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1 равномерно по
uniformly with respect touniformly continuous with respect to --- равномерно-непрерывный по
The inequalities are uniformly valid with respect to x --- Эти неравенства справедливы равномерно по x
Русско-английский словарь механических и общенаучных терминов > равномерно по
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2 number
1) число || числовой2) номер || нумеровать3) код числа4) количество5) колонцифра6) численность || считать, подсчитывать, исчислять8) числительное•a great number of — множество, большое количество
a number of — (целый) ряд, некоторое количество
- absolutely pseudoprime number - connectivity number - deficient number - edge attachment number - edge covering number - edge sensitivity number - expected sample number - general recursively irrational number - geodesic crossing number - integer number - integral number - internal stability number - international customer number - mass exchange number - mixed-radix number - Mohs hardness number - number of principal cotype - number of space dimensions - octonary number - one-digit number - one-figure number - one's complement number - rectilinear crossing number - recursively real number - serial number - Shore hardness number - strictly positive number - vertex covering numberwinding number of a curve with respect to the point — порядок кривой относительно точки (число оборотов вектора, соединяющего данную точку с точкой кривой при обходе кривой)
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3 aequalis
aequālis, e, adj. [aequo], that can be put on an equality with; conseq., equal, like; constr. with dat., absol. and as subst. with gen. (syn.: aequus, aequabilis, planus, par, similis).I.Lit.:II.partem pedis esse aequalom alteri parti,
Cic. Or. 56, 188:paupertatem divitiis etiam inter homines aequalem esse,
id. Leg. 2, 10, 24:aequalem se faciens Deo,
Vulg. Joan. 5, 18:aequales angelis sunt,
like, ib. Luc. 20, 36:nec enim aut linguā aut moribus aequales abhorrere (Bastarnas a Scordiscis),
Liv. 40, 57, 7:ut sententiae sint membris aequalibus,
Quint. 9, 3, 80:aequalis ponderis erunt omnes,
Vulg. Exod. 30, 34; ib. Deut. 19, 7; ib. Apoc. 21, 16.—As subst. with gen.:Creticus et ejus aequalis Paeon,
Cic. Or. 64, 215. (Another constr., v. II.)—Hence,Transf.A. 1.Of persons.a.Of the same age, equal in years: cum neque me aspicere aequales dignarent meae. Pac. ap. Non. 470, 20 (Trag. Rel. p. 97 Rib.): patris cognatum atque aequalem, Archidemidem, nostine? Ter Eun. 2, 3, 35:b.adulescens ita dilexi senem, ut aequalem,
Cic. Sen. 4, 10:P. Orbius, meus fere aequalis,
id. Brut. 48 init.:Aristides aequalis fere ruit Themistocli,
Nep. Arist. 1 al. —In gen., contemporary, coeval; and subst., a contemporary, without definite reference to equality in age;c.Livius (Andronicus) Ennio aequalis fuit,
Cic. Brut. 18:Philistus aequalis illorum temporum,
id. Div 1, 20; Liv. 8, 40.—In the comic poets, esp. in connection with amicus, of the same age:2.O amice salve mi atque aequalis, ut vales?
