-
61 law
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62 method
1) метод; способ; средство2) система; порядок3) технология4) методика•- method of applying liquid lubrication - method of calculation - method of column analogy - method of comparison - method of connecting - method of determining bending moments by fixed points - method of directions - method of elastic arch - method of elastic weights - method of electric needles - method of exchange of members - method of firing - method of fixed points - method of images - method of initial parameters - method of joints - method of least squares - method of least work - method of limit equilibrium - method of minimum strain energy - method of moments - method of movement - method of operation - method of payment - method of planning - method of production - method of redundant reactions - method of rotations - method of sections - method of separate joint displacement - method of slopes - method of stowage - method of strain measurement method - method of substitute redundant members - method of successive approximations - method of successive corrections - method of training - method of transportation - method of working - method of zero moment points - methods of network planning and control - ad hoc method - advertising method - aero-projection method - air-permeability method - airslide method - approximation method - arbitrary proportions method - area moment method - artificial islands method - ball method of testing - bench method - bidding methods - brush method of treatment timber - building methods - caisson method - cantilever method of design - cassette method of production of thin-slab structures - central mixing method - centre drift method - centrifuge method - centroidal method of design - change-in-stress method - chemical injection method - closed building method - column analogy method of design - compressed-air method of tunnelling - concrete testing method - cone method - construction works quality control method - core-drill method - correlation method - cut-and-cover method - cut-and-try method - cylinder method - deflection method - design methods - development method - dip method - dipping method of treatment timber - effective method - electrolytic method - emulsified-asphalt penetration method - energy method - equal load increments method - equal strain method - error method - fabrication method - fixing method - float and chains method - flow-line conveyer method - force method - graphical method - heading method of tunnelling - hot-air heating standpipe method - hot penetration method - hydraulic fill method - impact method - kinematic method - lacquer film method - land-assembly methods - lift-slab method - limit equilibrium method - limit stage design method - line production method - loading method - magnaflux method - mechanical method by pumps - membrane method of waterproofing - mixed-in-place method - mock-up methods of design - modular ratio method - moire fringe method - moment area method - moment-distribution method - moment-of-inertia method of designing - mud-jack method - mulch method - near end moment distribution method - neutral-points method - non-destructive testing methods - normal method - packing methods - patented method of construction - penetration method - percussive pneumatic method of riveting - photo-elastic method of stress-determination - photo-elasticity method - pilot method - pilot tunnel method - pin-and-string method - pipe-bridge method - plastic method of design - plastic theory method - polarized light method - portal method of design - pounding method of curing concrete - production line method of construction - qualitative methods - quantitative methods - relaxation method - ring-and-ball method - rolled-on method - safe method of heat insulation - safety methods - sampling method - sand-bearing method of testing clay pipes - sand-island method - scheduling method - seismic method of prospecting - simultaneous construction method - slope deflection method - spatial self-fixation erection method - statistical analysis method - stovepipe pipe-laying method - strain-energy method - successive construction method - surface-coating method of waterproofing - synthetic method of restoration - thixotropic liquid method - tilt-up method - top-heading method - transfiguration method - trial-load method - turnover method - ultimate-strength method - ultrasonic pulse velocity method - void method of proportioning - volume method of concrete mix design - volumetric method - water-jet method of pile-driving - weight method - well-point method of excavation - work method - working stress method of design* * *метод, способ; система; порядок; методика; технология- method of analysis
- method of application
- method of attack
- method of bearing and distances
- method of bipolar coordinates
- method of calculation
- method of design
- method of detail survey
- method of elastic weights
- method of electric needles
- method of expansion into series
- method of fixed points
- method of intersection
- method of joint isolation
- method of least work
- methods of manufacture
- method of minimum strain energy
- method of moment distribution
- method of radiation
- method of redistribution of pressure
- method of sections
- method of steam jet
- methods of structural analysis
- method of successive approximations
- methods of testing
- method of water needles
- accepted method of building
- accepted method of house construction
- accurate method of analysis
- adhesive nail-on method
- admittance method
- advanced methods of concreting
- advance slope method
- aggregate exposure method
- air permeability method
- alternate methods
- American method
- analytical method of determining reactions
- API method of pile design
- approximate method
- approximation method
- area method
- area-moment method
- assembly methods
- Austrian method
- autogenous curing method
- balanced cantilever method
- Belgian method
- Benoto method
- bentonite method
- Billner method
- "bin" method
- boiling water method
- boom placement concreting method
- bricklaying methods
- building method
- building block module method
- cable method of rock stressing
- calculation method
- cantilever method
- Chicago method
- circular-arc method
- Coast-Survey method
- collapse method of structural design
- combined finite strip-finite element method
- compaction methods of clays
- conjugate beam method
- consistency measurement method
- construction methods
- construction and erection methods
- contiguous pile method
- continuous-flight augers method
- continuous-sample method of advance
- convergence method
- critical method
- critical path method
- Cross moment distribution method
- Cross method
- cross-section method
- current design methods
- cut-and-cover method
- dampproofing methods
- displacement method
- displacement method of advance
- dual-rail method
- dummy unit-load method
- dust-spot method
- Dutch cone method
- earth pressure balanced tunneling method
- elastic center method
- elastic weights method
- electric analogy method
- electric resisting method
- energy method
- equal friction method of duct sizing
- equal friction method
- equivalent load method
- erection method
- fast track construction methods
- fatigue test method
- finite difference method
- finite element method
- finite strip method
- flight auger method
- flotation caisson method
- flue loss method
- folded plate method of analysis
- force method
- free cantilever method of construction
- general method of analysis
- Glotzl hydraulic cell method
- Gow method
- Hardy Cross method
- housing appraisal method
- in-duct method
- industrialized methods of construction
- iterative method
- jack method
- jacking method
- lacquer curtain coating method
- laser beam method
- leap-frog method
- limit equilibrium method
- limit state method
- listening methods
- load factor design method
- mandrel method
- mathematical method of design
- matrix method of structural analysis
- maturity method
- measuring method
- mixed-mode method
- mix-in-place method
- modern building methods
- modular ratio method
- moiré fringe method
- moment-balance method
- nondestructive methods of tests
- normal method of quality control
- null method
- numerical method
- one-rail method
- optical square method
- permissible stress method
- phototheodolite method
- plastic methods of structural analysis
- plate count method
- precast concrete manufacturing methods
- pressuremeter method
- proven construction methods
- p-y method of pile design
- rapid test method
- ratio method of balancing
- rebound hammer method
- reference point method
- relaxation method
- reproducible methods
- resistivity method
- resonant-frequency method
- reverberant field method
- Rockwell method of hardness testing
- safe method
- safe working methods
- secant interlocking pile method
- secant pile method
- seismic method of surveying
- seismic reflection method
- seismic refraction method
- semiprobabilistic design method
- shear transfer method
- shock response method of pile testing
- sliding-wedge method
- slope deflection method
- solar radiation method
- sonic method
- special method of quality control
