-
1 tratado
adj.processed.m.1 treaty (convenio).tratado de Libre Comercio NAFTA Treaty (entre EE.UU., Canadá y México)tratado de paz peace treaty2 treatise (escrito).past part.past participle of spanish verb: tratar.* * *1 (pacto) treaty2 (estudio) treatise* * *noun m.* * *SM1) (Com) agreement; (Pol) treaty, pact2) (=libro) treatise* * *1) (Der, Pol) treaty2) ( libro) treatise* * *= tract, treatise, treaty.Ex. This volume was written as a tract to promote the use of microcards.Ex. The treatise arose from Kaiser's work in indexing information relating to business and industry.Ex. Form headings are sometimes suggested -- for example, in the case of laws and treaties.----* bien tratado = well represented.* OTAN (Organización del Tratado del Atlántico Norte) = NATO (North Atlantic Treaty Organisation).* ratificar un tratado = ratify + treaty.* tratado armamentístico = arms treaty.* Tratado de Ginebra, el = Geneva Convention, the.* tratado de paz = peace treaty.* Tratado de Roma, el = Treaty of Rome, the, Rome Treaty, the.* tratado matemático = mathematical treatise.* * *1) (Der, Pol) treaty2) ( libro) treatise* * *= tract, treatise, treaty.Ex: This volume was written as a tract to promote the use of microcards.
Ex: The treatise arose from Kaiser's work in indexing information relating to business and industry.Ex: Form headings are sometimes suggested -- for example, in the case of laws and treaties.* bien tratado = well represented.* OTAN (Organización del Tratado del Atlántico Norte) = NATO (North Atlantic Treaty Organisation).* ratificar un tratado = ratify + treaty.* tratado armamentístico = arms treaty.* Tratado de Ginebra, el = Geneva Convention, the.* tratado de paz = peace treaty.* Tratado de Roma, el = Treaty of Rome, the, Rome Treaty, the.* tratado matemático = mathematical treatise.* * *A (Der, Pol) treatyfirmar un tratado to sign a treatyel Tratado de Roma the Treaty of RomeCompuestos:trade agreementfree trade treaty, free trade agreementpeace treatyB (libro) treatise* * *
Del verbo tratar: ( conjugate tratar)
tratado es:
el participio
Multiple Entries:
tratado
tratar
tratado sustantivo masculino
1 (Der, Pol) treaty;
2 ( libro) treatise
tratar ( conjugate tratar) verbo intransitivo
1 ( intentar) to try;
tratadoé de que no vuelva a suceder I'll try to make sure it doesn't happen again
2 [obra/libro/película] tratado de algo to be about sth;
tratado sobre algo to deal with sth;◊ la conferencia tratadoá sobre medicina alternativa the lecture will deal with alternative medicine
3 (tener contacto, relaciones) tratado con algn to deal with sb;
verbo transitivo
1 ‹persona/animal/instrumento› to treat;
2 ( frecuentar):
3 ‹tema/asunto› to discuss, to deal with
4a) (Med) to treat
tratarse verbo pronominal
1 tratadose con algn ( ser amigo de) to be friendly with sb;
( alternar) to socialize o mix with sb;
2 (+ compl) ( recípr):
3 (Med) to have o undergo treatment
4◊ tratarse de (en 3a pers)
◊ ¿de qué se trata? what's it about?
◊ se trata de participar, no de ganar it's a question of taking part, not of winning;
solo porque se trata de ti just because it's you
tratado sustantivo masculino
1 (ensayo, libro) treatise
2 (acuerdo, pacto) treaty
tratar
I verbo transitivo
1 (portarse) to treat
2 (cuidar) to look after, care: trátame el libro bien, look after my book
3 (dirigirse a una persona) address: nos tratamos de tú, we call each other "tú" o we're on first name terms
4 (considerar, llamar) me trató de tonto, he called me stupid
5 (someter a un proceso) to treat
6 (someter a tratamiento médico) to treat: le tienen que tratar la artritis, they have to treat his arthritis
7 (tener relación social) la he tratado muy poco, I don't know her very well
8 (considerar, discutir) to deal with: no hemos tratado la cuestión, we haven't discussed that subject
II verbo intransitivo 1 tratar de, (un libro, una película) to be about: ¿de qué trata?, what is it about?
