A Brief History of Mathematics: An Authorized Translation of Dr. Karl Fink's Geschichte Der Elementar-mathematik

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Open Court Publishing Company, 1900 - Mathematics - 333 pages

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Page 121 - If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions.
Page 280 - But mathematics have never been cultivated more zealously and diligently, or with greater success, than in this century— in the last half of it or at the present time ; the advances made have been enormous, the actual field is boundless, the future full of hope. In regard to pure mathematics we may most confidently say : " Yet I doubt not through the ages one increasing purpose runs, And the thoughts of men are widened with the process of the suns.
Page 335 - Price, $i oo net (5s.). DE MORGAN, AUGUSTUS. ON THE STUDY AND DIFFICULTIES OF MATHEMATICS. New Reprint edition with notes. Pp. viii+288. Cloth, $1.25 net (5s.).
Page 157 - At the end of the seventeenth and the beginning of the eighteenth century...
Page 336 - Cloth, $1.25 (6s. 6d.). KARMA. A STORY OF EARLY BUDDHISM. Illustrated by Japanese artists.
Page 336 - Edition. Cloth, $1.oo (5s.). THE GOSPEL OF BUDDHA. According to Old Records.
Page 73 - The square of a positive number as also of a negative number is positive and the square root of a positive number is two-fold, positive and negative. There is no square root of a negative number, for this is not & square.
Page 270 - ... then the lines are not parallel, but meet on that side of the transversal on which the sum of the interior angles is less than a straight angle. For the lines cannot be parallel, by prop. XVII and cor. 2. Further, suppose Z c + Z b' < st. Z ; then •/ Z a' + Z &' = st. Z , it follows that Z c < Z a'. .•. P and P' cannot meet towards P', for then Z c would be greater than Z a', prop.
Page 229 - Among the predecessors of Descartes we reckon, besides Apollonius, especially Vieta, Oresme, Cavalieri, Roberval, and Fermat, the last the most distinguished in this field; but nowhere, even by. Fermat, had any attempt been made to refer several curves of different orders simultaneously to one system of coordinates, which at most possessed special significance for one of the curves. It is exactly this thing which Descartes systematically accomplished.
Page 223 - Geometry has two great treasures, one is the Theorem of Pythagoras, the other the division of a line into extreme and mean ratio; the first we may compare to a measure of gold, the second we may name a precious jewel.

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