- standard test method
- static regain method of duct sizing
- static regain method
- statistical design method
- step-by-step method
- strength design method
- strength evaluation method
- successive approximations method
- suspended cantilever method
- swamp shooting method
- Tagg method
- tangent modulus method
- test methods
- Theis method
- thixotropic liquid method
- three-point method
- tilt-up method
- time-saving method of construction
- TNO method of analysis
- TNO method of pile testing
- transit and stadia method
- tremie method
- truss analogy method
- turn-of-nut method
- ultrasonic pulse velocity method
- vacuum concrete method of bridge construction
- valveless pulse-jet method
- vane shear method
- velocity reduction method of duct sizing
- velocity reduction method
- vibratory method
- Vickers method of hardness testing
- volume method of measuring aggregates
- warm water method
- water fog spray method
- western bricklaying method
- western method
- working-stress design method -
63 law
1) закон3) правило4) принцип•under the law — по закону, согласно закону, в соответствии с законом
- Biot law- converse law of double negation- cube law- distributive law of disjunction over conjunction - double law of the mean - fifth power law - first distributive law - first law of mean- gas law- idempotency law - infinitely decomposable law - infinitely divisible law - inverse sine law - inverse square law - law of addition of probability - law of alteration of quantifiers - law of associativity of disjunction - law of comparative judgment - law of constant angles - law of double complementation - law of equal significance - law of mass action - law of random function - law of random vector - law of requisite variety - law of right invertibility - law of statistical regularity - law of universal causation - law of universal gravitation - Newton's first law of motion - Newton's law of gravitation - Newton's second law of motion - Newton's third law of motion - normal law of composition - normal law of errors - one-sided modular law - probabilistic law - probability law - product law of probability - quadratic reciprocity law - second law of mean - second order law - similitude law- time law- weak law -
64 model
1) макет; модель || моделировать2) образец4) модель, тип ( изделия)5) шаблон•- countably saturated model - countably uniform model - coupled channels model - finite state model - finitely generated model - game-theory model - random trial increment model - random walk model - sampling model -
65 модель
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66 πρός
πρός, Prep., expressing direction,A on the side of, in the direction of, hence c. gen., dat., and acc., from, at, to: [dialect] Ep. also [full] προτί and [full] ποτί, in Hom. usually c. acc., more rarely c. dat., and each only once c. gen., Il.11.831, 22.198:—dialectal forms: [dialect] Dor.[full] ποτί (q. v.) and [full] ποί, but Cret. [full] πορτί Leg.Gort.5.44, etc., Argive [full] προτ( [full] ί) Schwyzer 84.3 (found at Tylisus, V B.C.), restored in Mnemos.57.208(Argos, vi B.C.), and in Alcm.30; Arc., Cypr. [full] πός SIG306.11 (Tegea, iv B.C.), Inscr.Cypr. 135.19H., also sts. in Asia Minor in compds., v. ποσάγω, ποσφέρω; [dialect] Aeol. [full] πρός Sapph.69 ([etym.] προς-), 109, Alc.20 (s. v.l.); [full] πρές Jo.Gramm. Comp.3.10; Pamphylian περτ ([etym.] ί) Schwyzer 686.7, 686a4. (With [full] προτί, [full] πρός cf. Skt. práti 'towards, near to, against, back, etc.', Slav. protiv[ucaron], Lett. pret 'against', Lat. pretium: [full] ποτί (q. v.) and [full] πός are not cogn.) A. WITH GEN., πρός refers to that from which something comes:I of Place, from,ἵκετο ἠὲ π. ἠοίων ἦ ἑσπερίων ἀνθρώπων Od. 8.29
;τὸν π. Σάρδεων ἤλεκτρον S.Ant. 1037
(v.l.).2 on the side of, towards, νήσοισι πρὸς Ἤλιδος towards Elis, Od.21.347; π. ἁλός, π. Θύμβρης, Il.10.428, 430;εἶναι π. θαλάσσης Hdt.2.154
;ἱδρῦσθαι π. τοῦ Ἑλλησπόντου Id.8.120
;ἐστρατοπεδεύοντο π. Ὀλύνθου Th.1.62
, etc.; φυλακαὶ π. Αἰθιόπων, π. Ἀραβίων, π. Διβύης, on the frontier towards the Ethiopians, etc., Hdt.2.30: freq. with words denoting the points of the compass, δύω θύραι εἰσίν, αἱ μὲν π. βορέαο, αἱ δ' αὖ π. νότου one on the north side, the other on the south side, Od.13.110;οἰκέουσι π. νότου ἀνέμου Hdt.3.101
; π. ἄρκτου τε καὶ βορέω ἀνέμου κατοικημένοι ib. 102; π. μεσαμβρίης ib. 107; π. τοῦ Τμώλου τετραμμένον τῆς πόλιος (in such phrases the acc. is more common) Id.1.84;π. Πλαταιῶν Th. 3.21
;π. Νεμέας Id.5.59
; ἀπὸ τῆσδε τῆς ὁδοῦ τὸ π. τοῦ λιμένος ἅπαν everything on the harbour- ward side of this road, IG12.892: combined with π. c. acc.,π. ἠῶ τε καὶ τοῦ Τανάϊδος Hdt.4.122
;τὸν μέν π. βορέω ἑστεῶτα, τὸν δὲ π. νότον Id.2.121
, cf. 4.17.3 before, in presence of,μάρτυροι ἔστων π. τε θεῶν μακάρων π. τε θνητῶν ἀνθρώπων Il.1.339
;οὐδ' ἐπιορκήσω π. δαίμονος 19.188
; ποίτοῦ Ἀπόλλωνος .. ὑπίσχομαι prob. in IG22.1126.7 (Amphict. Delph., iv B. C.); ὑποσχομένους πρὸς τοῦ Διός ib.1237.16: hence,b in the eyes of,ἄδικον οὐδὲν οὔτε π. θεῶν οὔτε π. ἀνθρώπων Th.1.71
, cf. X.An.1.6.6, etc.; ὅσιος π. θεῶν Lex ap.And.1.97; κατειπάτω.. ἁγνῶς π. τοῦ θεοῦ if he wishes to be pure in the sight of the god, SIG986.9, cf. 17 (Chios, v/iv B. C.);ὁ γὰρ καιρὸς π. ἀνθρώπων βραχὺ μέτρον ἔχει Pi.P.4.286
.4 in supplication or adjuration, before, and so, in the name of,σε.. γουνάζομαι.. π. τ' ἀλόχου καὶ πατρός Od.11.67
;π. θεῶν πατρῴων S.Ant. 839
(lyr.), etc.; ἱκετεύω, ἀντιβολῶ π. παίδων, π. γυναικῶν, etc., D.28.20, etc.: the verb is freq. omitted with π. θεῶν or τῶν θεῶν, E.Hec. 551, S.OT 1037, Ar.V. 760;π. τοῦ Διός Id.Av. 130
: less freq. with other words,π. τῆς ἑστίας E.Fr.953.39
;π. Χαρίτων Luc.Hist.Conscr.14
;μὴ π. γενείου S.El. 1208
;μὴ π. ξενίας τᾶς σᾶς Id.OC 515
(lyr.): sts. in questions, π. θεῶν, τίς οὕτως εὐήθης ἐστίν; in heaven's name, D.1.15;π. τῆς Ἀθηνᾶς.. ; Din.1.45
;ἆρ' οὖν, ὦ π. Διός,.. ; Pl.R. 459a
, cf. Ap. 26e: sts. in Trag. with the pron. σε between prep. and case,π. νύν σε πατρὸς π. τε μητρός.. ἱκνοῦμαι S.Ph. 468
;μὴ π. σε γονάτων E.Med. 324
.5 of origin or descent, from, on the side of, γένος ἐξ Ἁλικαρνησσοῦ τὰ π. πατρός by the father's side, Hdt.7.99;Ἀθηναῖον.. καὶ τὰ π. πατρὸς καὶ τὰ π. μητρός D.57.17
, cf. Isoc.3.42, SIG1015.7 (Halic.); πρόγονοι ἢ π. ἀνδρῶν ἢ γυναικῶν in the male or female line, Pl.Tht. 173d;ὁ πατὴρ π. μὲν ἀνδρῶν ἦν τῶν Εὐπατριδῶν Isoc.16.25
;οἱ συγγενεῖς τοῦ πατρὸς καὶ π. ἀνδρῶν καὶ π. γυναικῶν D.57.23
; οἱ π. αἵματος blood-relations, S.Aj. 1305;ἢ φίλων τις ἢ π. αἵματος φύσιν Id.El. 1125
.II of effects proceeding from what cause soever:1 from, at the hand of, with Verbs of having, receiving, etc.,ὡς ἂν.. τιμὴν καὶ κῦδος ἄρηαι π. πάντων Δαναῶν Il.16.85
, cf. 1.160, etc.;τιμὴν π. Ζηνὸς ἔχοντες Od.11.302
;δίδοι οἱ.. χάριν ποτ' ἀστῶν καὶ ποτὶ ξείνων Pi.O.7.90
; ;φυλακῆς π. δήμου κυρῆσαι Hdt.1.59
;τυχεῖν τινος π. θεῶν A.Th. 550
, cf. S.Aj. 527;λαχὼν π. δαιμόνων ὄλβον Pi.N.9.45
;κακόν τι π. θεῶν ἢ π. ἀνθρώπων λαβεῖν Hdt.2.139
, etc.;μανθάνειν π. ἀστῶν S.OC13
: with passive Verbs, προτὶ Ἀχιλλῆος δεδιδάχθαι to have been taught by.., Il.11.831, cf. S.OT 357;ἄριστα πεποίηται.. πρὸς Τρώων Il.6.57
; αἴσχε' ἀκούω π. Τρώων ib. 525, cf. Heraclit.79;ταῦτα.. π. τούτου κλύειν S.OT 429
;οὐ λέγεται π. οὐδαμῶν Hdt.1.47
; ἀτιμάζεσθαι, τετιμῆσθαι π. τινῶν, ib.61,2.75; alsoλόγου οὐδενὸς γίνεσθαι π. τινῶν Id.1.120
; παθεῖν τι π. τινός at the hand of, ib.73;π. ἀλλήλοιν θανεῖν E. Ph. 1269
, cf. S.OT 1237; π. τῆς τύχης ὄλωλεν ib. 949;τὸ ποιεύμενον π. τῶν Λακεδαιμονίων Hdt.7.209
;αἰτηθέντες π. τινὸς χρήματα Id.8.111
;ἱμέρου βέλει π. σοῦ τέθαλπται A.Pr. 650
: with an Adj. or Subst.,τιμήεσσα π. πόσιος Od.18.162
;ἐπίφθονος π. τῶν πλεόνων ἀνθρώπων Hdt.7.139
;ἔρημος π. φίλων S.Ant. 919
;ἀπαθὴς π. ἀστῶν Pi.P.4.297
;πειθὼ π. τινός S.El. 562
;π. Τρώων.. κλέος εἶναι Il.22.514
; ἄρκεσις π. ἀνδρός, δόξα π. ἀνθρώπων, S.OC73, E.Heracl. 624 (lyr.);ἐλίπετο ἀθάνατον μνήμην π. Ἑλλησποντίων Hdt.4.144
: with an Adv., οἶμαι γὰρ ἂν οὐκ ἀχαρίστως μοι ἔχειν οὔτε π. ὑμῶν οὔτε π. τῆς Ἑλλάδος I shall meet with no ingratitude at your hands, X.An.2.3.18, cf. Pl.R. 463d.2 of things, π. τίνος ποτ' αἰτίας [τέθνηκεν]; from of by what cause? S.OT 1236; π. ἀμπλακημάτων by or by reason of.., Id.Ant.51.III of dependence or close connexion: hence,1 dependent on one, under one's protection,π. Διός εἰσι ξεῖνοί τε πτωχοί τε Od.6.207
,14.57; δικασπόλοι, οἵ τε θέμιστας π. Διὸς εἰρύαται by commission from him, Il.1.239; π. ἄλλης ἱστὸν ὑφαίνοις at the bidding of another, 6.456.2 on one's side, in one's favour, Hdt.1.75, 124, S.OT 1434, Tr. 479, etc.;π. τῶν ἐχόντων.. τὸν νόμον τίθης E.Alc. 57
.IV of that which is derivable from: hence, agreeable to, becoming, like,τὰ τοιαῦτα ἔργα οὐ π. τοῦ ἅπαντος ἀνδρὸς νενόμικα γίνεσθαι, ἀλλὰπ. ψυχῆς τε ἀγαθῆς καὶ ῥώμης ἀνδρηΐης Hdt.7.153
, cf.5.12; ἦ κάρτα π. γυναικὸς αἴρεσθαι κέαρ 'tis very like a woman, A.Ag. 592, cf. 1636;οὐ π. ἰατροῦ σοφοῦ θρηνεῖν ἐπῳδάς S.Aj. 581
, cf. Ar.V. 369, E.Hel. 950, etc.;π. σοῦ ἐστι Id.HF 585
, etc.;οὐκ ἦν π. τοῦ Κύρου τρόπου X.An. 1.2.11
, etc.: of qualities, etc.,π. δυσσεβείας A.Ch. 704
; π. δίκης οὐδὲν τρέμων agreeably to justice, S.OT 1014, cf.El. 1211;οὐ π. τῆς ὑμετέρας δόξης Th.3.59
; ἐάν τι ἡμῖν π. λόγου ᾖ if it be at all to our purpose, Pl.Grg. 459c;εἰ τόδε π. τρόπου λέγω
correctly,Id.
