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1 celobrojno mnozenje i deljenje
• integer multiplication and division -
2 celobrojno množenje i deljenje
• integer multiplication and division -
3 целочисленное умножение и деление
целочисленное умножение и деление
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[ http://www.iks-media.ru/glossary/index.html?glossid=2400324]Тематики
- электросвязь, основные понятия
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Русско-английский словарь нормативно-технической терминологии > целочисленное умножение и деление
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4 Napier (Neper), John
SUBJECT AREA: Electronics and information technology[br]b. 1550 Merchiston Castle, Edinburgh, Scotlandd. 4 April 1617 Merchiston Castle, Edinburgh, Scotland[br]Scottish mathematician and theological writer noted for his discovery of logarithms, a powerful aid to mathematical calculations.[br]Born into a family of Scottish landowners, at the early age of 13 years Napier went to the University of St Andrews in Fife, but he apparently left before taking his degree. An extreme Protestant, he was active in the struggles with the Roman Catholic Church and in 1594 he dedicated to James VI of Scotland his Plaine Discovery of the Whole Revelation of St John, an attempt to promote the Protestant case in the guise of a learned study. About this time, as well as being involved in the development of military equipment, he devoted much of his time to finding methods of simplifying the tedious calculations involved in astronomy. Eventually he realized that by representing numbers in terms of the power to which a "base" number needed to be raised to produce them, it was possible to perform multiplication and division and to find roots, by the simpler processes of addition, substraction and integer division, respectively.A description of the principle of his "logarithms" (from the Gk. logos, reckoning, and arithmos, number), how he arrived at the idea and how they could be used was published in 1614 under the title Mirifici Logarithmorum Canonis Descriptio. Two years after his death his Mirifici Logarithmorum Canonis Constructio appeared, in which he explained how to calculate the logarithms of numbers and gave tables of them to eight significant figures, a novel feature being the use of the decimal point to distinguish the integral and fractional parts of the logarithm. As originally conceived, Napier's tables of logarithms were calculated using the natural number e(=2.71828…) as the base, not directly, but in effect according to the formula: Naperian logx= 107(log e 107-log e x) so that the original Naperian logarithm of a number decreased as the number increased. However, prior to his death he had readily acceded to a suggestion by Henry Briggs that it would greatly facilitate their use if logarithms were simply defined as the value to which the decimal base 10 needed to be raised to realize the number in question. He was almost certainly also aware of the work of Joost Burgi.No doubt as an extension of his ideas of logarithms, Napier also devised a means of manually performing multiplication and division by means of a system of rods known as Napier's Bones, a forerunner of the modern slide-rule, which evolved as a result of successive developments by Edmund Gunther, William Oughtred and others. Other contributions to mathematics by Napier include important simplifying discoveries in spherical trigonometry. However, his discovery of logarithms was undoubtedly his greatest achievement.