2 (intentar) to try [de, to]
3 Com tratar en, to trade in o with 4 tratar con, (negociar) to negotiate with
' tratado' also found in these entries:
Spanish:
firma
- marcar
- OTAN
- ratificar
- suscribir
- tratar
- concluir
- redacción
- redactar
- violar
English:
claim
- confirm
- confirmation
- discourse
- final
- NATO
- peace
- stir
- treatise
- treaty
- ultimately
- deal
- hard
- tract
* * *tratado nm1. [convenio] treatyTratado de Libre Comercio [en general] free trade agreement; [entre EE.UU., Canadá y México] NAFTA, North American Free Trade Agreement;el Tratado de Maastricht the Maastricht Treaty;tratado de paz peace treaty;tratado de no proliferación non-proliferation treaty;el Tratado de Roma the Treaty of Rome2. [escrito] treatise* * *m espPOL treaty* * *tratado nm1) : treatise2) : treaty* * * -
2 matemático
adj.mathematical, mathematic.m.mathematician.* * *► adjetivo1 mathematical► nombre masculino,nombre femenino1 mathematician* * *1. (f. - matemática)noun2. (f. - matemática)adj.* * *matemático, -a1. ADJ1) (Mat) mathematical; [cálculo] precise2) (=exacto) exact3) (Dep)4)• es matemático (=no falla) —
¡es matemático!, ¡cada vez que me siento, suena el teléfono! — it's like clockwork!, every time I sit down the phone rings!
2.SM / F mathematician, math specialist (EEUU)* * *I- ca adjetivoa) (Mat) mathematicalb) ( exacto) mathematicalII- ca masculino, femenino mathematician* * *I- ca adjetivoa) (Mat) mathematicalb) ( exacto) mathematicalII- ca masculino, femenino mathematician* * *matemático11 = mathematician.Ex: A mathematician is not a man who can readily manipulate figures; often he cannot.
matemático22 = mathematical, mathematic.Ex: Forms of symbol used for presentation are: 1 language, eg Arabic; 2 mathematical, eg. graphs, formulae; 3 pictorial, eg drawings.
Ex: This article presents Bradford's Law as an observation made from the outcome of searching rather than a mathematic development.* área de datos matemáticos = mathematical data area.* cálculo matemático = mathematical calculation.* de un modo matemático = mathematically.* error matemático = mathematical mistake, mathematical error.* expresión matemática = mathematical expression.* fórmula matemática = mathematical formula.* lógica matemática = mathematical logic.* modelo matemático = mathematical model.* pensamiento matemático = mathematical thinking.* tratado matemático = mathematical treatise.* * *1 ( Mat) mathematical2 (exacto) mathematicalcon precisión matemática with mathematical precisionmasculine, femininemathematician* * *
matemático◊ -ca adjetivo
mathematical
■ sustantivo masculino, femenino
mathematician
matemático,-a
I adjetivo mathematical
II sustantivo masculino y femenino mathematician
III sustantivo femenino mathematics
' matemático' also found in these entries:
Spanish:
índice
- matemática
English:
mathematical
- mathematician
* * *matemático, -a♦ adj1. [de la matemática] mathematical2. [exacto] mathematical♦ nm,f[científico] mathematician* * *I adj mathematicalII m, matemática f mathematician* * *matemático, -ca adj: mathematical♦ matemáticamente advmatemático, -ca n: mathematician* * *matemático1 adj mathematicalmatemático2 n mathematician -
3 tratado matemático
(n.) = mathematical treatiseEx. Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.* * *(n.) = mathematical treatiseEx: Socrates's description of astronomy and harmonics is less problematic when it is read against the background of certain Greek mathematical treatises.