R. 470c; but π. τρόπου τι ὠνεῖσθαι buy at a reasonable price, Thphr.Char.30.12;τὰ γενήματα π. ἐλάσσονος τιμᾶς πωλῶν IG5(2).515.14
([place name] Lycosura); π. ἀγαθοῦ, π. κακοῦ τινί ἐστι or γίγνεται, it is to one's advantage or otherwise, Arist.Mu. 397a30, Arr.An.7.16.5, Hld.7.12; π. ἀτιμίας λαβεῖν τι to take a thing as an insult, regard it so, Plu.Cic.13;π. δέους λαβεῖν τι Id.Flam.7
; λαβεῖν τι π. ὀργῆς (v.l. ὀργήν) J.AJ8.1.3; μοι π. εὐκλείας γένοιτο ib. 18.7.7; τῷ δήμῳ π. αἰσχύνης ἂν ἦν, π. ὀνείδους ἂν ἦν τῇ πόλει, Lib.Decl.43.27,28.B WITH DAT., it expresses proximity, hard by, near, at,ποτὶ γαίῃ Od.8.190
, 11.423;ποτὶ γούνασι Il.5.408
; ποτὶ δρυσίν among the oaks, 14.398 (nisi leg. περί); πρὸς ἄκμονι χαλκεύειν Pi.P.1.86
; ποτὶ γραμμᾷ στᾶσαί τινα ib.9.118; ἄγκυραν ποτὶ ναΐ κρημνάντων ib.4.24;δῆσαί τινα πρὸς φάραγγι A.Pr.15
;νεὼς καμούσης ποντίῳ π. κύματι Id.Th. 210
;π. μέσῃ ἀγορᾷ S.Tr. 371
;π. Ἀργείων στρατῷ Id.Aj.95
;π. πέδῳ κεῖται Id.OT 180
(lyr.); θακεῖν π. ναοῖς ib.20, cf. A.Eu. 855;π. ἡλίου ναίουσι πηγαῖς Id.Pr. 808
;π. τῇ γῇ ναυμαχεῖν Th. 7.34
; ἐς μάχην καθίστασθαι π. (v.l. ὑπ')αὐτῇ τῇ πόλει Id.2.79
;τεῖχος π. τῇ θαλάσσῃ Id.3.105
;αἱ π. θαλάττῃ πόλεις X.HG4.8.1
; τὸ π. Αἰγίνῃ στράτευμα off Aegina, Th.1.105; Αίβυες οἱ π. Αἰγύπτῳ bordering on.., ib. 104; τὸ π. ποσί that which is close to the feet, before one, S.OT 130, etc.; θρηνεῖν ἐπῳδὰς π... πήματι over it, Id.Aj. 582; αἱ π. τῇ βάσει γωνίαι the angles at the base, Euc.1.5,al.;τὴν π. τῷ.. ιερῷ κρήνην IG22.338.13
, cf. SIG1040.15 (Piraeus, iv B. C.), al.2 before, in the presence of, π. τοῖς θεσμοθέταις, π. τῷ διαιτητῇ λέγειν, D. 20.98,39.22;ὅσα π. τοῖς κριταῖς γέγονεν Id.21.18
;π. διαιτητῇ φεύγειν Id.22.28
.3 with Verbs denoting motion towards a place, upon, against,ποτὶ δὲ σκῆπτρον βάλε γαίῃ Il.1.245
, Od.2.80;με βάλῃ.. ποτὶ πέτρῃ 5.415
, cf. 7.279, 9.284; , cf. 5.401; λιαζόμενον ποτὶ γαίῃ sinking on the ground, Il.20.420;ἴσχοντες πρὸς ταῖς πόλεσι Th.7.35
.4 sts. with a notion of clinging closely, προτὶ οἷ λάβε clasped to him, Il.20.418;προτὶ οἷ εἷλε 21.507
;πρὸς ἀλλήλῃσιν ἔχονται Od.5.329
;προσπεπλασμένας.. π. ὄρεσι Hdt.3.111
; π. δμῳαῖσι κλίνομαι fall into the arms of.., S.Ant. 1189;π. τινί
close to,Men.
Epit. 204.II to express close engagement, at the point of,π. αὐτῷ γ' εἰμὶ τῷ δεινῷ λέγειν S.OT 1169
; engaged in or about,π. τῷ εἰρημένῳ λόγῳ ἦν Pl.Phd. 84c
, cf. Phdr. 249c, 249d;ἂν π. τῷ σκοπεῖν.. γένησθε D.18.176
;ἀεὶ π. ᾧ εἴη ἔργῳ, τοῦτο ἔπραττεν X. HG4.8.22
; διατρίβειν or σχολάζειν π. τινί, Epicr.11.3 (anap.), Arist. Pol. 1308b36 (butπ. ταῦτα ἐσχόλασα X.Mem.3.6.6
);ὅλος εἶναι π. τῷ λήμματι D.19.127
;π. τῇ ἀνάγκῃ ταύτῃ γίγνεσθαι Aeschin.1.74
; τὴν διάνοιαν, τὴν γνώμην ἔχειν π. τινί, Pl.R. 500b, Aeschin.3.192; κατατάξαι αὐτὸν π. γράμμασιν, i.e. give him a post as clerk, PCair.Zen. 342.3 (iii B. C.);ὁ π. τοῖς γράμμασι τεταγμένος Plb.15.27.7
, cf. 5.54.7, D.S.2.29,3.22;ἐπιμελητὴς π. τῇ εἰκασίᾳ τοῦ σησάμου PTeb.713.2
, cf.709.1 (ii B. C.).III to express union or addition, once in Hom., ἄασάν μ' ἕταροί τε κακοὶ π. τοῖσί τε ὕπνος and besides them sleep, Od.10.68;π. τοῖς παροῦσιν ἄλλα
in addition to,A.
Pr. 323, cf. Pers. 531, Xenoph.8.3. Emp.59.3;ἄλλους π. ἑαυτῷ Th.1.90
; π. ταῖς ἡμετέραις [τριήρεσι] Id.6.90;δέκα μῆνας π. ἄλλοις πέντε S.Tr.45
;τρίτος.. π. δέκ' ἄλλαισιν γοναῖς A.Pr. 774
; κυβερνήτης π. τῇ σκυτοτομίᾳ in addition to his trade of leather-cutter, Pl.R. 397e: freq. with neut. Adjs., π. τῷ νέῳ ἁπαλός besides his youth, Id.Smp. 195c, cf. Tht. 185e;π. τῷ βλαβερῷ καὶ ἀηδέστατον Id.Phdr. 240b
; π. τούτοισι besides this, Hdt.2.51, cf. A.Pers. 237 (troch.), etc.; rarely in sg.,π. τούτῳ Hdt.1.31
,41; π. τοῖς ἄλλοις besides all the rest, Th.2.61, etc.:—cf. the Advb. usage, infr. D.C WITH ACCUS., it expresses motion or direction towards an object:I of Place, towards, to, with Verbs of Motion,ἰέναι π. Ὄλυμπον Il.1.420
; ἰέναι π. δώματα, etc., Od.2.288, etc.;ἰέναι π. ἠῶ τ' ἠέλιόν τε Il.12.239
; φέρειν προτὶ ἄστυ, ἄγειν προτὶ Ἴλιον, etc., 13.538, 657, etc.; ἄγεσθαιπρὸς οἶκον, ἐρύεσθαι ποτὶ Ἴλιον, 9.147,18.174; ὠθεῖν, δίεσθαι προτὶ ἄστυ, 16.45, 15.681, etc.;ῥίπτασκε ποτὶ νέφεα Od.8.374
;βαλεῖν ποτὶ πέτρας 12.71
;κυλινδόμενα προτὶ χέρσον 9.147
; ἀπῆλθε πρὸς ἑαυτόν returned to his home, LXX Nu.24.25; κληθῆναι π. τὸ δεῖπνον (rarer than ἐπὶ δεῖπνον) Plu. Cat.Ma.3.2 with Verbs implying previous motion, upon, against, π. τεῖχος, π. κίονα ἐρείσας, Il.22.112, Od.8.66;ἅρματα.. ἔκλιναν π. ἐνώπια Il.8.435
;ἔγχος ἔστησε π. κίονα Od.1.127
;ποτὶ τοῖχον ἀρηρότες 2.342
;ποτὶ βωμὸν ἵζεσθαι 22.334
;πρὸς γοῦνα καθέζετό τινος 18.395
;π. ἄλλοτ' ἄλλον πημονὴ προσιζάνει A.Pr. 278
;τὰ πολλὰ πατρὸς π. τάφον κτερίσματα S.El. 931
; χῶρον π. αὐτὸν τόνδ' dub. in Id.Ph.23; later,ἔστη π. τὸν στῦλον LXX 4 Ki.23.3
;ὁ ὄχλος π. τὴν θάλασσαν ἐπὶ τῆς γῆς ἦσαν Ev.Marc.4.1
; π. ὑμᾶς παραμενῶ with you, 1 Ep.Cor.16.6;ἐκήδευσαν τὸν.. πατέρα.. π. τοὺς λοιποὺς συγγενεῖς
beside,Supp.Epigr.
6.106 ([place name] Cotiaeum).b of addition, (Argos, v B. C.);ἵππον προσετίθει πρὸς τοὔνομα Ar.Nu.63
, cf. Hdt.6.125, X.HG1.5.6, Pl.Phlb. 33c, Arist.Rh. 1359b28; προσεδαπάνησε π. τὸ μερισθὲν αὐτῷ εἰς τὸ ἔλαιον ἐκ τῶν ἰδίων over and above the sum allotted to him, IG22.1227.9; προσετέθη π. τὸν λαὸν αὐτοῦ was gathered to his people, LXX Ge.49.33.3 with Verbs of seeing, looking, etc., towards,ἰδεῖν π. τινά Od.12.244
, al.; ὁρᾶν, ἀποβλέπειν π. τι or τινά, A.Supp. 725, Ar.Ach. 291, etc.;ἀνταυγεῖ π. Ὄλυμπον Emp.44
; στάντε ποτὶ πνοιήν so as to face it, Il.11.622 (similarly, πέτονται πρὸς τὸ πνεῦμα against the wind, Arist.HA 597a32); κλαίεσκε π. οὐρανόν cried to heaven, Il.8.364: freq. of points of the compass, π. ζόφον κεῖσθαι lie towards the West, Od.9.26;ναίειν π. ἠῶ τ' ἠέλιόν τε 13.240
;στάντα π. πρώτην ἕω S.OC 477
; so in Prose,π. ἠῶ τε καὶ ἡλίου ἀνατολάς Hdt. 1.201
, cf. 4.40;π. βορέην τε καὶ νότον Id.2.149
; alsoἀκτὴ π. Τυρσηνίην τετραμμένη τῆς Σικελίης Id.6.22
(v. supr. A. 1.2); π. ἥλιον facing the sun, and so, in the sunlight, Ar.V. 772; so π. λύχνον by lamplight, Id. Pax 692, Jul.Ep.4;π. τὸ λύχνον Hippon.22
Diehl, cf. Arist.Mete. 375a27;πὸτ τὸ πῦρ Ar.Ach. 751
;πρὸς τὸ πῦρ Pl.R. 372d
, cf. Arist.Pr. 870a21; π. φῶς in open day, S.El. 640; but, by torch-light, Plu.2.237a.4 in hostile sense, against,π. Τρῶας μάχεαι Il.17.471
;ἐστρατόωνθ'.. π. τείχεα Θήβης 4.378
; π. δαίμονα against his will, 17.98;βεβλήκει π. στῆθος 4.108
;γούνατ' ἐπήδα π. ῥόον ἀΐσσοντος 21.303
;χρὴ π. θεὸν οὐκ ἐρίζειν Pi.P.2.88
;π. τοὐμὸν σπέρμα χωρήσαντα S.Tr. 304
;ἐπιέναι π. τινάς Th.2.65
;ὅσα ἔπραξαν οἱ Ἕλληνες π. τε ἀλλήλους καὶ τὸν βάρβαρον Id.1.118
;ἀγωνίζεσθαι π. τινά Pl.R. 579c
;ἀντιτάττεσθαι π. πόλιν X.Cyr.3.1.18
: also in argument, in reply to,ταῦτα π. τὸν Πιττακὸν εἴρηται Pl.Prt. 345c
