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mathematical astronomy

  • 1 mathematical astronomy

    Универсальный англо-русский словарь > mathematical astronomy

  • 2 mathematical astronomy

    English-russian astronautics dictionary > mathematical astronomy

  • 3 mathematical signs astronomy

    • matematička astronomija

    English-Serbian dictionary > mathematical signs astronomy

  • 4 гравитационная астрономия

    Универсальный русско-английский словарь > гравитационная астрономия

  • 5 математическая астрономия

    Универсальный русско-английский словарь > математическая астрономия

  • 6 небесная механика

    Универсальный русско-английский словарь > небесная механика

  • 7 matematička astronomija

    • mathematical signs astronomy

    Serbian-English dictionary > matematička astronomija

  • 8 tratado matemático

    Ex. Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.
    * * *

    Ex: Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.

    Spanish-English dictionary > tratado matemático

  • 9 Artificial Intelligence

       In my opinion, none of [these programs] does even remote justice to the complexity of human mental processes. Unlike men, "artificially intelligent" programs tend to be single minded, undistractable, and unemotional. (Neisser, 1967, p. 9)
       Future progress in [artificial intelligence] will depend on the development of both practical and theoretical knowledge.... As regards theoretical knowledge, some have sought a unified theory of artificial intelligence. My view is that artificial intelligence is (or soon will be) an engineering discipline since its primary goal is to build things. (Nilsson, 1971, pp. vii-viii)
       Most workers in AI [artificial intelligence] research and in related fields confess to a pronounced feeling of disappointment in what has been achieved in the last 25 years. Workers entered the field around 1950, and even around 1960, with high hopes that are very far from being realized in 1972. In no part of the field have the discoveries made so far produced the major impact that was then promised.... In the meantime, claims and predictions regarding the potential results of AI research had been publicized which went even farther than the expectations of the majority of workers in the field, whose embarrassments have been added to by the lamentable failure of such inflated predictions....
       When able and respected scientists write in letters to the present author that AI, the major goal of computing science, represents "another step in the general process of evolution"; that possibilities in the 1980s include an all-purpose intelligence on a human-scale knowledge base; that awe-inspiring possibilities suggest themselves based on machine intelligence exceeding human intelligence by the year 2000 [one has the right to be skeptical]. (Lighthill, 1972, p. 17)
       4) Just as Astronomy Succeeded Astrology, the Discovery of Intellectual Processes in Machines Should Lead to a Science, Eventually
       Just as astronomy succeeded astrology, following Kepler's discovery of planetary regularities, the discoveries of these many principles in empirical explorations on intellectual processes in machines should lead to a science, eventually. (Minsky & Papert, 1973, p. 11)
       Many problems arise in experiments on machine intelligence because things obvious to any person are not represented in any program. One can pull with a string, but one cannot push with one.... Simple facts like these caused serious problems when Charniak attempted to extend Bobrow's "Student" program to more realistic applications, and they have not been faced up to until now. (Minsky & Papert, 1973, p. 77)
       What do we mean by [a symbolic] "description"? We do not mean to suggest that our descriptions must be made of strings of ordinary language words (although they might be). The simplest kind of description is a structure in which some features of a situation are represented by single ("primitive") symbols, and relations between those features are represented by other symbols-or by other features of the way the description is put together. (Minsky & Papert, 1973, p. 11)
       [AI is] the use of computer programs and programming techniques to cast light on the principles of intelligence in general and human thought in particular. (Boden, 1977, p. 5)
       The word you look for and hardly ever see in the early AI literature is the word knowledge. They didn't believe you have to know anything, you could always rework it all.... In fact 1967 is the turning point in my mind when there was enough feeling that the old ideas of general principles had to go.... I came up with an argument for what I called the primacy of expertise, and at the time I called the other guys the generalists. (Moses, quoted in McCorduck, 1979, pp. 228-229)