-
4 matemático2
2 = mathematical, mathematic.Ex. Forms of symbol used for presentation are: 1 language, eg Arabic; 2 mathematical, eg. graphs, formulae; 3 pictorial, eg drawings.Ex. This article presents Bradford's Law as an observation made from the outcome of searching rather than a mathematic development.----* área de datos matemáticos = mathematical data area.* cálculo matemático = mathematical calculation.* de un modo matemático = mathematically.* error matemático = mathematical mistake, mathematical error.* expresión matemática = mathematical expression.* fórmula matemática = mathematical formula.* lógica matemática = mathematical logic.* modelo matemático = mathematical model.* pensamiento matemático = mathematical thinking.* tratado matemático = mathematical treatise. -
5 Bibliography
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Principles of teaching. New York: A. G. Seiler.■ Thorndike, E. L. (1970). Animal intelligence: Experimental studies. Darien, CT: Hafner Publishing Co. (Originally published in 1911.)■ Titchener, E. B. (1910). A textbook of psychology. New York: Macmillan.■ Titchener, E. B. (1914). A primer of psychology. New York: Macmillan.■ Toulmin, S. (1957). The philosophy of science. London: Hutchinson.■ Tulving, E. (1972). Episodic and semantic memory. In E. Tulving & W. Donaldson (Eds.), Organisation of memory. London: Academic Press.■ Turing, A. (1946). In B. E. Carpenter & R. W. Doran (Eds.), ACE reports of 1946 and other papers. Cambridge, MA: MIT Press.■ Turkle, S. (1984). Computers and the second self: Computers and the human spirit. New York: Simon & Schuster.■ Tyler, S. A. (1978). The said and the unsaid: Mind, meaning, and culture. New York: Academic Press.■ van Heijenoort (Ed.) (1967). From Frege to Goedel. Cambridge: Harvard University Press.■ Varela, F. J. (1984). The creative circle: Sketches on the natural history of circularity. In P. Watzlawick (Ed.), The invented reality (pp. 309-324). New York: W. W. Norton.■ Voltaire (1961). On the Penseґs of M. Pascal. In Philosophical letters (pp. 119-146). E. Dilworth (Trans.). Indianapolis: Bobbs-Merrill.■ Wagman, M. (1991a). Artificial intelligence and human cognition: A theoretical inter comparison of two realms of intellect. Westport, CT: Praeger.■ Wagman, M. (1991b). Cognitive science and concepts of mind: Toward a general theory of human and artificial intelligence. Westport, CT: Praeger.■ Wagman, M. (1993). Cognitive psychology and artificial intelligence: Theory and re search in cognitive science. Westport, CT: Praeger.■ Wagman, M. (1995). The sciences of cognition: Theory and research in psychology and artificial intelligence. Westport, CT: Praeger.■ Wagman, M. (1996). Human intellect and cognitive science: Toward a general unified theory of intelligence. Westport, CT: Praeger.■ Wagman, M. (1997a). Cognitive science and the symbolic operations of human and artificial intelligence: Theory and research into the intellective processes. Westport, CT: Praeger.■ Wagman, M. (1997b). The general unified theory of intelligence: Central conceptions and specific application to domains of cognitive science. Westport, CT: Praeger.■ Wagman, M. (1998a). Cognitive science and the mind- body problem: From philosophy to psychology to artificial intelligence to imaging of the brain. Westport, CT: Praeger.■ Wagman, M. (1998b). Language and thought in humans and computers: Theory and research in psychology, artificial intelligence, and neural science. Westport, CT: Praeger.■ Wagman, M. (1998c). The ultimate objectives of artificial intelligence: Theoretical and research foundations, philosophical and psychological implications. Westport, CT: Praeger.■ Wagman, M. (1999). The human mind according to artificial intelligence: Theory, re search, and implications. Westport, CT: Praeger.■ Wagman, M. (2000). Scientific discovery processes in humans and computers: Theory and research in psychology and artificial intelligence. Westport, CT: Praeger.■ Wall, R. (1972). Introduction to mathematical linguistics. Englewood Cliffs, NJ: Prentice-Hall.■ Wallas, G. (1926). The Art of Thought. New York: Harcourt, Brace & Co.