Timeline of scientific discoveries (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Timeline of scientific discoveries" in English language version.

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  • Bhishagratna, Kaviraj KL (1907). An English Translation of the Sushruta Samhita in Three Volumes. Calcutta. Archived from the original on 4 November 2008. Alt URL
  • Dicks, D.R. (1970). Early Greek Astronomy to Aristotle. Ithaca, N.Y.: Cornell University Press. pp. 68. ISBN 978-0-8014-0561-7.
  • E. At. Schwanbeck (1877). Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian. p. 101.
  • Knopp, Konrad (1951). Theory and Application of Infinite Series (English 2nd ed.). London and Glasgow: Blackie & Son, Ltd. p. 7. ISBN 0-486-66165-2.
  • Boyer 1991, "The Age of Plato and Aristotle" p. 93. "It was consequently a signal achievement on the part of Menaechmus when he disclosed that curves having the desired property were near at hand. In fact, there was a family of appropriate curves obtained from a single source – the cutting of a right circular cone by a plane perpendicular to an element of the cone. That is, Menaechmus is reputed to have discovered the curves that were later known as the ellipse, the parabola, and the hyperbola. [...] Yet the first discovery of the ellipse seems to have been made by Menaechmus as a mere by-product in a search in which it was the parabola and hyperbola that proffered the properties needed in the solution of the Delian problem." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Boyer 1991, "The Age of Plato and Aristotle" pp. 94–95. "Menaechmus apparently derived these properties of the conic sections and others as well. Since this material has a strong resemblance to the use of coordinates, as illustrated above, it has sometimes been maintained that Menaechmus had analytic geometry. Such a judgment is warranted only in part, for certainly Menaechmus was unaware that any equation in two unknown quantities determines a curve. In fact, the general concept of an equation in unknown quantities was alien to Greek thought. It was shortcomings in algebraic notations that, more than anything else, operated against the Greek achievement of a full-fledged coordinate geometry." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925] ed.). New York: Dover Publications.
  • Boyer 1991, "Greek Trigonometry and Mensuration" pp. 158–159. "Trigonometry, like other branches of mathematics, was not the work of any one man, or nation. Theorems on ratios of the sides of similar triangles had been known to, and used by, the ancient Egyptians and Babylonians. In view of the pre-Hellenic lack of the concept of angle measure, such a study might better be called "trilaterometry", or the measure of three sided polygons (trilaterals), than "trigonometry", the measure of parts of a triangle. With the Greeks we first find a systematic study of relationships between angles (or arcs) in a circle and the lengths of chords subtending these. Properties of chords, as measures of central and inscribed angles in circles, were familiar to the Greeks of Hippocrates' day, and it is likely that Eudoxus had used ratios and angle measures in determining the size of the earth and the relative distances of the sun and the moon. In the works of Euclid there is no trigonometry in the strict sense of the word, but there are theorems equivalent to specific trigonometric laws or formulas. Propositions II.12 and 13 of the Elements, for example, are the laws of cosines for obtuse and acute angles respectively, stated in geometric rather than trigonometric language and proved by a method similar to that used by Euclid in connection with the Pythagorean theorem. Theorems on the lengths of chords are essentially applications of the modern law of sines. We have seen that Archimedes' theorem on the broken chord can readily be translated into trigonometric language analogous to formulas for sines of sums and differences of angles." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Hoche, Richard, ed. (1866), Nicomachi Geraseni Pythagorei Introductionis arithmeticae libri II, Leipzig: B.G. Teubner, p. 31
  • Archimedes (1912), The method of Archimedes recently discovered by Heiberg; a supplement to the Works of Archimedes, Cambridge University Press
  • Boyer 1991, "Archimedes of Syracuse" p. 127. "Greek mathematics sometimes has been described as essentially static, with little regard for the notion of variability; but Archimedes, in his study of the spiral, seems to have found the tangent to a curve through kinematic considerations akin to differential calculus. Thinking of a point on the spiral 1=r = as subjected to a double motion — a uniform radial motion away from the origin of coordinates and a circular motion about the origin — he seems to have found (through the parallelogram of velocities) the direction of motion (hence of the tangent to the curve) by noting the resultant of the two component motions. This appears to be the first instance in which a tangent was found to a curve other than a circle.