Plaut. Trin. 1, 2, 10; 2, 2, 50; Ter. Heaut. 3, 1, 8; so id. Ad. 3, 4, 26:ne cuiquam suorum aequalium supplex siet,
id. Phorm. 5, 6, 47.—Of things, coexal, coexistent, etc.:B.Deiotari benevolentia in populum Romanum est ipsius aequalis aetati,
is as old as himself, has grown up with him, Cic. Phil. 11, 13:in memoriam notam et aequalem incurro,
i. e. which belongs to our time, id. Brut. 69; id. Leg. 1, 2: ne istud Juppiter sierit urbem in aeternum conditam fragili huic et mortali corpori aequalem esse, i. e. should exist for an equally short time, Liv 28, 28.—Rarely with cum:aequali tecum pubesceret aevo,
Verg. A. 3, 491:fuit cum ea cupressus aequalis,
Plin. 16, 44, 86, § 236.—That can be compared in respect to size or form; of equal size, looking alike, resembling, similar:C.florentes aequali corpore Nymphae,
Verg. Cir. 435:chorus aequalis Dryadum,
a chorus of Dryads alike, id. G. 4, 460.—Uniform, equable, unvarying; virtutes sunt inter se aequales et pares, Cic. de Or, 1, 18;3, 14, 55: nil aequale homini fuit illi,
Hor. S. 1, 3, 9:imber lentior aequaliorque,
and more uniform, Liv. 24, 46:aequali ictu freta scindere, Ov M. 11, 463: Euphranor in quocumque genere excellens ac sibi aequalis,
always equal to himself, Plin. 35, 11, 37, § 128:opus aequali quadam mediocritate,
Quint. 10, 1, 54.—Hence, but rarely, = aequus, of place, equal, uniform, level, smooth, even, plain, both in a horizontal and ascending direction:loca,
Sall. J. 79:terra,
Ov. M. 1, 34:gentes esse sine naribus aequali totius oris planitie,
Plin. 6, 30, 35, § 187:mons aequali dorso continuus,
Tac. A. 4, 47.— Comp. prob. not used.—* Sup.:aequalissima porticus,
Tert. Anim. 17.— Adv.: aequālĭter, equally, uniformly, in the same manner, Cic. Verr. 2, 3, 70; id. Ac. 2, 11; id. Lael. 16, 58; Caes. B. G. 2, 18; Vulg. Deut. 19, 3; ib. 1 Par. 24, 31; ib. Sap. 6, 8.— Comp., Tac. A. 15, 21.— Sup. not used. -
4 ζάω
ζάω contr. ζῶ (Hom.+) impf. ἔζων (Ro 7:9 B ἔζην; on this form s. Schwyzer I 675; B-D-F §88; Mlt-H. 194, both w. ref.); fut. ζήσω (uniformly attested Ro 6:2; Hb 12:9); the later (since Hippocr. VII p. 536 L.; LXX; AscIs 3:9; Jos., Ant. 1, 193 al.) form ζήσομαι (B-D-F §77; Rob. 356) is more common (on the fut. forms s. JLee, NovT 22, ’80, 289–98; GKilpatrick, ibid. 25, ’83, 146–51); 1 aor. ἔζησα. On the LXX usage s. Thackeray 269; for forms in pap, Gignac II 370.① to be alive physically, liveⓐ of physical life in contrast to deathα. gener. Ac 22:22; Ro 7:1, 2, 3; 14:8ac; 1 Cor 7:39; 2 Cor 5:15a; 6:9; Hb 9:17. ψυχὴ ζῶσα a living soul (Gen 1:20 al.; Just., D. 6, 1 ζῇ ψυχῇ) 1 Cor 15:45 (Gen 2:7); Rv 16:3 v.l. ὅσα ἔτη ζῇ as many years as he lives B 10:6 (cp. SIG 663, 6; Sb 173, 6 Αὐρήλιος ζήσας ἔτη νε´; En 10:10). τὸ ζῆν life (Attic wr., ins, pap, LXX) ὥστε ἐξαπορηθῆναι ἡμᾶς καὶ τοῦ ζῆν so that we even despaired of life 2 Cor 1:8. διὰ παντὸς τοῦ ζῆν during the whole lifetime Hb 2:15 (cp. Diod S 1, 74, 3 διατελεῖν πάντα τὸν τοῦ ζῆν χρόνον; 4, 46, 4). ἔτι ζῶν while he was still living= before