■ Wason, P. (1977). Self contradictions. In P. Johnson-Laird & P. Wason (Eds.), Thinking: Readings in cognitive science. Cambridge: Cambridge University Press.■ Wason, P. C., & P. N. Johnson-Laird. (1972). Psychology of reasoning: Structure and content. Cambridge, MA: Harvard University Press.■ Watson, J. (1930). Behaviorism. New York: W. W. Norton.■ Watzlawick, P. (1984). Epilogue. In P. Watzlawick (Ed.), The invented reality. New York: W. W. Norton, 1984.■ Weinberg, S. (1977). The first three minutes: A modern view of the origin of the uni verse. New York: Basic Books.■ Weisberg, R. W. (1986). Creativity: Genius and other myths. New York: W. H. Freeman.■ Weizenbaum, J. (1976). Computer power and human reason: From judgment to cal culation. San Francisco: W. H. Freeman.■ Wertheimer, M. (1945). Productive thinking. New York: Harper & Bros.■ Whitehead, A. N. (1925). Science and the modern world. New York: Macmillan.■ Whorf, B. L. (1956). In J. B. Carroll (Ed.), Language, thought and reality: Selected writings of Benjamin Lee Whorf. Cambridge, MA: MIT Press.■ Whyte, L. L. (1962). The unconscious before Freud. New York: Anchor Books.■ Wiener, N. (1954). The human use of human beings. Boston: Houghton Mifflin.■ Wiener, N. (1964). God & Golem, Inc.: A comment on certain points where cybernetics impinges on religion. Cambridge, MA: MIT Press.■ Winograd, T. (1972). Understanding natural language. New York: Academic Press.■ Winston, P. H. (1987). Artificial intelligence: A perspective. In E. L. Grimson & R. S. Patil (Eds.), AI in the 1980s and beyond (pp. 1-12). Cambridge, MA: MIT Press.■ Winston, P. H. (Ed.) (1975). The psychology of computer vision. New York: McGrawHill.■ Wittgenstein, L. (1953). Philosophical investigations. Oxford: Basil Blackwell.■ Wittgenstein, L. (1958). The blue and brown books. New York: Harper Colophon.■ Woods, W. A. (1975). What's in a link: Foundations for semantic networks. In D. G. Bobrow & A. Collins (Eds.), Representations and understanding: Studies in cognitive science (pp. 35-84). New York: Academic Press.■ Woodworth, R. S. (1938). Experimental psychology. New York: Holt; London: Methuen (1939).■ Wundt, W. (1904). Principles of physiological psychology (Vol. 1). E. B. Titchener (Trans.). New York: Macmillan.■ Wundt, W. (1907). Lectures on human and animal psychology. J. E. Creighton & E. B. Titchener (Trans.). New York: Macmillan.■ Young, J. Z. (1978). Programs of the brain. New York: Oxford University Press.■ Ziman, J. (1978). Reliable knowledge: An exploration of the grounds for belief in science. Cambridge: Cambridge University Press.Historical dictionary of quotations in cognitive science > Bibliography
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6 Boole, George
SUBJECT AREA: Electronics and information technology[br]b. 2 November 1815 Lincoln, Englandd. 8 December 1864 Ballintemple, Coounty Cork, Ireland[br]English mathematician whose development of symbolic logic laid the foundations for the operating principles of modern computers.[br]Boole was the son of a tradesman, from whom he learned the principles of mathematics and optical-component manufacturing. From the early age of 16 he taught in a number of schools in West Yorkshire, and when only 20 he opened his own school in Lincoln. There, at the Mechanical Institute, he avidly read mathematical journals and the works of great mathematicians such as Lagrange, Laplace and Newton and began to tackle a variety of algebraic problems. This led to the publication of a constant stream of original papers in the newly launched Cambridge Mathematical Journal on topics in the fields of algebra and calculus, for which in 1844 he received the Royal Society Medal.In 1847 he wrote The Mathematical Analysis of Logic, which applied algebraic symbolism to logical forms, whereby the presence or absence of properties could be represented by binary states and combined, just like normal algebraic equations, to derive logical statements about a series of operations. This laid the foundations for the binary logic used in modern computers, which, being based on binary on-off devices, greatly depend on the use of such operations as "and", "nand" ("not and"), "or" and "nor" ("not or"), etc. Although he lacked any formal degree, this revolutionary work led to his appointment in 1849 to the Chair of Mathematics at Queen's College, Cork, where he continued his work on logic and also produce treatises on differential equations and the calculus of finite differences.[br]Principal Honours and DistinctionsRoyal Society Medal 1844. FRS 1857.BibliographyBoole's major contributions to logic available in republished form include George Boole: Investigation of the Laws of Thought, Dover Publications; George Boole: Laws of Thought, Open Court, and George Boole: Studies in Logic \& Probability, Open Court.1872, A Treatise on Differential Equations.Further ReadingW.Kneale, 1948, "Boole and the revival of logic", Mind 57:149.G.C.Smith (ed.), 1982, George Boole \& Augustus de Morgan. Correspondence 1842– 1864, Oxford University Press.—, 1985, George Boole: His Life and Work, McHale.E.T.Bell, 1937, Men of Mathematics, London: Victor Gollancz.KF -
7 Hero of Alexandria
SUBJECT AREA: Architecture and building, Mechanical, pneumatic and hydraulic engineering, Photography, film and optics, Steam and internal combustion engines[br]fl. c.62 AD Alexandria[br]Alexandrian mathematician and mechanician.[br]Nothing is known of Hero, or Heron, apart from what can be gleaned from the books he wrote. Their scope and style suggest that he was a teacher at the museum or the university of Alexandria, writing textbooks for his students. The longest book, and the one with the greatest technological interest, is Pneumatics. Some of its material is derived from the works of the earlier writers Ctesibius of Alexandria and Philo of Byzantium, but many of the devices described were invented by Hero himself. The introduction recognizes that the air is a body and demonstrates the effects of air pressure, as when air must be allowed to escape from a closed vessel before water can enter. There follow clear descriptions of a variety of mechanical contrivances depending on the effects of either air pressure or heated gases. Most of the devices seem trivial, but such toys or gadgets were popular at the time and Hero is concerned to show how they work. Inventions with a more serious purpose are a fire pump and a water organ. One celebrated gadget is a sphere that is set spinning by jets of steam—an early illustration of the reaction principle on which modern jet propulsion depends.M echanics, known only in an Arabic version, is a textbook expounding the theory and practical skills required by the architect. It deals with a variety of questions of mechanics, such as the statics of a horizontal beam resting on vertical posts, the theory of the centre of gravity and equilibrium, largely derived from Archimedes, and the five ways of applying a relatively small force to exert a much larger one: the lever, winch, pulley, wedge and screw. Practical devices described include sledges for transporting heavy loads, cranes and a screw cutter.Hero's Dioptra describes instruments used in surveying, together with an odometer or device to indicate the distance travelled by a wheeled vehicle. Catoptrics, known only in Latin, deals with the principles of mirrors, plane and curved, enunciating that the angle of incidence is equal to that of reflection. Automata describes two forms of puppet theatre, operated by strings and drums driven by a falling lead weight attached to a rope wound round an axle. Hero's mathematical work lies in the tradition of practical mathematics stretching from the Babylonians through Islam to Renaissance Europe. It is seen most clearly in his Metrica, a treatise on mensuration.Of all his works, Pneumatics was the best known and most influential. It was one of the works of Greek science and technology assimilated by the Arabs, notably Banu Musa ibn Shakir, and was transmitted to medieval Western Europe.[br]BibliographyAll Hero's works have been printed with a German translation in Heronis Alexandrini opera quae supersunt omnia, 1899–1914, 5 vols, Leipzig. The book on pneumatics has been published as The Pneumatics of Hero of Alexandria, 1851, trans. and ed. Bennet Wood-croft, London (facs. repr. 1971, introd. Marie Boas Hall, London and New York).Further ReadingA.G.Drachmann, 1948, "Ktesibios, Philon and Heron: A Study in Ancient Pneumatics", Acta Hist. Sci. Nat. Med. 4, Copenhagen: Munksgaard.T.L.Heath, 1921, A History of Greek Mathematics, Oxford (still useful for his mathematical work).LRD -