       9) Artificial Intelligence Is Psychology in a Particularly Pure and Abstract Form
       The basic idea of cognitive science is that intelligent beings are semantic engines-in other words, automatic formal systems with interpretations under which they consistently make sense. We can now see why this includes psychology and artificial intelligence on a more or less equal footing: people and intelligent computers (if and when there are any) turn out to be merely different manifestations of the same underlying phenomenon. Moreover, with universal hardware, any semantic engine can in principle be formally imitated by a computer if only the right program can be found. And that will guarantee semantic imitation as well, since (given the appropriate formal behavior) the semantics is "taking care of itself" anyway. Thus we also see why, from this perspective, artificial intelligence can be regarded as psychology in a particularly pure and abstract form. The same fundamental structures are under investigation, but in AI, all the relevant parameters are under direct experimental control (in the programming), without any messy physiology or ethics to get in the way. (Haugeland, 1981b, p. 31)
       There are many different kinds of reasoning one might imagine:
        Formal reasoning involves the syntactic manipulation of data structures to deduce new ones following prespecified rules of inference. Mathematical logic is the archetypical formal representation. Procedural reasoning uses simulation to answer questions and solve problems. When we use a program to answer What is the sum of 3 and 4? it uses, or "runs," a procedural model of arithmetic. Reasoning by analogy seems to be a very natural mode of thought for humans but, so far, difficult to accomplish in AI programs. The idea is that when you ask the question Can robins fly? the system might reason that "robins are like sparrows, and I know that sparrows can fly, so robins probably can fly."
        Generalization and abstraction are also natural reasoning process for humans that are difficult to pin down well enough to implement in a program. If one knows that Robins have wings, that Sparrows have wings, and that Blue jays have wings, eventually one will believe that All birds have wings. This capability may be at the core of most human learning, but it has not yet become a useful technique in AI.... Meta- level reasoning is demonstrated by the way one answers the question What is Paul Newman's telephone number? You might reason that "if I knew Paul Newman's number, I would know that I knew it, because it is a notable fact." This involves using "knowledge about what you know," in particular, about the extent of your knowledge and about the importance of certain facts. Recent research in psychology and AI indicates that meta-level reasoning may play a central role in human cognitive processing. (Barr & Feigenbaum, 1981, pp. 146-147)
       Suffice it to say that programs already exist that can do things-or, at the very least, appear to be beginning to do things-which ill-informed critics have asserted a priori to be impossible. Examples include: perceiving in a holistic as opposed to an atomistic way; using language creatively; translating sensibly from one language to another by way of a language-neutral semantic representation; planning acts in a broad and sketchy fashion, the details being decided only in execution; distinguishing between different species of emotional reaction according to the psychological context of the subject. (Boden, 1981, p. 33)
       Can the synthesis of Man and Machine ever be stable, or will the purely organic component become such a hindrance that it has to be discarded? If this eventually happens-and I have... good reasons for thinking that it must-we have nothing to regret and certainly nothing to fear. (Clarke, 1984, p. 243)
       The thesis of GOFAI... is not that the processes underlying intelligence can be described symbolically... but that they are symbolic. (Haugeland, 1985, p. 113)
        14) Artificial Intelligence Provides a Useful Approach to Psychological and Psychiatric Theory Formation
       It is all very well formulating psychological and psychiatric theories verbally but, when using natural language (even technical jargon), it is difficult to recognise when a theory is complete; oversights are all too easily made, gaps too readily left. This is a point which is generally recognised to be true and it is for precisely this reason that the behavioural sciences attempt to follow the natural sciences in using "classical" mathematics as a more rigorous descriptive language. However, it is an unfortunate fact that, with a few notable exceptions, there has been a marked lack of success in this application. It is my belief that a different approach-a different mathematics-is needed, and that AI provides just this approach. (Hand, quoted in Hand, 1985, pp. 6-7)