his death Mt 27:63 (CB I/2 660 no. 618 Ζώσιμος ἔτι ζῶν κατεσκεύασεν; 3 Km 12:6). ζῶντες ἐβλήθησαν … εἰς τὴν λίμνην τοῦ πυρός they were thrown alive into the lake of fire Rv 19:20. ζῶσα τέθνηκεν though alive she is dead 1 Ti 5:6 (cp. Sextus 7). ἡμεῖς οἱ ζῶντες we during our (earthly) life 2 Cor 4:11; the same phrase= we who are still living 1 Th 4:15, 17. Here the opp. is νεκροί, as in Mt 22:32; Mk 12:27; Lk 20:38a. ζῶντες καὶ νεκροί the living and the dead Ac 10:42; Ro 14:9b; 2 Ti 4:1; 1 Pt 4:5; 2 Cl 1:1; B 7:2.—Occasionally the contrast betw. νεκρός and ζῆν is used fig. with ref. to the realm of religion and ethics Lk 15:24 v.l., 32.β. of dead persons who return to life become alive again: of humans in general (3 Km 17:23) Mt 9:18; Ac 9:41; 20:12; Rv 20:4, 5; AcPl Ha 11, 7. Of Jesus Mk 16:11; Lk 24:5, 23; Ac 1:3; 25:19; Ro 14:9a; 2 Cor 13:4a; Rv 1:18b; 2:8 (Just., D. 69, 6 νεκροὺς … ζῆν ποιήσας).γ. of sick persons, if their illness terminates not in death but in recovery be well, recover (Artem. 4, 4 ἔζησεν ὁ παῖς=became well; 5, 71; 72; PGM 1, 188; 4 Km 1:2; 8:8 εἰ ζήσομαι ἐκ τῆς ἀρρωστίας μου ταύτης; Jos., Vi. 421) Mk 5:23; J 4:50, 51, 53.—Of removal of anxiety 1 Th 3:8.δ. also of healthy persons live on, remain alive (X., An. 3, 2, 39 ὅστις δὲ ζῆν ἐπιθυμεῖ πειράσθω νικᾶν; Ep. 56 of Apollonius of Tyana [Philostrat. I 359, 14]; ApcMos 31 διὰ τί σὺ ἀποθνῄσκεις καγὼ ζῶ;) Ac 25:24; 28:4. ἐὰν ὁ κύριος θελήσῃ ζήσομεν Js 4:15. ὸ̓ς ἔχει τὴν πληγὴν τῆς μαχαίρης καὶ ἔζησεν Rv 13:14.ε. of beings that in reality, or as they are portrayed, are not subject to death: of Melchizedek Hb 7:8 (opp. ἀποθνῄσκοντες ἄνθρωποι). Jesus as everlasting high priest πάντοτε ζῶν 7:25.—In this sense it is most comprehensively applied to God (s. CBurchard, Untersuch. zu JosAs p. 103) (ὁ) θεὸς (ὁ) ζῶν (cp. 4 Km 19:4, 16; Is 37:4, 17; Hos 2:1; Da 6:21 Theod.; 3 Macc 6:28; TestAbr A 17 p. 99, 10 [Stone p. 46]; TestJob 37:2; JosAs 49:3 al.; SibOr 3, 763; POxy 924, 11 [IV A.D., Gnostic]; PGM 4, 1038 ὁ μέγας ζῶν θεός; 7, 823; 12, 79; Philo, Decal. 67 ὁ ζῶν ἀεὶ θεός; Orig., C. Cels. 8, 59, 18.—The phrase ‘the living God’ is not found in Joseph.) Mt 16:16; 26:63; J 6:69 v.l.; Ac 14:15; Ro 9:26 (Hos 2:1); 2 Cor 3:3; 6:16; 1 Th 1:9; 1 Ti 3:15; 4:10; 6:17 v.l.; Hb 3:12; 9:14; 10:31; 12:22; Rv 1:18a; 4:10; 7:2; 10:6; 2 Cl 20:2; GJs 20:1; AcPl Ha 2, 32; also ὁ ζῶν πατήρ J 6:57. W. the addition εἰς τοὺς αἰῶνας τῶν αἰώνων Rv 15:7; cp. 4:9 (cp. Tob 13:2; Sir 18:1). God takes a sovereign oath in the words ζῶ ἐγώ as surely as I live (Num 14:28 al.) Ro 14:11 (Is 49:18; classical parallels GStählin, NovT 5, ’62, 142 n. 2). ζῇ κύριος ὁ θεός [μου] as surely as the Lord my God lives GJs 4:1; 6:1; 13:3; 15:3; 19:3 (Judg 8:19; 1 Km 25:34 al; GrBar 1:7; cp. ApcEsdr 2:7); in expanded form καὶ ζῇ ὁ Χριστὸς αὐτοῦ 15:4 (s. deStrycker ad loc.).—Christ lives διὰ τὸν πατέρα because of the Father J 6:57b (s. Bultmann, comm. ad loc.).ⓑ w. mention of that upon which life depends ἐπί τινι on the basis of someth. (Andoc. 