; and so in the titles of judicial speeches, πρός τινα in reply to, less strong than κατά τινος against or in accusation, D.20 tit., etc.;μήτε π. ἐμὲ μήτε κατ' ἐμοῦ δίκην εἶναι Is.11.34
.5 without any hostile sense,π. ἀλλήλους ἔπεα πτερόεντ' ἀγόρευον Il.3.155
,cf.5.274,11.403,17.200;π.ξεῖνον φάσθαι ἔπος ἠδ' ἐπακοῦσαι Od.17.584
; λέγειν, εἰπεῖν, φράζειν π. τινά, Hdt. 1.8,90, Ar.V. 335, Nu. 359;ἀπαγγεῖλαι π. τινάς A.Ch. 267
;μνησθῆναι π. τινά Lys.1.19
, etc.;ἀμείψασθαι π. τινά Hdt.8.60
codd.;ἀποκρίνεσθαι π. τινάς Ar.Ach. 632
, Th.5.42; ὤμοσε δὲ π. ἔμ' αὐτόν he swore to me, Od.14.331: π. sts. governs the reflex. pron.,διαλογίζεσθαι π. ὑμᾶς αὐτούς Is.7.45
; ἀναμνήσθητε, ἐνθυμήθητε π. ὑμᾶς αὐτούς, Isoc.6.52, 15.60;π. ἐμαυτὸν.. ἐλογιζόμην Pl.Ap. 21d
; μινύρεσθαι, ἄδειν π. ἑαυτόν, Ar.Ec. 880, 931;ἐπικωκύω.. αὐτὴ π. αὑτήν S.El. 285
.b π. σφέας ἔχειν δοκέουσι, i.e. they think they are pregnant, Hp.Nat.Puer. 30.6 of various kinds of intercourse or reciprocal action, π... Διομήδεα τεύχε' ἄμειβεν changed arms with Diomedes, Il.6.235;ὅσα.. ξυμβόλαια.. ἦν τοῖς ἰδιώταις π. τοὺς ἰδιώτας ἢ ἰδιώτῃ π. τὸ κοινόν IG12.116.19
; σπονδάς, συνθήκας ποιεῖσθαι π. τινά, Th.4.15, Plb.1.17.6;ξυγχωρεῖν π. τινάς Th.2.59
;γίγνεται ὁμολογία π. τινάς Id.7.82
, cf. Hdt. 1.61;π. τινὰς ξυμμαχίαν ποιεῖς θαι Th.5.22
;π. ἀλλήλους ἡσυχίαν εἶχον καὶ π. τοὺς ἄλλους.. εἰρήνην ἦγον Isoc.7.51
;π. ἀλλήλους ἔχθραι τε καὶ στέργηθρα A.Pr. 491
; alsoσαίνειν ποτὶ πάντας Pi.P.2.82
, cf. O.4.6;παίζειν πρός τινας E.HF 952
, etc.;ἀφροδισιάζειν π. τινά X.Mem.1.3.14
;ἀγαθὸς γίγνεσθαι π. τινά Th.1.86
;εὐσεβὴς π. τινὰς πέλειν A.Supp. 340
; διαλέγεσθαι π. τινά converse with.., X.Mem.1.6.1, Aeschin.2.38,40, 3.219;κοινοῦσθαι π. τινάς Pl.Lg. 930c
;π. τοὺς οἰκέτας ἀνακοινοῦσθαι περὶ τῶν μεγίστων Thphr.Char.4.2
; διαλογίζεσθαι π. τινά balance accounts with.., D.52.3, cf. SIG241.127 (Delph., iv B. C.);ἃ ἔχει διελόμενος π. τὸν ἀδελφόν IG12(7).55.8
(Amorgos, iv/iii B. C.), cf. D. 47.34.b in phrases of the form ἡ π. τινὰ εὔνοια (ἔχθρα, etc.), π. sts. means towards, as ἡ π. αὑτοὺς φιλία the affection of their wives towards or for them, X.Cyr.3.1.39;ἡ π. ὑμᾶς ἔχθρα Id.HG3.5.10
;ἡ ἀπέχθεια ἡ π. τοὺς πλουσίους Arist.Pol. 1305a23
;τὴν π. τοὺς τετελευτηκότας εὔνοιαν ὑπάρχουσαν D.18.314
, cf. SIG352.13 (Ephesus, iv/iii B. C.), al.;φυσικαὶ τοκέων στοργαὶ π. τέκνα ποθεινά IG12(5).305.13
([place name] Paros): but sts. at the hands of, ἡ π. τὸ θεῖον εὐμένεια the favour of the gods, Th.5.105; φθόνος τοῖς ζῶσι π. τὸ ἀντίπαλον jealousy is incurred by the living at the hands of their rivals, Id.2.45; τὴν ἀπέχθειαν τὴν π. Θηβαίους.. τῇ πόλει γενέσθαι the hostility incurred by Athens at the hands of the Thebans, D.18.36, cf.6.3, 19.85; τῇ φιλίᾳ τῇ π. τὸν τετελευτηκότα the friendship with (not 'affection for') the deceased, Is.1.17, cf. Pl.Ap. 21c, 28a, Isoc.15.101,19.50, Lycurg.135, Din.1.19, etc.;τίνος ὄντος ἐμοὶ π. ὑμᾶς ἐγκλήματος; Lys.10.23
, cf. 16.10;τιμώμενος.. διὰ τὴν π. ὑμᾶς πίστιν Din.3.12
, cf. Lys.12.67, D.20.25; τῷ φόβῳ τῷ π. ὑμᾶς the fear inspired by you, Id.25.93; τῇ π. Ῥωμαίους εὐνοία his popularity with the Romans, Plb.23.7.5.7 of legal or other business transacted before a magistrate, witness, etc.,τάδε ὁ σύλλογος ἐβουλεύσατο.. π. μνήμονας SIG45.8
(Halic., v B. C.), cf. IG7.15.1 (Megara, ii B. C.); γράφεσθαι αὐτὸν κλοπῆς.. π. τοὺς ἐπιμελητάς ib.12.65.46; ἀτέλειαν εἶναι αὐτῷ καὶ δίκας π. τὸν πολέμαρχον ib.153.7; λόγον διδόντων τῶν.. χρημάτων.. π. τοὺς λογιστάς ib.91.27; before a jury,ἔστι δὲ τούτοις μὲν π. ὑμᾶς ἁγών, ὑμῖν δὲ π. ἅπασαν τὴν πόλιν Lys. 26.14
;ἀντιδικῆσαι τῷ παιδὶ.. π. ὑμᾶς Is.11.19
codd. (dub.); before a witness to whom an appeal for corroboration is made, Id.3.25; ([place name] Elis); φέρρεν αὐτὸν πὸ (τ) τὸν Δία in the eyes of Zeus, ib.415.7(ibid.); λαχεῖν πρὸς τὸν ἄρχοντα, γράφεσθαι π. τοὺς θεσμοθέτας, D.43.15, Lex ib.21.47, cf. Arist.Ath.56.6;τοῖς ἐμπόροις εἶναι τὰς δίκας π. τοὺς θεσμοθέτας D.33.1
; θέντων τὰ.. ποτήρια.. π. Πολύχαρμον having pawned the cups with P., IPE12.32A15 (Olbia, iii B. C.); alsoδιαβάλλειν τινὰ π. τοὺς πολλούς X. Mem. 1.2.31
, cf. D.7.33.II of Time, towards or near a certain time, at or about,ποτὶ ἕσπερα Od.17.191
;ποτὶἕσπερον Hes.Op. 552
;πρὸς ἑσπέραν Pl.R. 328a
;ἐπεὶ π. ἑσπέραν ἦν X.HG4.3.22
;π. ἡμέραν Id.An.4.5.21
;π. ὄρθρον Ar.Lys. 1089
; ποτ' ὄρθρον (nisi leg. πότορθρον) Theoc.5.126, Erinn. in PSI9.1090.48 + 8 (p.xii); ; π.ἀῶ ἐγρέσθαι, π. ἡμέραν ἐξεγρέσθαι, Theoc.18.55, Pl.Smp. 223c; π. γῆρας, π. τὸ γῆρας, in old age, E.Med. 592, Pl.Lg. 653a; π. εὐάνθεμον φυάν in the bloom of life, Pi.O.1.67; μέχρις ὅτου π. γυναῖκας ὦσι, i.e.of marriageable age, IG22.1368.41: later, π.τὸ παρόν for the moment, Luc.Ep. Sat.28, etc.; v. infr. 111.5.III of Relation between two objects,1 in reference to, in respect of, touching, τὰ π. τὸν πόλεμον military matters, equipments, etc., Th.2.17, etc.; τὰ π. τὸν βασιλέα our relations to the King, D.14.2; τὰ π. βασιλέα πράγματα the negotiations with the King, Th.1.128; τὰ π. τοὺς θεούς our relations, i.e. duties, to the gods, S.Ph. 1441;μέτεστι π. τὰ ἴδια διάφορα πᾶσι τὸ ἴσον.. ἐλευθέρως δὲ τὰ π. τὸ κοινὸν πολιτεύομεν Th.2.37
;οὐδὲν διοίσει π. τὸ γενέσθαι..
in respect of..,Arist.
APr. 24a25, cf. Pl.Phd. 111b; ἕτερος λόγος, οὐ π. ἐμέ that is another matter, and does not concern me, D.18.44, cf. 21,60, Isoc.4.12; τῶν φορέτρων ὄντων π. ἐμέ freightage shall be my concern, i.e. borne by me, PAmh.91.18 (ii A. D.);π. τοῦτον ἦν ἡ τῶν διαφόρων πρᾶξις LXX 2 Ma.4.28
; ἐὰν.. βοᾷ καὶ σχετλιάζῃ μηδὲν π. τὸ πρᾶγμα, nihil ad rem, D.40.61; οὐδὲν π. τὸν Διόνυσον Prov. ap.Plb.39.2.3, Suid.; οὐδὲν αὐτῷ π. τὴν πόλιν ἐστίν he owes no reckoning to the State, D.21.44;λόγος ἐστὶν ἐμοὶ π. Ἀθηναίους Philonid. 1
D.;π. Ἰάσονά ἐστιν αὐτῷ περὶ τῆς τιμῆς PHamb.27.8
(iii B. C.), cf. PCair.Zen.150.18 (iii B. C.); ἔσται αὐτῷ π. τὸν Θεόν (sc. ὁ λόγος ) he shall have to reckon with God, Supp.Epigr.6.188, cf. 194, al. ([place name] Eumenia); without αὐτῷ, ib.236 ([place name] Phrygia);ἔσται π. τὴν Τριάδαν MAMA1.168
, cf. Supp.Epigr.6.302 (Laodicea Combusta); ἕξει π. τὸν Θεόν ib.300, al. (ibid.); ἕξει π. τὴν ἐωνίαν κρίσιν ib.4.733 ([place name] Eukhaita), cf. 6.841 ([place name] Cyprus);π. πολλοὺς ἔχων ἀγωνιστάς Suid.
s.v. ὅσα μῦς ἐν πίσσῃ, cf. 2 Ep.Cor.5.12: with Advbs.,ἀσφαλῶς ἔχειν π. τι X.Mem.1.3.14
, etc.; [τὸ or τὰ] πρός τι, the relative term or terms, Arist.Cat. 1b25, 6a36, al.; τὸ π. τι, Pythag. name for two, Theol.Ar.8; π. ἡμᾶς relatively to us, opp. ἁπλῶς, Arist.APo. 72a1; ὀρθὸς πρός or ποτί c. acc., perpendicular to, Archim.Sph.Cyl.2.3, Spir.20; ἁ Δζ ποτὶ τὰν ΑΔ ἀμβλεῖαν ποιεῖ γωνίαν ib.16.2 in reference to, in consequence of,πρὸς τοῦτο τὸ κήρυγμα Hdt.3.52
, cf. 4.161;π. τὴν φήμην
in view of..,Id.
3.153, cf. Th.8.39;χαλεπαίνειν π. τι Id.2.59
;ἀθύμως ἔχειν π. τι X.HG4.5.4
, etc.: with neut. Pron.,π. τί;
wherefore? to what end?S.