       We might distinguish among four kinds of AI.
       Research of this kind involves building and programming computers to perform tasks which, to paraphrase Marvin Minsky, would require intelligence if they were done by us. Researchers in nonpsychological AI make no claims whatsoever about the psychological realism of their programs or the devices they build, that is, about whether or not computers perform tasks as humans do.
       Research here is guided by the view that the computer is a useful tool in the study of mind. In particular, we can write computer programs or build devices that simulate alleged psychological processes in humans and then test our predictions about how the alleged processes work. We can weave these programs and devices together with other programs and devices that simulate different alleged mental processes and thereby test the degree to which the AI system as a whole simulates human mentality. According to weak psychological AI, working with computer models is a way of refining and testing hypotheses about processes that are allegedly realized in human minds.
    ... According to this view, our minds are computers and therefore can be duplicated by other computers. Sherry Turkle writes that the "real ambition is of mythic proportions, making a general purpose intelligence, a mind." (Turkle, 1984, p. 240) The authors of a major text announce that "the ultimate goal of AI research is to build a person or, more humbly, an animal." (Charniak & McDermott, 1985, p. 7)
       Research in this field, like strong psychological AI, takes seriously the functionalist view that mentality can be realized in many different types of physical devices. Suprapsychological AI, however, accuses strong psychological AI of being chauvinisticof being only interested in human intelligence! Suprapsychological AI claims to be interested in all the conceivable ways intelligence can be realized. (Flanagan, 1991, pp. 241-242)
        16) Determination of Relevance of Rules in Particular Contexts
       Even if the [rules] were stored in a context-free form the computer still couldn't use them. To do that the computer requires rules enabling it to draw on just those [ rules] which are relevant in each particular context. Determination of relevance will have to be based on further facts and rules, but the question will again arise as to which facts and rules are relevant for making each particular determination. One could always invoke further facts and rules to answer this question, but of course these must be only the relevant ones. And so it goes. It seems that AI workers will never be able to get started here unless they can settle the problem of relevance beforehand by cataloguing types of context and listing just those facts which are relevant in each. (Dreyfus & Dreyfus, 1986, p. 80)
       Perhaps the single most important idea to artificial intelligence is that there is no fundamental difference between form and content, that meaning can be captured in a set of symbols such as a semantic net. (G. Johnson, 1986, p. 250)
        18) The Assumption That the Mind Is a Formal System
       Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped into the other (the computer). (G. Johnson, 1986, p. 250)
        19) A Statement of the Primary and Secondary Purposes of Artificial Intelligence
       The primary goal of Artificial Intelligence is to make machines smarter.
       The secondary goals of Artificial Intelligence are to understand what intelligence is (the Nobel laureate purpose) and to make machines more useful (the entrepreneurial purpose). (Winston, 1987, p. 1)
       The theoretical ideas of older branches of engineering are captured in the language of mathematics. We contend that mathematical logic provides the basis for theory in AI. Although many computer scientists already count logic as fundamental to computer science in general, we put forward an even stronger form of the logic-is-important argument....
       AI deals mainly with the problem of representing and using declarative (as opposed to procedural) knowledge. Declarative knowledge is the kind that is expressed as sentences, and AI needs a language in which to state these sentences. Because the languages in which this knowledge usually is originally captured (natural languages such as English) are not suitable for computer representations, some other language with the appropriate properties must be used. It turns out, we think, that the appropriate properties include at least those that have been uppermost in the minds of logicians in their development of logical languages such as the predicate calculus. Thus, we think that any language for expressing knowledge in AI systems must be at least as expressive as the first-order predicate calculus. (Genesereth & Nilsson, 1987, p. viii)