1, 100; Isocr. 10, 18; Ael. Aristid. 28, 103 K.=49 p. 525 D.) ζ. ἐπʼ ἄρτῳ live on bread Mt 4:4; Lk 4:4 (both Dt 8:3). ζ. ἔκ τινος obtain one’s living fr. someth. (Aristoph., Eccl. 591; Demosth. 57, 36; POxy 1117, 19; 1557, 12; TestJob 47:1f) 1 Cor 9:14.ⓒ w. more precise mention of the sphere (Artem. 3, 62 ἐν ἀγορᾷ ζ.=spend his life in the marketplace) ζ. ἐν σαρκί live in the flesh in contrast to the heavenly life Phil 1:22; Gal 2:20c; ζ. ἐν κόσμῳ live in the world Col 2:20. ζ. ἐν θεῷ, live in God (as the Being who penetrates and embraces everything) Ac 17:28 (s. κινέω 3). For AcPl Ha 1, 15 s. 2a end.② to live in a transcendent sense, live, of the sanctified life of a child of God (ζῆν in the sense of a higher type of life than the animal: X., Mem. 3, 3, 11; Cass. Dio 69, 19: after years of public service, Similis retires and prepares this epitaph: Σίμιλις ἐνταύθα κεῖται βιοὺς μὲν ἔτη τόσα, ζήσας δὲ ἔτη ἑπτά=Here lies Similis, existing for so many years, but alive for only seven.).ⓐ in the world ἐγὼ ἔζων χωρὶς νόμου ποτέ I was once (truly) alive without law (this has been interpr. to mean when no law existed; Paul is then regarded as speaking fr. the viewpoint of humanity in paradise before the command Gen 2:16 f; 3:3. Another interpr. thinks of Paul as referring to the period in his life when he was not conscious of the existence and significance of the law. In view of Paul’s climactic affirmation in Ro 7:25, Paul probably illustrates in the first person the perils of a Christian who succumbs to the illusion that moral action is connected with law rather than with the ‘spirit of life in Christ’ Ro 8:2) Ro 7:9. Even now those who listen to the voice of the Son of God enjoy this life J 5:25; cp. 11:26; likew. those who receive him into their being ὁ τρώγων τὸν ἄρτον 6:57c; cp. Ro 6:11, 13 (ἐκ νεκρῶν ζῶντας); Gal 2:19; Rv 3:1. This heavenly life on earth is a ζ. πνεύματι Gal 5:25 or a life not of mere human achievement, but of Christ who lives in Christians 2:20ab. Also of the superhuman power of the apostle ζήσομεν σὺν αὐτῷ ἐκ δυνάμεως θεοῦ εἰς ὑμᾶς we shall live with him (Christ) through God’s power in our dealings with you 2 Cor 13:4. ὁ κύριος βούλεται ζῆν ἡμᾶς ἐν θεῷ=the Lord wills that we live under God’s direction AcPl Ha 1, 15 (opp. ἀποθανεῖν ἐν ἁμαρτίαις; s. 1c end)ⓑ in the glory of the life to come (Sir 48:11; cp. Dt 4:1; 8:1; 30:16).α. abs. Lk 10:28; J 11:25; 14:19; Ro 8:13b; Hb 12:9. ἐμοὶ τ. ζῆν Χριστός= life is possible for me only where Christ is (hence death is gain) Phil 1:21 (s. OSchmitz, GHeinrici Festschr. 1914, 155–69). Another common interpr. is for me to live is Christ, i.e. while I am alive I experience real life in connection with Christ; w. death comes life in all fullness in the presence of Jesus.β. More specifically εἰς τὸν αἰῶνα have eternal life (Ps.-Lucian, Philopatr. 