OT 766, 1027, etc.; π. οὐδέν for nothing, in vain, Id.Aj. 1018; π. οὐδὲν ἀναγκαῖον unnecessarily, Sch.Il.9.23;π. ταῦτα
therefore, this being so,Hdt.
5.9,40, A.Pr. 915, 992, S.OT 426, etc.; cf. οὗτος c. v111.1b.3 in reference to or for a purpose,ἕστηκεν.. μῆλα π. σφαγάς A.Ag. 1057
; χρήσιμος, ἱκανὸς π. τι, Pl.Grg. 474d, Prt. 322b;ὡς π. τί χρείας; S.OT 1174
, cf. OC71, Tr. 1182;ἕτοιμος π. τι X.Mem.4.5.12
;ἱκανῶς ὡς π. τὴν παροῦσαν χρείαν Arist. Cael. 269b21
;ἢν ἀρήγειν φαίνηται π. τὴν σύμπασαν νοῦσον Hp.Acut. 60
; ποιεῖ π. ἐπιλημπτικούς is efficacious for cases of epilepsy, Dsc.1.6;ἐθέλοντες τὰ π. τὴν νοῦσον ἡδέα μᾶλλον ἢ τὰ π. τὴν ὑγιείην προσδέχεσθαι Hp. de Arte7
.b with a view to or for a future time,ὅπως.. γράμματα δῷ π. ἢν ἂν ἡμέραν ἑκάτεροι παραγίνωνται SIG679.62
(Senatus consultum, ii B. C.);θαυμάζεται τὰ Περικλέους ἔργα π. πολὺν χρόνον ἐν ὀλίγῳ γενόμενα Plu.Per.13
.c = πρός B. 11,ἐγίνετο π. ἀναζογήν Plb.3.92.8
;ὄντων π. τὸ κωλύειν Id.1.26.3
, cf. 1.29.3, al., Plu.Nic.5.4 in proportion or relation to, in comparison with,κοῖός τις δοκέοι ἀνὴρ εἶναι π. τὸν πατέρα Κῦρον Hdt.3.34
;ἔργα λόγου μέζω π. πᾶσαν χώρην Id.2.35
;π. πάντας τοὺς ἄλλους Id.3.94
, 8.44;πολλὴν ἂν οἶμαι ἀπιστίαν τῆς δυνάμεως.. π. τὸ κλέος αὐτῶν εἶναι Th.1.10
, cf. Pi.O.2.88, Pl. Prt. 327d, 328c, Phd. 102c, etc.; π. τὰς μεγίστας καὶ ἐλαχίστας ναῦς τὸ μέσον σκοπεῖν the mean between.., Th.1.10;τὸ κάλλιστον τῶν ἔργων π. τὸ αἴσχιστον συμβαλεῖν Lycurg.68
;ἓν π. ἓν συμβάλλειν Hdt.4.50
; alsoἔχεις π. τὰ ἔτη μέλαιναν τὴν τρίχα Thphr. Char.2.3
;ἐνδεεστέρως ἢ π. τὴν ἐξουσίαν Th.4.39
: also of mathematical ratio, οἷος ὁ πρῶτος (sc. ὅρος)ποτὶ τὸν δεύτερον, καὶ ὁ δεύτερος ποτὶ τὸν τρίτον Archyt.2
, cf. Philol.11, Pl.Ti. 36b, Arist.Rh. 1409a4, al., Euc. 5 Def.4, etc.; πρὸς παρεὸν.. μῆτις ἀέξεται ἀνθρώποισι in proportion to the existing (physical development), Emp.106: also of price, value, πωλεῖσθαι δὶς π. ἀργύριον sells twice against or relatively to silver, i.e. for twice its weight in silver, Thphr.HP9.6.4;πωλεῖται ὁ σταθμὸς αὐτοῦ π. διπλοῦν ἀργύριον Dsc.1.19
; [ἡ μαργαρῖτις λίθος] πωλεῖται.. π. χρυσίον for its weight in gold, Androsthenes ap.Ath.3.93b: metaph.,π. ἀρετήν Pl.Phd. 69a
; ὅπως π. τὰς τιμὰς τῶν κριθῶν τὰ ἄλφιτα πωλήσουσι on the basis of the price of barley, Arist.Ath.51.3; ἐξέστω αὐτοῦ ἀπογραφὴ τῆς οὐσίας π. τοῦτο τὸ ἀργύριον Ἀθηναίων τῷ βουλομένῳ property equal in value to this silver, IG22.1013.14, cf. PHib. 1.32.9 (iii B. C.), IG5(1).1390.78 (Andania, i B. C.);τῶν ἐγγύων τῶν ἐγγυωμένων π. [αὐτὰ] τὰ κτήματα SIG364.42
(Ephesus, iii B. C.);θέντων τὰ ποτήρια π. χρυσοῦς ἑκατόν IPE12.32A16
(Olbia, iii B. C.); τοὺς ἀπαγομένους εἰς φυλακὴν π. τὰ χρέα imprisoned for debt, Plb. 38.11.10, cf. 1.72.5, 5.27.4,5,7,5.108.1, PTeb.707.9 (ii B. C.);τοὺς π. καταδίκας ἐκπεπτωκότας Plb.25.3.1
, cf. SIG742.31 (Ephesus, i B. C.);ἐγδίδομεν τὸ ἔργον.. π. χαλκόν IG7.3073.6
(Lebad., ii B. C.), cf. PSI5.356.7 (iii B. C.), PTeb. 825 (a).16 (ii B. C.), Sammelb.5106.3 (ii B. C.);οἷον π. ἀργύριον τὴν δόξαν τὰς ψυχὰς ἀποδιδόμενοι Jul. Or.1.42b
; π. ἅλας ἠγορασμένος, i.e. 'dirt cheap', Men.828 (also π. ἅλα δειπνεῖν καὶ κύαμον, i.e. dine frugally, take pot-luck, Plu.2.684f); soἡδονὰς π. ἡδονὰς.. καταλλάττεσθαι Pl.Phd. 69a
; of measurements of time by the flow from the clepsydra,π. ἕνδεκα ἀμφορέας ἐν διαμεμετρημένῃ τῇ ἡμέρᾳ κρίνομαι Aeschin.2.126
, cf. Arist.Ath.67.2,3,69.2;λεγέσθω τᾶς δίκας ὁ μὲν πρᾶτος λόγος ἑκατέροις ποτὶ χόας δεκαοκτώ SIG953.17
(Calymna, ii B. C.); λεξάντων πρὸς τὴν τήρησιν τοῦ ὕδατος ib.683.60 (Olympia, ii B. C.); π. κλεψύδραν Eub.p.182 K., Epin. 2;π. κλεψύδρας Arist.Po. 1451a8
;π. ὀλίγον ὕδωρ ἀναγκαζόμενος λέγειν D.41.30
; hence later, π. ὀλίγον for a short time,ἐπανεῖναι π. ὀλίγον τὴν πολιορκίαν J.BJ5.9.1
, cf. Alex.Aphr. in Top.560.2, Hld.2.19, POxy67.14 (iv A.D.), Orib.Fr.116, Gp.4.15.8; π.ὀλίγον καιρόν, χρόνον, Antyll. ap. Orib.9.24.26, Paul.Aeg.Prooem.; π. ὀλίγον ἐστὶ τὸ ζῆν Poet. in Mus.Script.p.452 von Jan;μήτηρ δ' ἦν π. μικρόν Sammelb. 7288.4
([place name] Ptolemaic);π. βραχύ Jul.Or.1.47b
(but π. βραχὺ παρηβηκυίας (by) a little past their best, Gp.4.15.3);π. βραχὺν καιρόν Iamb. Protr. 21
.κα'; π. τὸ ἀκαρές Porph.Gaur.3.3
;π. μίαν ἢ δευτέραν ἡμέραν Dsc. 2.101
, cf. Sor.1.56;π. δύο ἡμέρας ἐκοίμησα ἐκεῖ BGU775.8
(ii A. D.);π.μόνην τὴν ἐνεστῶσαν ἡμέραν Sammelb. 7399
(ii A.D.), cf. M.Ant.12.4;προστιμάσθω π. χρόνον μὴ εἰσελθεῖν ὅσον ἂν δόξῃ IG22.1368.89
.5 in or by reference to, according to, in view of,π. τὸ παρεὸν βουλεύεσθαι Hdt. 1.20
, cf. 113, Th.6.46,47, IG22.1.20, etc.;π. τὴν παροῦσαν ἀρρωστίαν Th.7.47
;ἵνα π. τὸν ὑπάρχοντα καιρὸν ἕκαστα θεωρῆτε D.18.17
, cf. 314, etc.;εἴ τι δεῖ τεκμαίρεσθαι π. τὸν ἄλλον τρόπον Id.27.22
; τοῖς π. ὑμᾶς ζῶσι those who live with your interests in view, Id.19.226;ἐλευθέρου τὸ μὴ π. ἄλλον ζῆν Arist.Rh. 1367a32
;π. τοῦτον πάντ' ἐσκόπουν, π. τοῦτον ἐποιοῦντο τὴν εἰρήνην D.19.63
; τὸ παιδεύεσθαι π. τὰς πολιτείας suitably to them, Arist.Pol. 1310a14; ὁρῶ.. ἅπαντας π. τὴν παροῦσαν δύναμιν τῶν δικαίων ἀξιουμένους according to their power, D.15.28;π. τὰς τύχας γὰρ τὰς φρένας κεκτήμεθα
according to..,E.
Hipp. 701; πὸς τὰς συνθέσις in accordance with the agreements, IG5(2).343.41,60 (Orchom. Arc.); τὸν δικαστὰν ὀμνύντα κρῖναι πορτὶ τὰ μωλιόμενα having regard to the pleadings, Leg.Gort.5.44, cf. 9.30; αἱ ἀρχαὶ.. πρὸς τὰ κατεσκευασμένα σύμβολα σηκώματα ποιησάμεναι after making weights and measures in accordance with, or by reference to, the established standards, IG22.1013.7; π. τὰ στάθμια τὰ ἐν τῷ ἀργυροκοπίῳ as measured by the weights in the mint, ib. 30, cf. PAmh.43.10 (ii B. C.); [Εόλων] ἐποίησε σταθμὰ π. τὸ νόμισμα made (trade-) weights on the basis of (i.e. proportional to) the coinage, Arist.Ath.10.2;ὀρθὸν π. τὸν διαβήτην IG22.1668.9
, cf. 95,7.3073.108 (Lebad., ii B. C.); π. τὸ δικαιότατον in accordance with the most just principle, D.C.Fr.104.6.6 with the accompaniment of musical instruments,π. κάλαμον Pi.O.10(11).84
; π. αὐλόν or τὸν αὐλόν, E.Alc. 346, X.Smp.6.3, etc.;π. λύραν.. ᾄδειν SIG662.13
(Delos, ii B. C.); π. ῥυθμὸν ἐμβαίνειν to step in time, D.S.5.34.7 [full] πρός c.acc. freq. periphr. for Adv., π. βίαν, = βιαίως, under compulsion,νῦν χρὴ.. τινα π. βίαν πώνην Alc.20
(s.v.l.);π. βίαν ἐπίνομεν Ar.Ach.73
;τὸ π. βίαν πίνειν ἴσον πέφυκε τῷ διψῆν κακόν S.Fr. 735
; ἥκω.. π. βίαν under compulsion, Critias 16.10 D.; by force, forcibly, A.Pr. 210, 355, etc.; οὐ π. βίαν τινός not forced by any one, Id.Eu.5 (but also, in spite of any one, S.OC 657);π. τὸ βίαιον A.Ag. 130
(lyr.);π. τὸ καρτερόν Id.Pr. 214
; π. ἀλκήν, π. ἀνάγκαν, Id.Th. 498, Pers. 569 (lyr.);οὐ διαχωρέεει [ἡ γαστὴρ] εἰ μὴ π. ἀνάγκην Hp. Prog.8
,19;π. ἰσχύος κράτος S.Ph. 594
;π. ἡδονὴν εἶναί τινι A.Pr. 494
; π. ἡδονὴν λέγειν, δημηγορεῖν, so as to please, Th.2.65, S.El. 921, D.4.38, cf. E.Med. 773;οἱ πάντα π. ἡδονὴν ἐπαινοῦντες Arist.EN 1126b13
;ἅπαντα π. ἡδ. ζητεῖν D.1.15
, cf. 18.4; λούσασθαι τὸ σῶμα π. ἡδ. as much or little as one like s, Hp.Mul.2.133;πίνειν π. ἡδ. Pl. Smp. 176e
; π. τὸ τερπνόν calculated to delight, Th.2.53; π. χάριν so as to gratify,μήτε π. ἔχθραν ποιεῖσθαι λόγον μήτε π. χ. D.8.1
, cf. S.OT 1152;π. χάριν δημηγορεῖν D.3.3
, etc.: c. gen. rei, π. χάριν τινός for the sake of,π. χ. βορᾶς S.Ant.30
, cf. Ph. 1156 (lyr.);π. ἰσχύος χ.
by means of,E.
Med. 538; π. ὀργήν with anger, angrily, S.El. 369, Th.2.65, D.53.16 (v.l.);π. ὀργὴν ἐλθεῖν τινι Id.39.23
, etc.; π. τὸ λιπαρές importunately, S.OC 1119;π. εὐσέβειαν Id.El. 464
; π. καιρόν seasonably, Id.Aj.38, etc.;π. φύσιν Id.Tr. 308
; π. εὐτέλειαν cheaply, Antiph.226.2; π. μέρος in due proportion, D.36.32;π. ὀλίγον μέρος Gp.2.15.1
; τέτραπτο π. ἰθύ οἱ straight towards him, Il.14.403; π. ὀρθὰς (sc. γωνίας ( .. τῇ AEB at right angles to, Arist.Mete. 373a14, cf. Euc.1.11, Archim.Sph.Cyl.1.3;π. ὀρθὴν τέμνουσα Arist.Mete. 363b2
; π. ἀχθηδόνα, π. ἀπέχθειαν, Luc.Tox.9, Hist.Conscr.38; γυνὴ π. ἀλήθειαν οὖσα in truth a woman, a very woman, Ath.15.687a, cf. Luc. JTr.48, Alex.61: c. [comp] Sup., π. τὰ μέγιστα in the highest degree, Hdt.8.20.8 of Numbers. up to, about, Plb.16.7.5, etc.: cf. πρόσπου.D ABS. AS ADV., besides, over and above; in Hom. always π. δέ or ποτὶ δέ, Il.5.307, 10.108, al., cf. Hdt.1.71, etc.; π. δὲ καί ib. 164, 207;π. δὲ ἔτι Id.3.74
;καὶ π. Id.7.154
, 184, prob. in A.Ch. 301, etc.;καὶ π. γε E.Hel. 110
, Pl.R. 328a, 466e;καὶ.. γε π. A.Pr.73
;καὶ δὴ π. Hdt.5.67
; freq. at the end of a second clause,τάδε λέγω, δράσω τε π. E.Or. 622
;ἀλογία.., καὶ ἀμαθία γε π. Pl.Men. 90e
, cf. E.Ph. 610;ἐνενήκοντα καὶ μικρόν τι π. D.4.28
, cf. 22.60.E IN COMPOS.,I motion towards, as προσάγω, προσέρχομαι, etc.II addition, besides, as προσκτάομαι, προσδίδωμι, προστίθημι, etc.III a being on, at, by, or beside: hence, a remaining beside, and metaph. connexion and engagement with anything, as πρόσειμι, προσγίγνομαι, etc.F REMARKS,1 in poetry πρός sts. stands after its case and before an attribute,ποίμνας βουστάσεις τε π. πατρός A.Pr. 653
, cf. Th. 185, S.OT 178 (lyr.), E.Or.94; ἄστυ πότι (or ποτὶ)σφέτερον Il.17.419
, cf. Pi.O.4.5.2 in Hom. it is freq. separated from its Verb by tmesis. -
67 Ampère, André-Marie
SUBJECT AREA: Electricity[br]b. 22 Jan 1775 Lyon, Franced. 10 June 1836 Marseille, France[br]French physicist and mathematician who established laws and principles relating magnetism and electricity to each other.[br]Ampère was reputed to have mastered all the then-known mathematics by the age of 12. He became Professor of Physics and Chemistry at Bourg in 1801 and a professor of mathematics at the Ecole Polytechnique in Paris in 1809. Observing a demonstration in 1820 of Oersted's discovery that a magnetic needle was deflected when placed near a current-carrying wire, Ampère was inspired to investigate the subject of electricity, of which he had no previous experience. Within a week he had prepared the first of several important communications on his discoveries to the Academy of Sciences in Paris. Included was a new hypothesis formed on the basis of his experiments on the relation between electricity and magnetism. He investigated the forces exerted on each other by current-carrying conductors and the properties of a solenoid. His mathematical theory describing these phenomena provided the foundations for the development of electro-dynamics and his classic work Théorie mathématique des phénomènes électro-dynamiques was published in 1827.The name "ampere" was adopted to replace the name "weber" as a unit of current after Helmholtz proposed such a change in 1881.[br]Principal Honours and DistinctionsBibliography1827, Théorie mathématique des phénomènes électro-dynamiques, Paris; repub. 1958, Paris (his chief published work).Further ReadingP.Lenard, 1933, Great Men of Science, London, pp. 223–30 (provides a short account). C.C.Gillispie (ed.), 1970, Dictionary of Scientific Biography, Vol. 1, New York, pp.139–46.GW -
68 Byron, Ada Augusta, Countess of Lovelace
SUBJECT AREA: Electronics and information technology[br]b. 12 December 1815 Piccadilly Terrace, London, Englandd. 23 November 1852 East Horsley, Surrey, England[br]English mathematician, active in the early development of the calculating machine.[br]Educated by a number of governesses in a number of houses from Yorkshire to Ealing, she was the daughter of a hypochondriac mother and her absent, separated, husband, the poet George Gordon, Lord Byron. As a child a mysterious and undiagnosed illness deprived her "of the use of her limbs" and she was "obliged to use crutches". The complaint was probably psychosomatic as it cleared up when she was 17 and was about to attend her first court ball. On 8 July 1835 she was married to William King, 1st Earl of Lovelace. She later bore two sons and a daughter. She was an avid student of science and in particular mathematics, in the course of which Charles Babbage encouraged her. In 1840 Babbage was invited to Turin to present a paper on his analytical engine. In the audience was a young Italian military engineer, L.F.Menabrea, who was later to become a general in Garibaldi's army. The paper was written in French and published in 1842 in the Bibliothèque Universelle de Genève. This text was translated into English and published with extensive annotations by the Countess of Lovelace, appearing in Taylor's Scientific Memoirs. The Countess thoroughly understood and appreciated Babbage's machine and the clarity of her description was so great that it is undoubtedly the best contemporary account of the engine: even Babbage recognized the Countess's description as superior to his own. Ada often visited Babbage in his workshop and listened to his explanations of the structure and use of his engines. She shared with her husband a love of horse-racing and, with Babbage, tried to develop a system for backing horses. Babbage and the Earl apparently stopped their efforts in time, but the Countess lost so heavily that she had to pawn all her family jewels. Her losses at the 1851 Derby alone amounted to £3,200, while borrow-ing a further £1,800 from her husband. This situation involved her in being blackmailed. She became an opium addict due to persistent pain from gastritis, intermittent anorexia and paroxys-mal tachycardia. Charles Babbage was always a great comfort to her, not only for their shared mathematical interests but also as a friend helping in all manner of small services such as taking her dead parrot to the taxidermist. She died after a protracted illness, thought to be cancer, at East Horsley Towers.[br]Further ReadingD.Langley Moore, 1977, Ada, Countess of Lovelace: Byron's Legitimate Daughter, John Murray.P.Morrison and E.Morrison, 1961, Charles Babbage and His Calculating Engine, Dover Publications.Biographical history of technology > Byron, Ada Augusta, Countess of Lovelace
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69 Donkin, Bryan I
[br]b. 22 March 1768 Sandoe, Northumberland, Englandd. 27 February 1855 London, England[br]English mechanical engineer and inventor.[br]It was intended that Bryan Donkin should follow his father's profession of surveyor and land agent, so he spent a year or so in that occupation before he was apprenticed to John Hall, millwright of Dartford, Kent. Donkin remained with the firm after completing his apprenticeship, and when the Fourdrinier brothers in 1802 introduced from France an invention for making paper in continuous lengths they turned to John Hall for help in developing the machine: Donkin was chosen to undertake the work. In 1803 the Fourdriniers established their own works in Bermondsey, with Bryan Donkin in charge. By 1808 Donkin had acquired the works, but he continued to manufacture paper-making machines, paying a royalty to the patentees. He also undertook other engineering work including water-wheels for driving paper and other mills. He was also involved in the development of printing machinery and the preservation of food in airtight containers. Some of these improvements were patented, and he also obtained patents relating to gearing, steel pens, paper-making and railway wheels. Other inventions of Bryan Donkin that were not patented concerned revolution counters and improvements in accurate screw threads for use in graduating mathematical scales. Donkin was elected a member of the Society of Arts in 1803 and was later Chairman of the Society's Committee of Mechanics and a Vice-President of the society. He was also a member of the Royal Astronomical Society. In 1818 a group of eight young men founded the Institution of Civil Engineers; two of them were apprentices of Bryan Donkin and he encouraged their enterprise. After a change in the rules permitted the election of members over the age of 35, he himself became a member in 1821. He served on the Council and became a Vice- President, but he resigned from the Institution in 1848.[br]Principal Honours and DistinctionsFRS 1838. Vice-President, Institution of Civil Engineers 1826–32, 1835–45. Member, Smeatonian Society of Civil Engineers 1835; President 1843. Society of Arts Gold Medal 1810, 1819.Further ReadingS.B.Donkin, 1949–51, "Bryan Donkin, FRS, MICE 1768–1855", Transactions of the Newcomen Society 27:85–95.RTS -
70 Krylov, Alexei Nicolaevitch
SUBJECT AREA: Ports and shipping[br]b. 15 August 1863 Visyoger, Siberiad. 26 October 1945 Leningrad (now St Petersburg), Russia[br]Russian academician and naval architect) exponent of a rigorous mathematical approach to the study of ship motions.[br]After schooling in France and Germany, Krylov returned to St Petersburg (as it then was) and in 1878 entered the Naval College. Upon graduating, he started work with the Naval Hydrographic Department; the combination of his genius and breadth of interest became apparent, and from 1888 until 1890 he undertook simultaneously a two-year university course in mathematics and a naval architecture course at his old college. On completion of his formal studies, Krylov commenced fifty years of service to the academic bodies of St Petersburg, including eight years as Superintendent of the Russian Admiralty Ship Model Experiment Tank. For many years he was Professor of Naval Architecture in the city, reorganizing the methods of teaching of his profession in Russia. It was during this period that he laid the foundations of his remarkable research and published the first of his many books destined to become internationally accepted in the fields of waves, rolling, ship motion and vibration. Practical work was not overlooked: he was responsible for the design of many vessels for the Imperial Russian Navy, including the battleships Sevastopol and Petropavlovsk, and went on, as Director of Naval Construction, to test anti-rolling tanks aboard military vessels in the North Atlantic in 1913. Following the Revolution, Krylov was employed by the Soviet Union to re-establish scientific links with other European countries, and on several occasions he acted as Superintendent in the procurement of important technical material from overseas. In 1919 he was appointed Head of the Marine Academy, and from then on participated in many scientific conferences and commissions, mainly in the shipbuilding field, and served on the Editorial Board of the well-respected Russian periodical Sudostroenie (Shipbuilding). The breadth of his personal research was demonstrated by the notable contributions he made to the Russian development of the gyro compass.[br]Principal Honours and DistinctionsMember, Russian Academy of Science 1814. Royal Institution of Naval Architects Gold Medal 1898. State Prize of the Soviet Union (first degree). Stalin Premium for work on compass deviation.BibliographyKrylov published more than 500 books, papers and articles; these have been collected and published in twelve volumes by the Academy of Sciences of the USSR. 1942, My Memories (autobiography).AK / FMWBiographical history of technology > Krylov, Alexei Nicolaevitch