        21) Perceptual Structures Can Be Represented as Lists of Elementary Propositions
       In artificial intelligence studies, perceptual structures are represented as assemblages of description lists, the elementary components of which are propositions asserting that certain relations hold among elements. (Chase & Simon, 1988, p. 490)
       Artificial intelligence (AI) is sometimes defined as the study of how to build and/or program computers to enable them to do the sorts of things that minds can do. Some of these things are commonly regarded as requiring intelligence: offering a medical diagnosis and/or prescription, giving legal or scientific advice, proving theorems in logic or mathematics. Others are not, because they can be done by all normal adults irrespective of educational background (and sometimes by non-human animals too), and typically involve no conscious control: seeing things in sunlight and shadows, finding a path through cluttered terrain, fitting pegs into holes, speaking one's own native tongue, and using one's common sense. Because it covers AI research dealing with both these classes of mental capacity, this definition is preferable to one describing AI as making computers do "things that would require intelligence if done by people." However, it presupposes that computers could do what minds can do, that they might really diagnose, advise, infer, and understand. One could avoid this problematic assumption (and also side-step questions about whether computers do things in the same way as we do) by defining AI instead as "the development of computers whose observable performance has features which in humans we would attribute to mental processes." This bland characterization would be acceptable to some AI workers, especially amongst those focusing on the production of technological tools for commercial purposes. But many others would favour a more controversial definition, seeing AI as the science of intelligence in general-or, more accurately, as the intellectual core of cognitive science. As such, its goal is to provide a systematic theory that can explain (and perhaps enable us to replicate) both the general categories of intentionality and the diverse psychological capacities grounded in them. (Boden, 1990b, pp. 1-2)
       Because the ability to store data somewhat corresponds to what we call memory in human beings, and because the ability to follow logical procedures somewhat corresponds to what we call reasoning in human beings, many members of the cult have concluded that what computers do somewhat corresponds to what we call thinking. It is no great difficulty to persuade the general public of that conclusion since computers process data very fast in small spaces well below the level of visibility; they do not look like other machines when they are at work. They seem to be running along as smoothly and silently as the brain does when it remembers and reasons and thinks. On the other hand, those who design and build computers know exactly how the machines are working down in the hidden depths of their semiconductors. Computers can be taken apart, scrutinized, and put back together. Their activities can be tracked, analyzed, measured, and thus clearly understood-which is far from possible with the brain. This gives rise to the tempting assumption on the part of the builders and designers that computers can tell us something about brains, indeed, that the computer can serve as a model of the mind, which then comes to be seen as some manner of information processing machine, and possibly not as good at the job as the machine. (Roszak, 1994, pp. xiv-xv)
       The inner workings of the human mind are far more intricate than the most complicated systems of modern technology. Researchers in the field of artificial intelligence have been attempting to develop programs that will enable computers to display intelligent behavior. Although this field has been an active one for more than thirty-five years and has had many notable successes, AI researchers still do not know how to create a program that matches human intelligence. No existing program can recall facts, solve problems, reason, learn, and process language with human facility. This lack of success has occurred not because computers are inferior to human brains but rather because we do not yet know in sufficient detail how intelligence is organized in the brain. (Anderson, 1995, p. 2)