    Archimedes' study of the spiral, a curve that he ascribed to his friend Conon of Alexandria, was part of the Greek search for the solution of the three famous problems." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Boyer 1991, "Greek Trigonometry and Mensuration" p. 163. "In Book I of this treatise Menelaus establishes a basis for spherical triangles analogous to that of Euclid I for plane triangles. Included is a theorem without Euclidean analogue – that two spherical triangles are congruent if corresponding angles are equal (Menelaus did not distinguish between congruent and symmetric spherical triangles); and the theorem A + B + C > 180° is established. The second book of the Sphaerica describes the application of spherical geometry to astronomical phenomena and is of little mathematical interest. Book III, the last, contains the well known "theorem of Menelaus" as part of what is essentially spherical trigonometry in the typical Greek form – a geometry or trigonometry of chords in a circle. In the circle in Fig. 10.4 we should write that chord AB is twice the sine of half the central angle AOB (multiplied by the radius of the circle). Menelaus and his Greek successors instead referred to AB simply as the chord corresponding to the arc AB. If BOB' is a diameter of the circle, then chord A' is twice the cosine of half the angle AOB (multiplied by the radius of the circle)." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Luke Hodgkin (2005). A History of Mathematics: From Mesopotamia to Modernity. Oxford University Press. p. 88. ISBN 978-0-19-152383-0. Liu is explicit on this; at the point where the Nine Chapters give a detailed and helpful 'Sign Rule'
  • Boyer 1991, p. [page needed]. Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Boyer 1991, "The Mathematics of the Hindus" p. 207. "He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes." Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  • Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)
  • Joseph, G. G. (2000), The Crest of the Peacock: The Non-European Roots of Mathematics, Princeton, NJ: Princeton University Press, 416 pages, ISBN 978-0-691-00659-8
  • Katz, Victor J. (1998). A History of Mathematics: An Introduction (2nd ed.). Addison Wesley. p. 255. ISBN 978-0-321-01618-8.
  • Bruno, Leonard C (2003) [1999]. Math and mathematicians: the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 60. ISBN 0787638137. OCLC 41497065.
  • Jourdain, Philip E. B. (1913). The Nature of Mathematics.
  • Robert Recorde, The Whetstone of Witte (London, England: John Kyngstone, 1557), p. 236 (although the pages of this book are not numbered). From the chapter titled "The rule of equation, commonly called Algebers Rule" (p. 236): "Howbeit, for easie alteration of equations. I will propounde a fewe examples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in worke use, a paire of paralleles, or Gemowe [twin, from gemew, from the French gemeau (twin / twins), from the Latin gemellus (little twin)] lines of one lengthe, thus: = , bicause noe .2. thynges, can be moare equalle." (However, for easy manipulation of equations, I will present a few examples in order that the extraction of roots may be more readily done. And to avoid the tedious repetition of these words "is equal to", I will substitute, as I often do when working, a pair of parallels or twin lines of the same length, thus: = , because no two things can be more equal.)

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  • Kurt Vogel, "Diophantus of Alexandria." in Complete Dictionary of Scientific Biography, Encyclopedia.com, 2008. Quote: The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation... Since an abbreviation is also employed for the word ‘equals’, Diophantus took a fundamental step from verbal algebra towards symbolic algebra.

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  • Cajori, Florian (1928). A History of Elementary Mathematics. Vol. 5. The Open Court Company, Publishers. pp. 516–7. doi:10.1126/science.5.117.516. ISBN 978-1-60206-991-6. PMID 17758371. S2CID 36235120. It will be remembered that the scratch method did not spring into existence in the form taught by the writers of the sixteenth century. On the contrary, it is simply the graphical representation of the method employed by the Hindus, who calculated with a coarse pencil on a small dust-covered tablet. The erasing of a figure by the Hindus is here represented by the scratching of a figure. {{cite book}}: |journal= ignored (help)

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