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71 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 -
72 Riefler, Sigmund
SUBJECT AREA: Horology[br]b. 9 August 1847 Maria Rain, Germanyd. 21 October 1912 Munich, Germany[br]German engineer who invented the precision clock that bears his name.[br]Riefler's father was a scientific-instrument maker and clockmaker who in 1841 had founded the firm of Clemens Riefler to make mathematical instruments. After graduating in engineering from the University of Munich Sigmund worked as a surveyor, but when his father died in 1876 he and his brothers ran the family firm. Sigmund was responsible for technical development and in this capacity he designed a new system of drawing-instruments which established the reputation of the firm. He also worked to improve the performance of the precision clock, and in 1889 he was granted a patent for a new form of escapement. This escapement succeeded in reducing the interference of the clock mechanism with the free swinging of the pendulum by impulsing the pendulum through its suspension strip. It proved to be the greatest advance in precision timekeeping since the introduction of the dead-beat escapement about two hundred years earlier. When the firm of Clemens Riefler began to produce clocks with this escapement in 1890, they replaced clocks with Graham's dead-beat escapement as the standard regulator for use in observatories and other applications where the highest precision was required. In 1901 a movement was fitted with electrical rewind and was encapsulated in an airtight case, at low pressure, so that the timekeeping was not affected by changes in barometric pressure. This became the standard practice for precision clocks. Although the accuracy of the Riefler clock was later surpassed by the Shortt free-pendulum clock and the quartz clock, it remained in production until 1965, by which time over six hundred instruments had been made.[br]Principal Honours and DistinctionsFranklin Institute John Scott Medal 1894. Honorary doctorate, University of Munich 1897. Vereins zur Förderung des Gewerbefleisses in Preussen Gold Medal 1900.Bibliography1907, Präzisionspendeluhren und Zeitdienstanlagen fürSternwarten, Munich (for a complete bibliography see D.Riefler below).Further ReadingD.Riefler, 1981, Riefler-Präzisionspendeluhren, Munich (the definitive work on Riefler and his clock).A.L.Rawlings, 1948, The Science of Clocks and Watches, 2nd edn; repub. 1974 (a technical assessment of the Riefler escapement in its historical context).See also: Marrison, Warren AlvinDV -
73 Shannon, Claude Elwood
[br]b. 30 April 1916 Gaylord, Michigan, USA[br]American mathematician, creator of information theory.[br]As a child, Shannon tinkered with radio kits and enjoyed solving puzzles, particularly crypto-graphic ones. He graduated from the University of Michigan in 1936 with a Bachelor of Science in mathematics and electrical engineering, and earned his Master's degree from the Massachusetts Institute of Technology (MIT) in 1937. His thesis on applying Boolean algebra to switching circuits has since been acclaimed as possibly the most significant this century. Shannon earned his PhD in mathematics from MIT in 1940 with a dissertation on the mathematics of genetic transmission.Shannon spent a year at the Institute for Advanced Study in Princeton, then in 1941 joined Bell Telephone Laboratories, where he began studying the relative efficiency of alternative transmission systems. Work on digital encryption systems during the Second World War led him to think that just as ciphers hide information from the enemy, "encoding" information could also protect it from noise. About 1948, he decided that the amount of information was best expressed quantitatively in a two-value number system, using only the digits 0 and 1. John Tukey, a Princeton colleague, named these units "binary digits" (or, for short, "bits"). Almost all digital computers and communications systems use such on-off, or two-state logic as their basis of operation.Also in the 1940s, building on the work of H. Nyquist and R.V.L. Hartley, Shannon proved that there was an upper limit to the amount of information that could be transmitted through a communications channel in a unit of time, which could be approached but never reached because real transmissions are subject to interference (noise). This was the beginning of information theory, which has been used by others in attempts to quantify many sciences and technologies, as well as subjects in the humanities, but with mixed results. Before 1970, when integrated circuits were developed, Shannon's theory was not the preferred circuit-and-transmission design tool it has since become.Shannon was also a pioneer in the field of artificial intelligence, claiming that computing machines could be used to manipulate symbols as well as do calculations. His 1953 paper on computers and automata proposed that digital computers were capable of tasks then thought exclusively the province of living organisms. In 1956 he left Bell Laboratories to join the MIT faculty as Professor of Communications Science.On the lighter side, Shannon has built many devices that play games, and in particular has made a scientific study of juggling.[br]Principal Honours and DistinctionsNational Medal of Science. Institute of Electrical and Electronics Engineers Medal of Honor, Kyoto Prize.BibliographyHis seminal paper (on what has subsequently become known as information theory) was entitled "The mathematical theory of communications", first published in Bell System Technical Journal in 1948; it is also available in a monograph (written with Warren Weaver) published by the University of Illinois Press in 1949, and in Key Papers in the Development of Information Theory, ed. David Slepian, IEEE Press, 1974, 1988. For readers who want all of Shannon's works, see N.J.A.Sloane and A.D.Wyner, 1992, TheCollected Papers of Claude E.Shannon.HO -
74 Stibitz, George R.
SUBJECT AREA: Electronics and information technology[br]b. 20 April 1904 York, Pennsylvania, USA[br]American mathematician responsible for the conception of the Bell Laboratories "Complex " computer.[br]Stibitz spent his early years in Dayton, Ohio, and obtained his first degree at Denison University, Granville, Ohio, his MS from Union College, Schenectady, New York, in 1927 and his PhD in mathematical physics from Cornell University, Ithaca, New York, in 1930. After working for a time for General Electric, he joined Bell Laboratories to work on various communications problems. In 1937 he started to experiment at home with telephone relays as the basis of a calculator for addition, multiplication and division. Initially this was based on binary arithmetic, but later he used binary-coded decimal (BCD) and was able to cope with complex numbers. In November 1938 the ideas were officially taken up by Bell Laboratories and, with S.B.Williams as Project Manager, Stibitz built a complex-number computer known as "Complex", or Relay I, which became operational on 8 January 1940.With the outbreak of the Second World War, he was co-opted to the National Defence Research Council to work on anti-aircraft (AA) gun control, and this led to Bell Laboratories Relay II computer, which was completed in 1943 and which had 500 relays, bi-quinary code and selfchecking of errors. A further computer, Relay III, was used for ballistic simulation of actual AA shell explosions and was followed by more machines before and after Stibitz left Bell after the end of the war. Stibitz then became a computer consultant, involved in particular with the development of the UNIVAC computer by John Mauchly and J.Presper Eckert.[br]Principal Honours and DistinctionsInstitute of Electrical and Electronics Engineers Emanuel R.Priore Award 1977.Bibliography1957, with J.A.Larrivee, Mathematics and Computers, New York: McGraw-Hill. 1967, "The Relay computer at the Bell Laboratories", Datamation 35.Further ReadingE.Loveday, 1977, "George Stibitz and the Bell Labs Relay computer", Datamation 80. M.R.Williams, 1985, A History of Computing Technology, London: Prentice-Hall.KF -
75 Torricelli, Evangelista
SUBJECT AREA: Photography, film and optics[br]b. 15 October 1608 Faenza, Italyd. 25 October 1647 Florence, Italy[br]Italian physicist, inventor of the mercury barometer and discoverer of atmospheric pressure.[br]Torricelli was the eldest child of a textile artisan. Between 1625 and 1626 he attended the Jesuit school at Faenza, where he showed such outstanding aptitude in mathematics and philosophy that his uncle was persuaded to send him to Rome to a school run by Benedetto Castelli, a mathematician and engineer and a former pupil of Galileo Galilei. Between 1630 and 1641, Torricelli was possibly Secretary to Giovanni Ciampoli, Galileo's friend and protector. In 1641 Torricelli wrote a treatise, De motugravium, amplifying Galileo's doctrine on the motion of projectiles, and Galileo accepted him as a pupil. On Galileo's death in 1642, he was appointed as mathematician and philosopher to the court of Grand Duke Ferdinando II of Tuscany. He remained in Florence until his early death in 1647, possibly from typhoid fever. He wrote a great number of mathematical papers on conic sections, the cycloid, the logarithmic curve and other subjects, which made him well known.By 1642 Torricelli was producing good lenses for telescopes; he subsequently improved them, and attained near optical perfection. He also constructed a simple microscope with a small glass sphere as a lens. Galileo had looked at problems of raising water with suction pumps, and also with a siphon in 1630. Torricelli brought up the subject again in 1640 and later produced his most important invention, the barometer. He used mercury to fill a glass tube that was sealed at one end and inverted it. He found that the height of mercury in the tube adjusted itself to a well-defined level of about 76 cm (30 in.), higher than the free surface outside. He realized that this must be due to the pressure of the air on the outside surface and predicted that it would fall with increasing altitude. He thus demonstrated the pressure of the atmosphere and the existence of a vacuum on top of the mercury, publishing his findings in 1644. He later noticed that changes in the height of the mercury were related to changes in the weather.[br]Bibliography1641, De motu gravium.Further ReadingT.I.Williams (ed.), 1969, A Biographical Dictionary of Scientists, London: A. \& C.Black.Chambers Concise Dictionary of Scientists, 1989, Cambridge.A Dictionary of Scientific Biography, 1976, Vol. XIII, New York: C.Scribner's Sons.A.Stowers, 1961–2, "Thomas Newcomen's first steam engine 250 years ago and the initial development of steam power", Transactions of the Newcomen Society 34 (provides an account of his mercury barometer).W.E.Knowles Middleton, 1964, The History of the Barometer, Baltimore.RLHBiographical history of technology > Torricelli, Evangelista
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76 Computers
The brain has been compared to a digital computer because the neuron, like a switch or valve, either does or does not complete a circuit. But at that point the similarity ends. The switch in the digital computer is constant in its effect, and its effect is large in proportion to the total output of the machine. The effect produced by the neuron varies with its recovery from [the] refractory phase and with its metabolic state. The number of neurons involved in any action runs into millions so that the influence of any one is negligible.... Any cell in the system can be dispensed with.... The brain is an analogical machine, not digital. Analysis of the integrative activities will probably have to be in statistical terms. (Lashley, quoted in Beach, Hebb, Morgan & Nissen, 1960, p. 539)It is essential to realize that a computer is not a mere "number cruncher," or supercalculating arithmetic machine, although this is how computers are commonly regarded by people having no familiarity with artificial intelligence. Computers do not crunch numbers; they manipulate symbols.... Digital computers originally developed with mathematical problems in mind, are in fact general purpose symbol manipulating machines....The terms "computer" and "computation" are themselves unfortunate, in view of their misleading arithmetical connotations. The definition of artificial intelligence previously cited-"the study of intelligence as computation"-does not imply that intelligence is really counting. Intelligence may be defined as the ability creatively to manipulate symbols, or process information, given the requirements of the task in hand. (Boden, 1981, pp. 15, 16-17)The task is to get computers to explain things to themselves, to ask questions about their experiences so as to cause those explanations to be forthcoming, and to be creative in coming up with explanations that have not been previously available. (Schank, 1986, p. 19)In What Computers Can't Do, written in 1969 (2nd edition, 1972), the main objection to AI was the impossibility of using rules to select only those facts about the real world that were relevant in a given situation. The "Introduction" to the paperback edition of the book, published by Harper & Row in 1979, pointed out further that no one had the slightest idea how to represent the common sense understanding possessed even by a four-year-old. (Dreyfus & Dreyfus, 1986, p. 102)A popular myth says that the invention of the computer diminishes our sense of ourselves, because it shows that rational thought is not special to human beings, but can be carried on by a mere machine. It is a short stop from there to the conclusion that intelligence is mechanical, which many people find to be an affront to all that is most precious and singular about their humanness.In fact, the computer, early in its career, was not an instrument of the philistines, but a humanizing influence. It helped to revive an idea that had fallen into disrepute: the idea that the mind is real, that it has an inner structure and a complex organization, and can be understood in scientific terms. For some three decades, until the 1940s, American psychology had lain in the grip of the ice age of behaviorism, which was antimental through and through. During these years, extreme behaviorists banished the study of thought from their agenda. Mind and consciousness, thinking, imagining, planning, solving problems, were dismissed as worthless for anything except speculation. Only the external aspects of behavior, the surface manifestations, were grist for the scientist's mill, because only they could be observed and measured....It is one of the surprising gifts of the computer in the history of ideas that it played a part in giving back to psychology what it had lost, which was nothing less than the mind itself. In particular, there was a revival of interest in how the mind represents the world internally to itself, by means of knowledge structures such as ideas, symbols, images, and inner narratives, all of which had been consigned to the realm of mysticism. (Campbell, 1989, p. 10)[Our artifacts] only have meaning because we give it to them; their intentionality, like that of smoke signals and writing, is essentially borrowed, hence derivative. To put it bluntly: computers themselves don't mean anything by their tokens (any more than books do)-they only mean what we say they do. Genuine understanding, on the other hand, is intentional "in its own right" and not derivatively from something else. (Haugeland, 1981a, pp. 32-33)he debate over the possibility of computer thought will never be won or lost; it will simply cease to be of interest, like the previous debate over man as a clockwork mechanism. (Bolter, 1984, p. 190)t takes us a long time to emotionally digest a new idea. The computer is too big a step, and too recently made, for us to quickly recover our balance and gauge its potential. It's an enormous accelerator, perhaps the greatest one since the plow, twelve thousand years ago. As an intelligence amplifier, it speeds up everything-including itself-and it continually improves because its heart is information or, more plainly, ideas. We can no more calculate its consequences than Babbage could have foreseen antibiotics, the Pill, or space stations.Further, the effects of those ideas are rapidly compounding, because a computer design is itself just a set of ideas. As we get better at manipulating ideas by building ever better computers, we get better at building even better computers-it's an ever-escalating upward spiral. The early nineteenth century, when the computer's story began, is already so far back that it may as well be the Stone Age. (Rawlins, 1997, p. 19)According to weak AI, the principle value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion than before. But according to strong AI the computer is not merely a tool in the study of the mind; rather the appropriately programmed computer really is a mind in the sense that computers given the right programs can be literally said to understand and have other cognitive states. And according to strong AI, because the programmed computer has cognitive states, the programs are not mere tools that enable us to test psychological explanations; rather, the programs are themselves the explanations. (Searle, 1981b, p. 353)What makes people smarter than machines? They certainly are not quicker or more precise. Yet people are far better at perceiving objects in natural scenes and noting their relations, at understanding language and retrieving contextually appropriate information from memory, at making plans and carrying out contextually appropriate actions, and at a wide range of other natural cognitive tasks. People are also far better at learning to do these things more accurately and fluently through processing experience.What is the basis for these differences? One answer, perhaps the classic one we might expect from artificial intelligence, is "software." If we only had the right computer program, the argument goes, we might be able to capture the fluidity and adaptability of human information processing. Certainly this answer is partially correct. There have been great breakthroughs in our understanding of cognition as a result of the development of expressive high-level computer languages and powerful algorithms. However, we do not think that software is the whole story.In our view, people are smarter than today's computers because the brain employs a basic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at.... hese tasks generally require the simultaneous consideration of many pieces of information or constraints. Each constraint may be imperfectly specified and ambiguous, yet each can play a potentially decisive role in determining the outcome of processing. (McClelland, Rumelhart & Hinton, 1986, pp. 3-4)Historical dictionary of quotations in cognitive science > Computers
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77 Heuristics
[A]t one point AM [Automatic Mathematician] had some notions of sets, set-operations, numbers, and simple arithmetic. One heuristic rule it knew said " If F is an interesting relation, then look at its inverse". This rule fired after AM had studied "multiplication" for a while. The r.h.s. of the rule then directed AM to define and study the relation "divisors-of" (e.g. divisors-of (12) {1,2,3,4,6,12}. Another heuristic rule that later fired said " If f is a relation from A into B, then it's worth examining those members of A which map into extremal members of B." In this case, f was matched to "divisors-of", A was "numbers", B was "sets of numbers", and an extremal member of B might be, e.g., a very small set of numbers. Thus this heuristic rule caused AM to define the set of numbers with no divisors, the set of numbers with only 1 divisor, with only 2 divisors, etc. One of these sets (the last [ sic] mentioned) turned out subsequently to be quite important; these numbers are of course the primes. (Lenat & Harris, 1978, p. 30)Extraordinarily rapid progress during the early stages of an attack on a new problem area is a rather common occurrence in AI research; it merely signifies that the test cases with which the system has been challenged are below the level of difficulty where combinatorial explosion of the number of pathways in the problem space sets in.... It is the goal of AI research to move that threshold higher and higher on the scale of problem complexity through the introduction of heuristics-heuristics to reduce the rate of growth of the solution tree, heuristics to guide the development of the tree so that it will be rich in pathways leading to satisfactory problem solutions, and heuristics to direct the search to the "best" of these pathways. (Gelernter, quoted in Barr & Feigenbaum, 1982, pp. 139-140)Historical dictionary of quotations in cognitive science > Heuristics
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78 Intelligence
There is no mystery about it: the child who is familiar with books, ideas, conversation-the ways and means of the intellectual life-before he begins school, indeed, before he begins consciously to think, has a marked advantage. He is at home in the House of intellect just as the stableboy is at home among horses, or the child of actors on the stage. (Barzun, 1959, p. 142)It is... no exaggeration to say that sensory-motor intelligence is limited to desiring success or practical adaptation, whereas the function of verbal or conceptual thought is to know and state truth. (Piaget, 1954, p. 359)ntelligence has two parts, which we shall call the epistemological and the heuristic. The epistemological part is the representation of the world in such a form that the solution of problems follows from the facts expressed in the representation. The heuristic part is the mechanism that on the basis of the information solves the problem and decides what to do. (McCarthy & Hayes, 1969, p. 466)Many scientists implicitly assume that, among all animals, the behavior and intelligence of nonhuman primates are most like our own. Nonhuman primates have relatively larger brains and proportionally more neocortex than other species... and it now seems likely that humans, chimpanzees, and gorillas shared a common ancestor as recently as 5 to 7 million years ago.... This assumption about the unique status of primate intelligence is, however, just that: an assumption. The relations between intelligence and measures of brain size is poorly understood, and evolutionary affinity does not always ensure behavioral similarity. Moreover, the view that nonhuman primates are the animals most like ourselves coexists uneasily in our minds with the equally pervasive view that primates differ fundamentally from us because they lack language; lacking language, they also lack many of the capacities necessary for reasoning and abstract thought. (Cheney & Seyfarth, 1990, p. 4)Few constructs are asked to serve as many functions in psychology as is the construct of human intelligence.... Consider four of the main functions addressed in theory and research on intelligence, and how they differ from one another.1. Biological. This type of account looks at biological processes. To qualify as a useful biological construct, intelligence should be a biochemical or biophysical process or at least somehow a resultant of biochemical or biophysical processes.2. Cognitive approaches. This type of account looks at molar cognitive representations and processes. To qualify as a useful mental construct, intelligence should be specifiable as a set of mental representations and processes that are identifiable through experimental, mathematical, or computational means.3. Contextual approaches. To qualify as a useful contextual construct, intelligence should be a source of individual differences in accomplishments in "real-world" performances. It is not enough just to account for performance in the laboratory. On [sic] the contextual view, what a person does in the lab may not even remotely resemble what the person would do outside it. Moreover, different cultures may have different conceptions of intelligence, which affect what would count as intelligent in one cultural context versus another.4. Systems approaches. Systems approaches attempt to understand intelligence through the interaction of cognition with context. They attempt to establish a link between the two levels of analysis, and to analyze what forms this link takes. (Sternberg, 1994, pp. 263-264)High but not the highest intelligence, combined with the greatest degrees of persistence, will achieve greater eminence than the highest degree of intelligence with somewhat less persistence. (Cox, 1926, p. 187)There are no definitive criteria of intelligence, just as there are none for chairness; it is a fuzzy-edged concept to which many features are relevant. Two people may both be quite intelligent and yet have very few traits in common-they resemble the prototype along different dimensions.... [Intelligence] is a resemblance between two individuals, one real and the other prototypical. (Neisser, 1979, p. 185)Given the complementary strengths and weaknesses of the differential and information-processing approaches, it should be possible, at least in theory, to synthesise an approach that would capitalise upon the strength of each approach, and thereby share the weakness of neither. (Sternberg, 1977, p. 65)Historical dictionary of quotations in cognitive science > Intelligence
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