    Historical dictionary of quotations in cognitive science > Artificial Intelligence

  • 10 armonía

    f.
    1 harmony, agreement, concord, concordance.
    2 harmonics, harmony.
    * * *
    1 harmony
    * * *
    noun f.
    * * *
    * * *
    femenino harmony
    * * *
    = harmonisation [harmonization, -USA], harmony, unity, harmonics.
    Ex. The difficult issue of copyright will not be resolved as the EC is not at present looking at reprography as an area of harmonization.
    Ex. A harmony is an arrangement of passages of the Bible on the same topic into parallel columns so that similarities and differences are readily compared.
    Ex. The part chosen should have a unity of its own, a wholeness that offers a complete experience without at the same time giving away everything.
    Ex. Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.
    ----
    * algo que rompe la armonía = a blot on the landscape.
    * armonía racial = racial harmony.
    * armonía social = social harmony.
    * con armonía = harmoniously.
    * en armonía = harmoniously, in harmony.
    * en armonía con = in harmony with, in harness with, in keeping with, in tune with, in sync with.
    * falta de armonía = disharmony.
    * que rompe la armonía = eyesore.
    * * *
    femenino harmony
    * * *
    = harmonisation [harmonization, -USA], harmony, unity, harmonics.

    Ex: The difficult issue of copyright will not be resolved as the EC is not at present looking at reprography as an area of harmonization.

    Ex: A harmony is an arrangement of passages of the Bible on the same topic into parallel columns so that similarities and differences are readily compared.
    Ex: The part chosen should have a unity of its own, a wholeness that offers a complete experience without at the same time giving away everything.
    Ex: Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.
    * algo que rompe la armonía = a blot on the landscape.
    * armonía racial = racial harmony.
    * armonía social = social harmony.
    * con armonía = harmoniously.
    * en armonía = harmoniously, in harmony.
    * en armonía con = in harmony with, in harness with, in keeping with, in tune with, in sync with.
    * falta de armonía = disharmony.
    * que rompe la armonía = eyesore.

    * * *
    1 ( Mús) harmony
    2 (de colores, estilos) harmony
    accesorios en armonía con las ricas telas de los vestidos accessories in harmony with o which complement the rich fabrics of the dresses
    3 (en relaciones) harmony
    conviven en perfecta armonía they live together in perfect harmony
    vivir en armonía con la naturaleza to live in harmony with nature
    * * *

    armonía sustantivo femenino
    harmony
    armonía sustantivo femenino harmony
    ' armonía' also found in these entries:
    Spanish:
    consonancia
    - discorde
    - sintonía
    - acorde
    - unidad
    English:
    accord
    - harmonics
    - harmony
    - harmonize
    * * *
    armonía, harmonía nf
    1. Mús harmony
    2. [de colores, formas] harmony
    3. [amistad] harmony;
    la falta de armonía entre los miembros del gabinete the lack of agreement within the cabinet;
    vivir en armonía con alguien to live in harmony with sb
    * * *
    f harmony
    * * *
    : harmony
    * * *
    armonía n harmony [pl. harmonies]

    Spanish-English dictionary > armonía

  • 11 μαθηματικός

    II scientific,

    τὸ μ. εἶδος Id.Sph. 219c

    ; esp. mathematical, μαθηματικός, ὁ, mathematician, Arist.Ph. 193b31, EN 1142a17, Phld.Acad.Ind.p.16 M., Ceb.34: ἡ-κή (sc. ἐπιστήμη) mathematics, Archyt.1 tit., Arist.Metaph. 1026a14; αἱ -καί ib.26; φιλοσοφία μ. ib.19; τὰ μ. mathematics, Id.EN 1151 a17; also, mathematical entities, Id.Metaph. 1076a17; γραμμὴ μ. a mathematicalline, opp. γ. φυσική, Id.Ph. 194a11;

    κύκλοι μ. Id.Metaph. 1036a4

    ;

    ἁρμονικὴ ἥ τε μ. καὶ ἡ κατὰ τὴν ἀκοήν Id.APo. 79a1

    : [comp] Comp. - κωτέρα ὕλη too mathematical, Id.Metaph. 992b2. Adv. - κῶς ib. 995a6, Str.2.5.1, etc.
    2 astronomical,

    οἱ μ. κανόνες Plu.2.974f

    ; ἡ -κή astronomy, S.E.M.5.104.
    b astrological,

    ἡ μ. τέχνη Sallust.9

    , cf. Gal. 19.529; ὁ μ. astrologer, M.Ant.4.48, S.E.M.5.2, Porph. ap. Eus.PE 6.1, etc.
    3 among the Pythagoreans, οἱ μ. (opp. οἱ ἀκουσματικοί) advanced students, Porph.VP37, Iamb.VP18.81.

    Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > μαθηματικός

  • 12 математический горизонт

    2) Mathematics: mathematical horizon
    3) Astronomy: rational horizon

    Универсальный русско-английский словарь > математический горизонт

  • 13 Mathematica

    măthēmătĭcus, a, um, adj., = mathêmatiko:s, of or belonging to mathematics, mathematical (class.).
    I.
    Adj.:

    mathematica nota,

    Vitr. 1, 1:

    artes,

    Plin. 30, 1, 1, § 2:

    cogitatio,

    Macr. Somn. Scip. 2, 2:

    disciplinae,

    i. e. geometry, arithmetic, astronomy, music, geography, optics, Gell. 1, 9, 6.—
    II.
    Subst.
    A. 1.
    A mathematician, Cic. de Or 1, 3, 10; id. Ac. 2, 36, 116; id. Tusc. 1, 2, 5; Sen. Ep. 88, 26.—
    2.
    An astrologer (post-Aug.):

    mathematici, genus hominum potentibus infidum, sperantibus fallax, quod in civitate nostra et vetabitur semper et retinebitur,

    Tac. H. 1, 22:

    nota mathematicis genesis tua,

    Juv. 14, 248; Tert. Apol. 43:

    qui de salute principis... mathematicos consulit, cum eo qui responderit, capite punitur,

    Paul. Sent. 5, 21, 3.—
    B. 1.
    Mathematics, Sen. Ep. 88, 23; v. l. mă-thēmătĭcē ( = mathêmatikê, sc. technê).—
    2.
    Astrology:

    addictus mathematicae, persuasionisque plenus, cuncta fato agi,

    Suet. Tib. 69.

    Lewis & Short latin dictionary > Mathematica

  • 14 Mathematicus

    măthēmătĭcus, a, um, adj., = mathêmatiko:s, of or belonging to mathematics, mathematical (class.).
    I.
    Adj.:

    mathematica nota,

    Vitr. 1, 1:

    artes,

    Plin. 30, 1, 1, § 2:

    cogitatio,

    Macr. Somn. Scip. 2, 2:

    disciplinae,

    i. e. geometry, arithmetic, astronomy, music, geography, optics, Gell. 1, 9, 6.—
    II.
    Subst.
    A. 1.
    A mathematician, Cic. de Or 1, 3, 10; id. Ac. 2, 36, 116; id. Tusc. 1, 2, 5; Sen. Ep. 88, 26.—
    2.
    An astrologer (post-Aug.):

    mathematici, genus hominum potentibus infidum, sperantibus fallax, quod in civitate nostra et vetabitur semper et retinebitur,

    Tac. H. 1, 22:

    nota mathematicis genesis tua,

    Juv. 14, 248; Tert. Apol. 43:

    qui de salute principis... mathematicos consulit, cum eo qui responderit, capite punitur,

    Paul. Sent. 5, 21, 3.—
    B. 1.
    Mathematics, Sen. Ep. 88, 23; v. l. mă-thēmătĭcē ( = mathêmatikê, sc. technê).—
    2.
    Astrology:

    addictus mathematicae, persuasionisque plenus, cuncta fato agi,

    Suet. Tib. 69.

    Lewis & Short latin dictionary > Mathematicus

  • 15 mathematicus

    măthēmătĭcus, a, um, adj., = mathêmatiko:s, of or belonging to mathematics, mathematical (class.).
    I.
    Adj.:

    mathematica nota,

    Vitr. 1, 1:

    artes,

    Plin. 30, 1, 1, § 2:

    cogitatio,

    Macr. Somn. Scip. 2, 2:

    disciplinae,

    i. e. geometry, arithmetic, astronomy, music, geography, optics, Gell. 1, 9, 6.—
    II.
    Subst.
    A. 1.
    A mathematician, Cic. de Or 1, 3, 10; id. Ac. 2, 36, 116; id. Tusc. 1, 2, 5; Sen. Ep. 88, 26.—
    2.
    An astrologer (post-Aug.):

    mathematici, genus hominum potentibus infidum, sperantibus fallax, quod in civitate nostra et vetabitur semper et retinebitur,