8 γράμμα
γράμμα, ατος, τό, [dialect] Dor. [full] γράθμα, prob. in IG4.506 (Heraeum, vi/v B. C.), cf. An.Ox.1.102, but [full] γράσσμα, IG4.554 (Argos, v B. C.): late [dialect] Aeol. pl. [full] γρόππατα, Epigr.Gr.990.11 ([place name] Balbilla): ([etym.] γράφω):—A that which is drawn: pl., lines of a drawing, picture, etc., E. Ion 1146 (of tapestry), Theoc.15.81; picture,Ἀπέλλεω γ. Herod.4.73
, cf. AP 6.352 ([place name] Erinna): sg., drawing, picture, Pl.R. 472d, Cra. 430e, cf. 431c: pl., figures in a picture, Procop.Gaz.Ecphr.p.157B.II written character, letter, Hdt.1.139, 148, etc.: in pl., letters, characters,γραμμάτων τε συνθέσεις A.Pr. 460
;πηλίκοις γ. Ep.Gal.6.11
; the letters, the alphabet, Hdt.5.58;τὰ γ. καὶ τὰς συλλαβάς Pl.Cra. 390e
;γ. Φοινίκια S.Fr. 514
; Ἀσσύρια, Ἑλληνικά, Hdt.4.87;γράμματα ἐπίστασθαι Pl.Lg. 689d
; μαθεῖν to have learnt to read, Id.Prt. 325e;γ. μὴ εἰδέναι SIG2844.6
; ἐδίδασκες γράμματα, ἐγὼ δ' ἐφοίτων you kept school—I went there, D.18.265;ἤτοι τέθνηκεν ἢ διδάσκει γ. Com.Adesp.20
;παιδεύειν γράμματα Arist.Pol. 1337b24
; τέχνη ἡμῶν γ. our profession is that of the scribe, PTeb.316.16 (i A. D.).b articulate sound, letter, Pl.Phlb. 18c;τὰ γ. πάθη ἐστὶ τῆς φωνῆς Arist.Pr. 895a12
; γράμματα φθέγγεσθαι ib.8, cf. PA 660a5.c παρὰ γράμμα λέγοντα.. σκοπεῖν etymologically, Id.MM 1185b39; τὰ παρὰ γ. σκώμματα puns, Id.Rh. 1412a28; but ἀρετὴν παρὰ γ. διώκοντες, with ref. to Νικαρέτη, the mistress of Stilpo, Crates Theb.1.d inscription,τὸ Δελφικὸν γ. Pl.Phdr. 229e
, cf. Chrm. 164d, X.Mem.4.2.24, etc., IG 2.2876, al.: prov.,εἰς πέλαγος.. γράμματα γράψαι Epigr.Gr.1038.8
([place name] Attalia).2 in pl., notes in music, AP11.78 (Lucill.).3 mathematical diagram, Epigr. ap. D.L.8.12.4 letter inscribed on the lots which the δικασταί drew, Ar.Pl. 277, al., Arist.Ath.64.4; practically, = division of dicasts,ἐν ὁποίῳ γ. δειπνεῖ Ar.Ec. 683
; ἁ κατὰ γράμμα φυλακά the roster of guards, SIG569.21 (Cos, iii B. C.).5 a small weight, 1/24 ounce, scruple, Androm. ap. Gal.13.114, Gp.7.13.2, PLips. 62 ii 27 (iv A. D.).III in pl., set of written characters, piece of writing, Hdt.1.124: hence, letter, Id.5.14, IG22.103.8, etc.;γραμμάτων πτυχαί S.Fr. 144
, cf. E.IT 594, al., Pl.Ep. 347c; inscription, epitaph, etc.,ἐκόλαψε ἐς τὸν τάφον γράμματα λέγοντα τάδε Hdt. 1.187
, cf. 4.91, And.3.12, Theoc.18.47, IG3.751.2 papers, documents, Antipho 1.30, D.36.21, etc. (sg., D.Chr.65.14); τούτων τὰ γ. the documents to prove this, Lys.32.14;τὰ γ. τῆς δίκης Ar.Nu. 772
; τὰ δημόσια γ. the public records, Decr. ap. D.18.55; title-deeds, D.C.65.14; account of loans, D.49.59; ; contract or estimate, BCH46.323 ([place name] Teos); catalogue, X.Cyr.7.4.12: in sg., bond, Ev. Luc.16.7; note of hand, J.AJ18.6.3.3 a man's writings, i.e. book, treatise,τὰ τοῦ Ζήνωνος γ. Pl.Prm. 127c
(but sg., ib. 128a): pl., books, X.Mem.4.2.1;Πλάτωνος τὸ περὶ ψυχῆς γ. Call.Epigr.25
, cf. AP9.63 (Asclep.), Gal.18(2).928; τὰ ἱερὰ γ. the Holy Scriptures, OGI56.36 (iii B. C.), Ph.2.574, 2 Ep.Ti.3.15, J.Ap.1.10; ἱερὰ γ., = Imperial rescripts, IG12(5).132 (Paros, iii A. D.); = hieroglyphics, OGI90.54 (Rosetta, ii B. C.): in sg., the Law of Moses, Ep.Rom.2.27, al.; opp. πνεῦμα, ib.29: sg., article of a treaty, Th. 5.29.4 laws or rules, Pl.R. 425b, Plt. 292a, al., Ar.Ec. 1050; κατὰ γράμματα ἄρχειν, opp. ἄνευ γραμμάτων, Pl.Plt. 293a;ἡ κατὰ γ. καὶ νόμους πολιτεία Arist.Pol. 1286a15
, cf. 1272a38: οἱ κατὰ γ. νόμοι, opp. οἱ κατὰ τὰ ἔθη, ib. 1287b5, cf. Pl.Plt. 299d;κατὰ γράμματα ἰατρεύεσθαι Arist.Pol. 1287a34
; ἡ ἐκ τῶν γ. θεραπεία ib.40.IV in pl., also, letters, learning,ἀπείρους γραμμάτων Pl.Ap. 26d
, etc. -
9 ἁρμονικός
II musical: theory of music,Pl.
