A history of elementary mathematics

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Macmillan, 1896 - Mathematics - 304 pages

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Page 130 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 68 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 71 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Page 284 - The Connexion of Number and Magnitude; An attempt to explain the fifth book of Euclid.
Page 160 - Napier lord of Markinston, hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it please God ; for I never saw a book which pleased me better, and made me more wonder.
Page 229 - He spoke of imaginary quantities, and inferred by induction that every equation has as many roots as there are units in the number expressing its degree.
Page 100 - These problems are proposed simply for pleasure; the wise man can invent a thousand others, or he can solve the problems of others by the rules given here. As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.
Page 134 - The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three dimensions.
Page 236 - The neglect which he had shown of the elementary truths of geometry he afterwards regarded as a mistake in his mathematical studies ; and on a future occasion he expressed to Dr. Pemberton his regret that " he had applied himself to the works of Descartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserved."3 The study of Descartes...
Page 101 - the second value is in this case not to be taken, for it is inadequate ; people do not approve of negative roots.

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