[br]BibliographyNapier's "Descriptio" and his "Constructio" were published in English translation as Description of the Marvelous Canon of Logarithms (1857) and W.R.MacDonald's Construction of the Marvelous Canon of Logarithms (1889), which also catalogues all his works. His Rabdologiae, seu Numerationis per Virgulas Libri Duo (1617) was published in English as Divining Rods, or Two Books of Numbering by Means of Rods (1667).Further ReadingD.Stewart and W.Minto, 1787, An Account of the Life Writings and Inventions of John Napier of Merchiston (an early account of Napier's work).C.G.Knott (ed.), 1915, Napier Tercentenary Memorial Volume (the fullest account of Napier's work).KF -
5 συνάγω
A (lyr.), prob. in E.IA 290 (lyr.), [dialect] Ep.σύνᾰγον Il.14.448
: [tense] fut. συνάξω: [tense] aor. 1 συνῆξα, [dialect] Dor. ,1791 (Delph., ii B.C.); inf. συνάξαι v.l. in Ev.Luc. 3.17; part. συνάξας f.l. for συννάξας in Hdt.7.60: but the regul. [tense] aor. is συνήγαγον: [dialect] Att. [tense] pf.συνῆχα X.Mem.4.2.8
; (v.l. -γιοχ-, -γιωχ-, γειοχ-), Dsc.1.68, Iamb.VP35.254, etc.; [dialect] Dor.συναγάγοχα Test.Epict.3.12
: [tense] pf. [voice] Pass. συνῆγμαι, [dialect] Dor.- ᾶγμαι Ti.Locr.101b
.--Old [dialect] Att. [full] ξυνάγω, which Hom. also uses metri gr.:—bring together, gather together:I of persons, animals, etc., ἡ δὲ ξυνάγουσα γεραιὰς νηόν.. to the temple, Il.6.87, cf. Hdt.2.111, 3.150, etc.;ἐς ἕνα Χῶρον σ. μυριάδα ἀνθρώπων Id.7.60
;ἔνθα ποτ' Ὀρφεὺς σύναγεν δένδρεα μούσαις, σύναγεν θῆρας E.Ba. 563
(lyr.); ποίμνας Ὀλύμπου ς. S.Fr. 522; Ἕλληνας εἰς ἓν καὶ Φρύγας ς. E.Or. 1640, cf. Ar.Lys. 585 (anap.); σ. ἐς ὀλίγον crowd them into a narrow compass, Th.2.84;σ. εἰς ταὐτόν Pl.Phdr. 256c
, cf. Tht. 194b; εἰς ἕν, εἰς μίαν ἀρχήν, Arist.Pol. 1280b13, 1299b13; much like συνοικίζω, ib. 1285b7.2 bring together for deliberation or festivity,βουλήν Batr.134
;δικαστήριον Hdt.6.85
;τοὺς στρατηγούς Id.8.59
;ἐκκλησίαν τινὸς ἕνεκα Th.2.60
; ἔς τι, περί τινος, Id.1.120, X.HG7.1.27;οἱ νόμοι σ. ὑμᾶς, ἵνα.. D.19.1
;τὴν βουλὴν καὶ τὸν δῆμον Arist.Ath.43.3
; σ. πανηγύρεις, ἑταιρείας, συσσίτια, etc., Isoc.4.1,79, Pl.R. 365d, Lg. 625e, etc.;σ. ἔρανον Μηνὶ Τυράννῳ IG3.74.21
, cf. GDI1772, 1791 (Delph., ii B.C.):—[voice] Pass.,πανήγυρις.. συναγομένη SIG888.129
(Scaptopara, iii A.D.): abs., hold a club dinner or meeting, Thphr.Char.30.18, and so perh. OGI130.5 (Egypt, ii B.C.);σ. ἀπὸ συμβολῶν Diph.43.28
;ἔλεγον συνάγειν τὸ μετ' ἀλλήλων πίνειν Ath.8.365c
, cf. Sophil.4.2, Men.158, Hsch.; νυνὶ.. συνάγουσι they are at dinner, Men.Epit. 195.3 in hostile sense, ξ. Ἄρηα, ἔριδα Ἄρηος, ὑσμίνην, join battle, begin the battle-strife, etc., Il.2.381, 5.861, 14.448, al.; πόλεμον ς. Isoc.4.84.b match, pit two warriors one against the other, A.Th. 508: hence intr., ἐς μέσσον ς. engage in fight, Theoc.22.82;σ. τινί Plb.11.18.4
;εἰς Χεῖρας Plu.Publ.9
.4 bring together, join in one, unite,ἄμφω ἐς φιλότητα h.Merc. 507
;παράνοια σ. νυμφίους φρενώλεις A.Th. 756
(lyr.); τὸ κακὸν σέ τε κἀμὲ ς. E. Hel. 644 (lyr.), cf. Ar.Ach. 991 (lyr.);ἀνθρώπους εἰς κηδείαν X.Mem.2.6.36
; γυναῖκα καὶ ἄνδρα, of Isis, IG12(5).14.20 (Ios, iii A.D.): hence γάμους ς. contract marriages, X.Smp.4.64.5 bring together, make friends of, reconcile, Emp. ap. Arist.Metaph. 1000b11, D.58.42, 59.45; bring persons together in works of fiction,Κρέοντα καὶ Τειρεσίαν Pl. Ep. 311b
.6 σ. ἑαυτόν collect oneself, Plu.Phil.20.7 lead with one, receive,σ. εἰς τὸν οἶκον LXX 2 Ki.11.27
, cf. Jd.19.15; gave hospitality to..,Ev.Matt.