    Tac. H. 1, 22:

    nota mathematicis genesis tua,

    Juv. 14, 248; Tert. Apol. 43:

    qui de salute principis... mathematicos consulit, cum eo qui responderit, capite punitur,

    Paul. Sent. 5, 21, 3.—
    B. 1.
    Mathematics, Sen. Ep. 88, 23; v. l. mă-thēmătĭcē ( = mathêmatikê, sc. technê).—
    2.
    Astrology:

    addictus mathematicae, persuasionisque plenus, cuncta fato agi,

    Suet. Tib. 69.

    Lewis & Short latin dictionary > mathematicus

  • 16 quadrivium

    quā̆drĭvĭum, ii, n. [quattuor-via].
    I.
    Lit., a place where four ways meet, a crossway, cross-road:

    in quadriviis et angiportis,

    Cat. 58, 4; so Juv. 1, 63:

    DII,

    the tutelar gods of cross-roads, Inscr. Grut. 84, 5; 1015, 1; Inscr. Rein. col. 1, n. 14.—
    II.
    Transf., the assemblage of the four mathematical sciences (arithmetic, music, geometry, and astronomy), Boëth. Arithmet. 1, 1.

    Lewis & Short latin dictionary > quadrivium

  • 17 γραμμή

    γραμμή, ἡ, ([etym.] γράφω)
    A stroke or line of a pen, line, as in mathematical figures, γραμμῆς λόγος ὁ τῶν δύο Pythagorei ap.Arist. Metaph. 1036b12, cf. Pl.Men. 82c, R. 509d, etc.; περὶ ἀλόγων γ. title of work by Democritus, περὶ ἀτόμων γ., title of work ascribed to Arist.: hence γραμμαί, αἱ, astronomy, AP9.344 (Leon.); also in forming letters, line traced by teacher, Pl.Prt. 326d; outline, opp. σκιά, Metop. ap. Stob.3.1.116, cf. Plb.2.14.8;

    ἡ ἐκτὸς γ. Hero Aut.27.2

    .
    II = βαλβίς, line across the course, starting- or winning-point, Pi.P.9.118, cf. Ar.Ach. 483;

    εὐθὺς ἀπὸ γ. Lib.Or.59.13

    : metaph. of life,

    πέλας γραμμῆς ἱκέσθαι E.El. 956

    ;

    ἐπ' ἄκραν ἥκομεν γ. κακῶν Id.Fr. 169

    ;

    ἡ ἐσχάτη τοῦ βίου γ. D.S.17.118

    : hence, boundary-line, edge, dub. l. in Hp.Art.80; cutting edge of a knife, Gal.2.673.
    III line or square on a chequer-board: hence prov., τὸν ἀπὸ γραμμᾶς κινεῖν λίθον to move a piece from this line, i. e. try one's last chance, Theoc. 6.18 (usu. called ἡ ἱερά (sc. γραμμή), cf. ἱερός) ; αἱ γ. the board itself, Poll.9.99.
    V Medic., linea alba, Gal.2.514.
    2 = ζέα, Hippiatr.1.

    Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > γραμμή

  • 18 μάθημα

    A that which is learnt, lesson,

    τὰ παθήματα μαθήματα Hdt.1.207

    ;

    μ. μαθεῖν S.Ph. 918

    ; μ. τινός or περί τι, Pl.Smp. 211 c, R. 525d;

    προσπορεύεται πρὸς τὰ λοιπὰ μ. PCair.Zen.60.7

     (iii B. C.);