17 ζῆν εἰς τὸν αἰῶνα; PsSol 14:2) J 6:51, 58 (in J the blessed life which the follower of Jesus enjoys here and now in the body is simply continued in the heavenly life of the future. In other respects also the dividing line betw. the present and the future life is somet. nonexistent or at least not discernible); B 6:3; 8:5; 9:2; 11:10f; ἅμα σὺν αὐτῷ (i.e. Χριστῷ) ζ. live together with Christ 1 Th 5:10; ζ. διʼ αὐτοῦ (i.e. Chr.) 1J 4:9; ζ. κατὰ θεὸν πνεύματι live, as God (lives), in the Spirit 1 Pt 4:6. ὁ δίκαιος ἐκ πίστεως ζήσεται (cp. Hab 2:4) he that is just through faith will have life Ro 1:17 (AFeuillet, NTS 6, ’59, 52–80; but s. Fitzmyer, Ro [AB] ad loc.); Gal 3:11; Hb 10:38. This life is τὸ ἀληθινὸν ζῆν ITr 9:2; IEph 11:1. Christ is called τὸ ἀδιάκριτον ἡμῶν ζῆν our unshakable or inseparable life 3:2. τὸ διὰ παντὸς ἡμῶν ζῆν our total life 1 Mg 1:2—The law-directed pers. believes concerning legal performance: ὁ ποιήσας αὐτὰ ζήσεται ἐν αὐτοῖς (Lev 18:5) Gal 3:12; cp. Ro 10:5 (cp. Dio Chrys. 58 [75], 1 οἱ τοῦτον [= τ. νόμον] φυλάττοντες ἔχονται τῆς σωτηρίας=those who observe law have a firm grip on security).③ to conduct oneself in a pattern of behavior, live (Hom. et al.)ⓐ used w. adverbs or other modifiers: adv. (Sallust. 19 p. 34, 25 κακῶς ζῆν [Just., A I, 4, 7]; SIG 889, 13ff; Wsd 14:28; Philo; Jos., Ant. 12, 198; Ath. 3, 1 δίκην θηρίων) ἀσώτως Lk 15:13. ἐθνικῶς and ἰουδαϊκῶς Gal 2:14. εὐσεβῶς 2 Ti 3:12. πανούργως Hm 3, 3. σωφρόνως κ. δικαίως κ. εὐσεβῶς Tit 2:12 (Plut., Mor. 1108c ζῆν σωφρόνως κ. δικαίως; cp. Diog. L. 10, 132; 140; Ar. 15, 10).—Φαρισαῖος live as a Pharisee Ac 26:5. ἐν πίστει Gal 2:20d. ἐν ἁμαρτίᾳ Ro 6:2; ζ. ἐν τούτοις live in these (sins) Col 3:7. κατὰ ἀλήθειαν in keeping w. the truth IEph 6:2 (cp. Philo, Post. Cai. 73 κατὰ βούλημα τὸ τοῦ θεοῦ ζ.; Jos., Ant. 4, 302 κατὰ τ. νόμους ζ.; Just., D. 47, 4 κατὰ τὸν νόμον; Orig., C. Cels. 7, 12, 7 κατὰ τὰς θείας γραφάς). κατὰ θεόν 8:1 (cp. SIG 910 A and B). κατὰ Ἰησοῦν Χριστόν IPhld 3:2. κατὰ Χριστιανισμόν live in accordance w. (our) commitment to Christ IMg 10:1. κατὰ σάρκα Ro 8:12f; Dg 5:8; κατὰ κυριακὴν ζ. (opp. σαββατίζειν) include the observance of the Lord’s day in one’s life IMg 9:1. Of a married woman ζ. μετὰ ἀνδρός live w. her husband Lk 2:36 (for the added acc. of extent of time cp. Ael. Aristid. 46 p. 332 D.; Pr 28:16; ἥτις ἔζησεν καλῶς μετʼ ἐμοῦ ἔτη 28, μῆνας 4, ἡμέρας 5: SEG II, 384, 6–8 [restored]; s. also FDanker, Jesus and the New Age ’88, 71).ⓑ τινί live for someone or someth., for the other’s benefit (Hom. et al.; Demosth. 7, 17 οἳ οὐκ αἰσχύνονται Φιλίππῳ ζῶντες καὶ οὐ τῇ ἑαυτῶν πατρίδι; Dionys. Hal. 3, 17 … παῖδες, τῷ πατρὶ ζῶντες) ζ. τῷ θεῷ (4 Macc 7:19; 16:25; Philo, Mut. Nom. 13, Rer. Div. Her. 111; s. SAalen, NTS 13, ’67, 10) Lk 20:38b (cp. Soph., Ajax 970); Ro 6:10, 11; Gal 2:19; Hm 3:5; AcPl Ha 10, 7; τῷ κυρίῳ Ro 14:8b (cp. Plut., Cleom. 819 [31, 5]). For Christ 2 Cor 5:15; τῷ ἐμῷ βασιλεῖ AcPl Ha 9, 26 (restored after Aa I 112, 14) τῇ δικαιοσύνῃ ζ. 1 Pt 2:24; ἑαυτῷ ζ. live for oneself (Menand., Fgm. 646 Kö. οὐχ ἑαυτῷ ζῆν μόνον; Diod S 10, 33, 2 ζ. ἑαυτοῖς=live for themselves) Ro 14:7.