruction. καὶ εὐαγγελιζόμενος τὴν βασιλείαν τοῦ θεοῦ

Matthew Mark Luke Luke Greek Reconstruction Hebrew Reconstruction. καὶ εὐαγγελιζόμενος τὴν βασιλείαν τοῦ θεοῦ Calling and Training Disciples: "Mission of the Twelve" complex: Sending the Twelve: Commissioning 1 1 9:35 καὶ περιῆγεν 6:6b καὶ περιῆγεν [8:1 καὶ ἐγένετο ἐν τῷ καθεξῆς καὶ αὐτὸς διώδευεν And / was going

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους ΑΛΕΞΑΝΔΡΕΙΟ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΑΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΜΗΜΑ ΔΙΑΤΡΟΦΗΣ ΚΑΙ ΔΙΑΙΤΟΛΟΓΙΑΣ Πτυχιακή Εργασία Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους Εκπόνηση:

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

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ Νικόλας Χριστοδούλου Λευκωσία, 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

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

Διαβάστε περισσότερα

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

Problem Set 3: Solutions

Problem Set 3: Solutions CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C

Διαβάστε περισσότερα

Subject - Students love Greek.

Subject - Students love Greek. A Summer Greek 2009 Ω Parts of Speech NOUN - person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE - describes a noun (includes in/definite articles) VERB

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ

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

Διαβάστε περισσότερα

Lecture 2. Soundness and completeness of propositional logic

Lecture 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 περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα