Ancient notionsc.360 B.C. Eudoxus of Cnidus provides a ``method of exhaustion'',

07:27 Aug 30, 2005
English to Malay translations [Non-PRO]
Science - Mathematics & Statistics
English term or phrase: Ancient notionsc.360 B.C. Eudoxus of Cnidus provides a ``method of exhaustion'',
Ancient notionsc.

360 B.C. Eudoxus of Cnidus provides a ``method of exhaustion'', close to the limiting concept of calculus, which is used by himself and later Greeks to find areas and volumes of curvilinear figures; it was based on the lemma that any non-zero quantity can be made as large as one wishes by multiplying it by a large enough constant.

Pre-calculus


1615 Johannes Kepler uses infinitesimals to calculate volumes of revolution in New Measurement of the Volume of Wine Casks.
1635 Bonaventura Cavalieri calculates volumes using infinitely small sections.
1655 John Wallis studies infinite series in Arithmetic of Infinitesimals
1658 Blaise Pascal, working on the sine function, ``almost'' discovers calculus. Early calculus1665 Isaac Newton retires to the country to escape the Great Plague in London; there he invents the first form of calculus.
1668 James Gregory includes a geometrical version of the fundamental theorem of calculus in Geometrical Exercises and the Universal Part of Geometry.
1669 Newton includes his method for finding areas under curves in his On the Analysis of Equations Unlimited in the Number of Their Terms, circulated privately.
1670 Isaac Barrow uses methods similar to calculus to draw tangents to curves, find the lengths of curves, and the areas bounded by curves.
1675 Gottfried Leibniz introduces the modern notation for integration and the notation dx/dy for differentiation; he also determines the product rule for differentiation.
1676 Newton writes two letters to Leibniz, hinting at his work with infinite series and fluxions (his form of calculus); also this year, Leibniz discovers how to differentiate any fractional power of x.
1677 Leibniz finds the quotient rule for differentiation. Big-time calculus1684 Leibniz publishes ``A new method for maxima and minima as well as tangents, which is impeded neither by fractional nor by irrational quantities, and a remarkable type of calculus for this''; although only six pages long, few can understand it. 1686 Leibniz publishes his method of integral calculus in an issue of Acta Eruditorum. 1691 Michel Rolle states without proof the theorem named after him. 1693 John Wallis publishes Newton's method of fluxions in volume two of his Mathematical Works. 1694 Jean Bernoulli discovers the method known as l'Hospital's Rule; it is known by that name because Marquis Antoine de l'Hospital bought it from Bernoulli and introduced it in his influential 1696 textbook Analysis of Infinitesimals. 1715 Brook Taylor introduces his famous series in Methodus Incrementorum Directa et Inversa, in which he develops the calculus of finite differences. Later calculus1797 Joseph-Louis Lagrange introduces the notations f'x and y' for the derivatives of f(x) and y, respectively. 1800 Louis F. A. Arbogast introduces the symbol D for the operation of differentiation. 1841 Carl Gustav Jacob Jacobi adopts the modern notation for partial differentiation; Adrien-Marie Legendre originally introduced it in 1786, but immediately abandoned it. 1854 Bernhard Riemann defines the integral in a way that does not require continuity. 1872 H. Eduard Heine, a student of Karl Weierstrass, presents the modern ``epsilon-delta'' definition of a limit in his Elements. Other interesting stuff2000 B.C. to 200 B.C.c.1975 B.C. Mesopotamian mathematicians discover how to solve quadratic equations. c.1850 B.C. Mesopotamian mathematicians discover the so-called Pythagorean theorem approximately 12 centuries before the time of Pythagoras. 876 B.C. The first known use of a symbol for zero appears in India. c.465 B.C. The Pythagorean Hippasus of Metapontum discovers the dodecahedron, a regular solid whose 12 faces are regular pentagons. There are only 4 other regular solids: the tetrahedron (4 equilateral triangles), the cube (6 squares), the octahedron (8 equilateral triangles), and the icosahedron (20 equilateral triangles). c.450 B.C. ``Achilles'' paradox of Zeno. c.350 B.C. Menaechmus discovers the conic sections: the parabola, ellipse, and hyperbola. c.300 B.C. The thirteen books of Euclid's Elements (the most widely read textbook ever written) contains propositions on plane geometry, the distributive, commutative, and associative laws of arithmetic, quadratic equations, prime numbers (including the theorem that the set of primes is infinite), perfect numbers, greatest common divisors, geometric series, irrational numbers, and solid geometry, including the five regular solids. Unlike the modern treatment of these ideas, the Greeks used an entirely geometrical approach in mathematics, using line segments to represent all magnitudes (numbers). Although the Elements compiles already-known Greek mathematics, some of the proofs are probably Euclid's own. See my Euclid paperfor more information. c.250 B.C. Archimedes of Syracuse and the quadrature of the parabola. 1500 A.D. to present1575 The first known proof by mathematical induction is included in Francesco Maurolico's Arithmeticorum Libri Duo; he proves that the sum of the first n odd integers is n^2. 1635 Rene Descartes discovers that any simple convex polyhedron having V vertices, E edges, and F faces obeys the rule V - E + F = 2; since his discovery is not published until 1860, the theorem is named after Leonhard Euler, who rediscovered it in 1752. 1679 Gottfried Leibniz introduces binary arithmetic in a letter written to Joachim Bouvet, showing that any number may be expressed by 0's and 1's only. 1781 Joseph-Louis Lagrange expresses in a letter to his mentor Jean le Rond d'Alembert his fear that no further progress can be made in mathematics; despite this dire prophesy, many of his own contributions are still to come. 1843 While strolling along the Royal Canal, Sir William Rowan Hamilton devises a mathematical system which is not commutative; he develops his idea into a system of ``quaternions'', similar to that of three-dimensional vectors. His ideas help to usher in modern abstract algebra. 1844 Hermann Gunther-Grassman publishes The Study of Extensions, which deals with multidimensional vectors; he almost single-handedly creates modern linear algebra. 1865 August Ferdinand Mobius unveils his single-sided, single-edged figure, the Mobius strip. 1877 Georg Cantor proves that the number of points on a line segment is the same as the number of points in the interior of a square, publication of the result is delayed for a year because mathematicians refuse to believe it. 1890 Giuseppe Peano discovers a one-dimensional, continuous curve that passes through all the points in the interior of a square. 1902 Bertrand Russell discovers his ``great paradox''. 1908 The final edition of Giuseppe Peano's Mathematical Formulas contains about 4,200 theorems. 1976 Haken, Appel, and Koch prove with the use of a computer that only four colors are required to color in any two-dimensional map in such a way that no two adjacent regions share the same color; this was conjectured in 1850 by Francis Guthrie. Sources CRC Standard Mathematical Tables, 26th edition - William H. Beyer, ed. (CRC Press, 1981) The Historical Development of the Calculus - C. H. Edwards, Jr. (Springer-Verlag, 1979) A History of Mathematical Notations/Volume II: Notations Mainly in Higher Mathematics - Florian Cajori (Open Court Publishing, 1952) A History of Mathematics, second edition - Carl B. Boyer and Uta C. Merzbach (John Wiley & Sons, 1989) The History of the Calculus and Its Conceptual Development - Carl D. Boyer (Dover Publications, 1959) The Timetables of Science: A Chronology of the Most Important People and Events in the History of Science - Alexander Hellemans and Bryan Bunch (Simon & Schuster, 1991)
muhammad albukhari


Summary of answers provided
4Tanggapan-tanggapan purba sekitar 360 S.M.: Euxodus daripada Cnidus memberikan “kaedah exhaustion”
kualalumpur
3Konsep kuno kira-kira dalam tahun 360 S.M. Eudoxus dari Cnidus memberi "kaedah habis-habisan"
malaybuddy


  

Answers


1 day 7 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
ancient notionsc.360 b.c. eudoxus of cnidus provides a ``method of exhaustion'',
Konsep kuno kira-kira dalam tahun 360 S.M. Eudoxus dari Cnidus memberi "kaedah habis-habisan"


Explanation:
ancient = "kuno; purba". notions = "tanggapan". c. = circa = "kira-kira dalam tahun; lebih kurang dalam tahun". 360 = "360". B.C. = before christ = "sebelum Christ = sebelum masihi = S.M." provides = "membekal; menyediakan". method of exhaustion = "kaedah habis-habisan".

malaybuddy
Local time: 17:29
Native speaker of: Malay
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1 day 19 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
ancient notionsc.360 b.c. eudoxus of cnidus provides a ``method of exhaustion'',
Tanggapan-tanggapan purba sekitar 360 S.M.: Euxodus daripada Cnidus memberikan “kaedah exhaustion”


Explanation:
I think the sentence should read “Ancient notions c.360B.C” as opposed to “Ancient notionsc 360B.C”

Ancient = Purba or Kuno (I would opt for the former though because ‘ancient’ relates to a time early in history and ‘purba’ effectively conveys this, whereas ‘kuno’ could refer to something existing even a decade back, as long as it is outdated and old-fashioned)

Notions = Tanggapan-tanggapan (‘Notion’ in the singular form would be ‘Tanggapan”)

c.360B.C = around 360 B.C (here, ‘c’ is an abbreviation for the latin word ‘circa’ which means ‘around’ or ‘approximately’. B’C = “before Christ” and the accepted Malay translation is S.M (sebelum Masehi). Therefore “c.360 B.C” would be “sekitar 360 S.M”

Now the term “Method of Exhaustion” refers to an ancient Greek method of calculation and the term was coined years ago. As it is now a recognised term amongst Mathematicians the world over, I would not translate the word ‘Exhaustion’ and would only use the Malay translation if there is an official Malay translation for the phrase, and I know of none though I stand corrected. I therefore suggest “Kaedah Exhaustion”.


kualalumpur
Native speaker of: Native in EnglishEnglish, Native in MalayMalay
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