④ to be full of vitality, be lively the ptc. is used fig. w. respect to things (cp. τῶν δένδρων τῶν ζῶντων ParJer 9:3), of spring water in contrast w. cistern water ὕδωρ ζῶν (Gen 26:19; Lev 14:5; Jer 2:13 v.l.; Zech 14:8.—Stagnant water is called ὕ. νεκρόν: Synes., Ep. 114, 254d) J 4:10f (Hdb. exc. on J 4:14); 7:38; D 7:1f (Wengst p. 77 n. 57). ζώσας πηγάς Rv 7:17 v.l.⑤ to be life-productive, offer life ptc. used w. respect to things (SIG 1173 [138 A.D.], 5 ζῶσαι ἀρεταὶ ἐγένοντο=miracles full of divine life occurred) λόγια ζῶντα words that meant life Ac 7:38. λόγος ζῶν θεοῦ 1 Pt 1:23; cp. Hb 4:12. ὁδὸς ζῶσα a living way 10:20. ἐλπὶς ζῶσα a living hope 1 Pt 1:3.—ζ. is also used of things which serve as descriptions of pers. who communicate divine life: of Christ ὁ ἄρτος ὁ ζῶν J 6:51a. λίθος ζῶν 1 Pt 2:4. Of Christians: θυσία ζῶσα a living sacrifice Ro 12:1. λίθοι ζῶντες 1 Pt 2:5.—τὰ παρὰ ζώσης φωνῆς καὶ μενούσης the (words) of a living and abiding voice Papias (2:4) (opp. ἐκ τῶν βιβλίων).—Lit. s. ζωή end. DELG s.v. ζώω.M-M. TW. -
5 Logical Empiricism
Modern analytical empiricism... differs from that of Locke, Berkeley, and Hume by its incorporation of mathematics and its development of a powerful logical technique. It is thus able, in regard to certain problems, to achieve definite answers, which have the quality of science rather than of philosophy. It has the advantage, as compared with the philosophies of the system-builders, of being able to tackle its problems one at a time, instead of having to invent at one stroke a block theory of the whole universe. Its methods, in this respect, resemble those of science. I have no doubt that, in so far as philosophical knowledge is possible, it is by such methods that it must be sought: I also have no doubt that, by these methods, many ancient problems are completely soluble.... Take such questions as: What is number? What are space and time? What is mind, and what is matter? I do not say that we can here and now give definitive answers to all these ancient questions, but I do say that a method has been discovered by which, as in science, we can make successive approximations to the truth, in which each new stage results from an improvement, not a rejection, of what has gone before. (Russell, 1961, pp. 788-789)Not a single one of the great theses of Logical Empiricism (that Meaning is Method of Verification; that metaphysical propositions are literally without sense; that Mathematics is True by Convention) has turned out to be correct. It detracts from the excitement of the fact that, by turning philosophical theses into linguistic ones [as Carnap had tried to do]... one can make philosophy more scientific and settle the truth value of philosophical propositions by hard scientific research, if the results one obtains are uniformly negative. (Putnam, 1975, p. 20)Historical dictionary of quotations in cognitive science > Logical Empiricism
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