Phdr. 268e, Arist.Metaph. 1077a5; ἡ ἐν τοῖς μαθήμασιν -κή (sc. ἐπιστήμη ) mathematical theory of music, ib. 997b21; ἁ. πραγματεία a treatise thereon, Plu.2.1142f; ἁρμονικὰ στοιχεῖα, title of work by Aristoxenus; ἁρμονικοί, οἱ, students of-κή, οἱ κατὰ τοὺς ἀριθμοὺς ἁ. Arist.Top. 107a16
; with play on (b), Aristox. Harm.p.I M.c ἁ. κίνησις, of the pulse, in harmony with physical state, Gal.19.376.III Arith., harmonic,μέσα Archyt.2
;ἁ. ἀναλογία Ph.1.27
, Nicom.Ar.2.22, Theo Sm.p.114H.;μεσότης Arist.Fr.47
;λόγοι Ph.1.22
([comp] Sup.);λόγοι κατ' ἀριθμὼς ἁ. συγκεκραμένοι Ti.Locr. 96a
, cf. Arist.de An. 406b29.IV ἁ. γυμνάσιον training by rule of thumb, Philostr.Gym.53.V metaph., capable of harmonizing,τακτικοὶ καὶ ἁ. Plu.2.618c
; of God, ib.946f.VI Adv. - κῶς ib.1138e, Iamb.Comm.Math.32.Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > ἁρμονικός
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10 Rondelet, Jean-Baptiste
[br]b. 1734 Lyons, France d. 1829[br]French architect particularly interested in the scientific and mathematical basis of architectural structure, and who at an early date introduced reinforced concrete into supporting piers in his buildings.[br]From 1795 Rondelet was Professor at the Ecole Centrale des Travaux Publics and while there was responsible for a major treatise on building construction: this was his Traité théorique et pratique de l'art de bâtir, published in four volumes in 1802–17. From 1806 he taught at the Ecole Spéciale d'Architecture, which was soon afterwards merged with the Ecole Polytechnique. It was when Rondelet took over the work of com-pleting the Panthéon in Paris, after the death of Jacques-Germain Soufflot, that he had the opportunity of putting some of his particular structural ideas into practice. In 1755 the King had appointed Soufflot architect of the great new church to be dedicated to the patron saint of the city, Sainte Geneviève. In this neo-classical structure based upon Greek cross plan, Soufflot intended four slender piers, each encased in three engaged columns, to support the pendentives for the dome to rise over the crossing. It was a fine and elegant building on a large scale, but by the early nineteenth century, when the church had become a pantheon, cracks were appearing in the masonry. When Rondelet succeeded as architect after Soufflot's death, he strengthened and enlarged the piers, employing a faced concrete structure reinforced with metal. He used a metalreinforced mortar with rubble aggregate.[br]BibliographyAn article by Rondelet appears in: 1989, Le Panthéon: Symbole des Révolutions, pp. 308–10 (book of the Exhibition at the Hôtel de Sully, Paris), ed. Picard, Caisse Nationale des Monuments Historiques et des Sites en France.Further ReadingM.N.Mathuset-Bandouin, 1980, "Biographie de Jean Rondelet", Soufflot et son temps, Caisse Nationale des Monuments Historiques et des Sites en France, 155ö7.DYBiographical history of technology > Rondelet, Jean-Baptiste
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11 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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