    ἀφεῖσθαι τοὺς παῖδας ἀπὸ τῶν μ. SIG577.77

     (Milet., iii/ii B. C.), cf. 578.28 (Teos, ii B. C.), al.
    2 learning, knowledge, Ar.Nu. 1231, Av. 380, Th.2.39, PSI1.94.9 (ii A. D.), etc.; οἱ καθιστάμενοι ἐπὶ τῶν μ. educational authorities, SIG578.66 (Teos, ii B. C.); τὸ μ. τὸ περὶ τὰς τάξεις the science of tactics, Pl.La. 182b: freq. in pl., Isoc.12.27, etc.;

    μαθημάτων φρόντιζε μᾶλλον χρημάτων· τὰ γὰρ μαθήματ' εὐπορεῖ τὰ χρήματα Philem. 232

    .
    3 esp. the mathematical sciences, Archyt.1,3 tit.; τρία μ., i. e. arithmetic, geometry, and astronomy, acc. to Pl.Lg. 817e, cf. Phld. Ind.Sto.66; later τὰ τέσσαρα μ. ( ἁρμονική being added) Theol.Ar.17; Arist. distd. pure from mixed

    μ., τὰ φυσικώτερα τῶν μ., οἷον ὀπτικὴ καὶ ἁρμονικὴ καὶ ἀστρονομία Ph. 194a8

    ;

    ἡ ἐν τοῖς μ. ἁρμονική Metaph. 997b21

    ;

    τὰ μ. περὶ τὰ εἴδη ἐστίν APo. 79a7

    ; οἱ ἀπὸ τῶν μ. mathematicians, Cleom.1.8.
    4 astrology, AP7.687 (Pall.).
    5 creed, Cod.Just.1.1.7.11, al.

    Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > μάθημα

  • 19 Napier (Neper), John

    [br]
    b. 1550 Merchiston Castle, Edinburgh, Scotland
    d. 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]
    Bibliography
    Napier'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 Reading
    D.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

    Biographical history of technology > Napier (Neper), John

  • 20 Schickhard(t), Wilhelm

    [br]
    b. 22 April 1592 Herrenberg, Stuttgart, Germany
    d. 24 October 1635 Tübingen, Germany
    [br]
    German polymath who described, and apparently built, a calculating "clock", possibly the first mechanical adding-machine.
    [br]
    At an early age Schickhard won a scholarship to the monastery school at Tübingen and then progressed to the university, where he obtained his BA and MA in theology in 1609 and 1611, respectively. He then specialized in oriental languages and eventually became Professor of Hebrew, Oriental Languages, Mathematics, Astronomy and Geography at Tübingen. Between 1613 and 1619 he was also deacon or pastor to a number of churches in the area. In 1617 he met Johannes Kepler, who, impressed by his ability, asked him to draw up tables of figures for his Harmonica Mundi (1619). As a result of this, Schickhard designed and constructed a mechanical adding-machine that he called a calculating clock. This he described in a letter of 20 September 1623 to Kepler, but a subsequent letter of 25 February 1624 reported its destruction by fire. After his death, probably from bubonic plague, his papers and the letter to Kepler were discovered in the regional library in Stuttgart in 1930 by Franz Hamme, who described them to the 1957 Mathematical Congress. As a result, a Dr Baron von Freytag Lovinghoff, who was present at that meeting, built a reconstruction of Schickard's machine in 1960.
    [br]
    Further Reading
    F.Hamme, 1958, "Nicht Pascal sondern der Tübingen Prof. Wilhelm Schickhard erfund die Rechenmaschin", Buromarkt 20:1,023 (describes the papers and letter to Kepler).
    B.von F.Lovinghoff, 1964, "Die erste Rechenmaschin: Tübingen 1623", Humanismus und
    Technik 9:45.
    ——1973, "Wilhelm Schickhard und seine Rechenmaschin von 1625", in M.Graef (ed.), 350 Jahre Rechenmaschin.
    M.R.Williams, 1985, History of Computing Technology, London: Prentice-Hall.
    See also: Pascal, Blaise
    KF

    Biographical history of technology > Schickhard(t), Wilhelm

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