A Treatise on Algebra, Volume II: On Symbolical Algebra, and Its Applications to the Geometry of Position

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This second book of a two-volume set investigates the basic properties of numbers that underlie the subject of algebra and demonstrates their applications to geometry. Topics include equivalent forms; square roots; quadratic equations; binomial theory; sines, cosines, tangents, cotangents, secants, cosecants and versed sines of angles; logarithms; trigonometry; binomial equations; and more. 1940 edition.
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Dover Publications, 2005. 455 pp. Hardcover. Part 2 of series. Fine. Bright, tight and clean; no names, marks or wear to boards. ISBN: 0486439216.

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2004 Hardcover Good Connecting readers with great books since 1972. Used books may not include companion materials, some shelf wear, may contain highlighting/notes, and may not ... include cd-rom or access codes. Customer service is our top priority! Read more Show Less

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2004. Hardcover As new, clean, tight & bright condition without dust jacket 455pp.

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Overview


This second book of a two-volume set investigates the basic properties of numbers that underlie the subject of algebra and demonstrates their applications to geometry. Topics include equivalent forms; square roots; quadratic equations; binomial theory; sines, cosines, tangents, cotangents, secants, cosecants and versed sines of angles; logarithms; trigonometry; binomial equations; and more. 1940 edition.
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Product Details

  • ISBN-13: 9780486439211
  • Publisher: Dover Publications
  • Publication date: 12/17/2004
  • Series: Phoenix Edition Series
  • Pages: 480
  • Product dimensions: 5.70 (w) x 8.50 (h) x 1.20 (d)

Table of Contents

Chapter XI On the operations of addition and subtraction in Symbolical Algebra 1
Chapter XII On the operations of multiplication and division in Symbolical Algebra 17
Chapter XIII On the determination of the highest common divisors, and the lowest common multiples of two or more algebraical expressions 36
Chapter XIV On the reduction of algebraical expressions to their most simple equivalent forms 52
Chapter XV Formal statement of the principle of the permanence of equivalent forms 59
Chapter XVI The theory of indices 61
Chapter XVII On the extraction of square roots in Symbolical Algebra: origin of ambiguous roots and of the sign [radical -1] 67
Chapter XVIII Applications of the fundamental operations of Symbolical Algebra to expressions involving the sign [radical -1] 74
Chapter XIX On the general theory and solution of quadratic equations 77
Chapter XX On the solution of equations of higher orders than the second, which are resolvible into simple or quadratic factors 96
Chapter XXI The binomial theorem and its applications 110
Chapter XXIII On the use of the square and higher roots of 1 as signs of affection 120
Chapter XXIV On the symbolical properties of different orders of the root of 1 123
Chapter XXV On the general principles of the interpretation of the signs of affection which are symbolized by the roots of 1 135
Chapter XXVI On the representation and measures of angles 144
Chapter XXVII On the theory of the sines and cosines of angles 156
Chapter XXVIII On the tangents, cotangents, secants, cosecants and versed sines of angles 181
Chapter XXIX On the construction of a canon of sines and cosines, tangents and cotangents, secants and cosecants 188
Chapter XXX On Demoivre's formula and the expression, by means of it, of the roots of 1 and of a [plus or minus] b [radical -1] 194
Chapter XXXI On the representation of straight lines both in position and magnitude, and the application of Algebra to the theory of rectilinear figures 207
Chapter XXXII On logarithms, and logarithmic tables and their use 234
Chapter XXXIII On the determination of the sides and angles of triangles, or trigonometry, properly so called 246
Chapter XXXIV On the use and application of subsidiary angles 260
Chapter XXXV On exponential and logarithmic series 268
Chapter XXXVI On the limits of the values of series proceeding according to ascending or descending powers of a symbol, which is capable of indefinite diminution or increase 278
Chapter XXXVII On the series and exponential expressions for the sine and cosine of an angle 284
Chapter XXXVIII On the relations of zero and infinity 294
Chapter XXXIX On the decomposition of rational fractions with compound denominators into partial fractions 308
Chapter XL On the assumption and determination of series 316
Chapter XLI On the solution and theory of cubic equations 326
Chapter XLII On the solution and theory of biquadratic equations 346
Chapter XLIII On the solution and reduction of recurring equations 361
Chapter XLIV On the solution of simultaneous equations, and the theory of elimination 366
Chapter XLV On the algebraical solution of binomial equations 391
Chapter XLVI Sources of ambiguity 420
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