25.35:—[voice] Pass., Act.Ap.11.26.II of things,σύναγεν νεφέλας Od.5.291
, cf. Thphr.Vent.42;ἵνα οἱ σὺν φόρτον ἄγοιμι Od.14.296
;κήρυκες ὅρκια πιστὰ θεῶν σύναγον Il.3.269
;τὰ Χρήματα ἐκ τῶν ἀγρῶν X.An.6.2.8
; τὸ ἔλαιον ἐν ἀγγείοις interpol. in Hdt.6.119;τὰς εἰσφοράς Arist.Pol. 1314b15
, cf. PHib.1.157 (iii B.C.), PCair.Zen.315.1 (iii B.C.), etc.;καρπόν Plb.12.2.5
;κόγχον καὶ κύαμον Crates Theb.7
; τρυγᾶν καὶ ς. PRev.Laws 24.14 (iii B.C.); τὴν μήκωνα ς. Sammelb. 4305 (iii B.C.);σ. εἰς μίαν γωνίαν τὸ ἀποκτένισμα τοῦ στιππύου PCair.Zen.176.41
(iii B.C.);συναγαγεῖν καὶ συναθροῖσαι τὸ θερμόν Thphr.Ign.17
;εἰς ἀποθήκας Ev.Matt.6.26
;κοινὸν σ. τὸν βίον Pl.Plt. 311c
;σ. ἐκ δικαίων τὸν βίον Men.Mon. 196
; of an artist,σ. τὰ κάλλιστα ἐκ πολλῶν X. Mem.3.10.2
, cf. Pl.R. 488a.b of a historical writer,σ. τὰς πράξεις Isoc.12.252
, 15.45; συνηγμένος concise in speech, D.L.4.33; of an anthologist, ὅλας ῥήσεις εἰς ταὐτὸν ς. Pl.Lg. 811a; σ. εἰς ταὐτὸν τὰ κάλλιστα τοῖς αἰσχίστοις jumble together, identify, Aeschin.2.145, cf. Pl.Sph. 251d;Σειληνὸν καὶ Μαρσύαν.. εἰς ἕν Str.10.3.14
.2 draw together, so as to make the extremities meet, τὰ κέρεα (of an army) Hdt.6.113; Αἴας δὲ.. δεξιὸν κέρας πρὸς τὸ λαιὸν (dub. l.) (lyr.);σ. ἐς τετράγωνον τάξιν τοὺς ὁπλίτας Th.4.125
, cf. 1.63, etc.; σ. τὰ τέρματα, of two rivers which gradually approach one another, Hdt.4.52; σ. ἑαυτόν, of a snake, Arist.HA 594a19; σ. τοὺς πόρους, of a styptic, Thphr.Od.36; σ. τὰν ἁφάν, τὰν γεῦσιν, Ti.Locr. 101c; συναγμένα [φωνά] ib. 101b.b draw together, narrow, contract, [ τὴν διώρυχα] Hdt.7.23; πρῴρην ς. bring it to a point, Id.1.194; τὸν.. Χρόνον ὡς εἰς μικρότατον ς. D.Prooem.36;τὴν πόλιν Plb.5.93.5
, etc.;ἐκ μεγάλας δαπάνας εἰς μικρόν IG12(2).645
a.16 (Nesos, iv B.C.):—[voice] Pass.,συνάγεται καὶ διοίγεται ὁ φάρυγξ Arist.PA 664b25
;εἰς ὀξὺ συνῆχθαι Id.HA 496a19
;εἰς μικρόν Id.Mete. 354a7
, Democr. ap. Thphr.Ign.52; εἰς στενόν Didym. ap. Ath.11.477f;ποτήριον συνηγμένον εἰς μέσον Callix.3
; συνῆκται ἡ κοιλία is pinched in, drawn in, Archig. ap. Aët.6.3;ἐπὶ στενὸν συνάγεται τὸ στόμιον Sor.1.9
.cσ. τὰς ὀφρῦς S.Fr. 1121
, Ar.Nu. 582 (troch.), Antiph.218.2;ἐπισκύνιον Ar.Ra. 823
(lyr.); ; σ. τὰ βλέφαρα close the eyelids, ib.38, Gal.18(2).62; but σ. τὰ ὦτα prick the ears, of dogs, X.Cyn.3.5, cf. Ar.Eq. 1348;τὰ σκέλη πρὸς ἄλληλα Sor.1.101
, cf. 2.61 ([voice] Pass.), Diocl.Fr.141.d metaph.,σ. τινὰς ἐς κίνδυνον ἔσχατον App.Hann.60
; συνάγεσθαι to be straitened, afflicted, λιμῷ, σιτοδείᾳ, Plb.1.18.7,10; συνάγεσθαι τοῖς Χαρακτῆρσι to become pinched in its features, Sor.1.108; but πεφυκότος τοῦ θερμοῦ συνάγειν καὶ τονοῦν τὴν γαστέρα pull the stomach together, Gal.15.195; τὰ στύφοντα ἐδέσματα σ. καὶ σφίγγει τὰ σώματα ib.462, cf. 6.90, al.3 conclude from premisses, infer, prove, Arist.Rh. 1357a8, 1395b25, Metaph. 1042a3, Pol. 1299b12, Phld.Sign.12, al.;σ. ὅτι.. Arist.Rh. 1377b6
, cf. A.D. Conj.249.7: c. inf., Luc.Hist.Conscr.16: c. gen. abs., σ. ὥς τινος γενομένου form a conclusion of his having been.., Arist.Pol. 1274a25; συνάγοντες λόγοι cogent arguments, Stoic.2.77, Arr.Epict.1.7.12: also, sum up numbers, D.H.4.6, Ptol.Alm.9.10, Dioph.3.6, al.; also, obtain them by multiplication, ὁ συνηγμένος [ἀριθμὸς] ἐκ τῶν κβ καὶ πθ the product.., Aristarch.Sam.13, cf. Papp.22.7, Paul.Al.K.1; of division, give a quotient, Dioph.2.9; of an integer, yield a fraction (9 = 72/8), ib.12; of any calculation, yield a result, Id.1.25, al. ([voice] Pass.).4 [voice] Pass., συνάγεται τᾷ περιφορᾷ is carried along with it, Ti.Locr.98e.
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