A Treatise on Infinitesimal Calculus, Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics; Differential Calculus. 1857.- V.2. Integral Calculus, Volume 1

A Treatise on Infinitesimal Calculus, Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics; Differential Calculus. 1857.- V.2. Integral Calculus, Volume 1

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1857 edition. Excerpt: ...putting x = a + r cos p, y = r sin f; whence r = 2a (1-cos f). (40) The curve is called the Cardioid, from its heart-like shape. y = o which equations express a straight line on the axis of x, of length 2 a, which is coincident with the diameter of the circle. Section 4.--On certain general properties of curves as expressed by algebraical equations of the nth degree. 207. In the following Chapter I shall enter on a formal inquiry into the properties of plane curves referred to rectangular coordinates, as exhibited by means of differentiation; but preliminary to that investigation it is necessary to explain certain general properties of a particular class of such curves, those, viz., which are expressed by algebraical equations; because these will receive further illustration hereafter; and it cannot be that such illustration will be adequately compreliended, unless the finite and more elementary properties which are illustrated are first known. The matter of the present section is collected from various sources; chiefly from the works of Cramer and Plucker, the Journals of Liouville and Crelle, the Nouvelles Annales de Mathematiques of Terquem and Gerono, and the Cambridge and Dublin Mathematical Journal. This last Journal contains many papers on the subject by Professor Boole, Mr. Cayley, and the Rev. George Salmon. I must however add that the following is only a sketch of the most elementary parts of a subject which contains matter of the deepest reflection; and which is daily receiving large additions from the most eminent mathematicians of the present age. But it will be sufficient for the object of this work. An algebraical equation of the nth degree in terms of two variables x and y contains a constant term, and all possible combinations of...show more

Product details

  • Paperback | 136 pages
  • 189 x 246 x 7mm | 254g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236649877
  • 9781236649874