Tracts on the Resolution of Affected Algebräick Equations by Dr. Halley's, Mr. Raphson's, and Sir Isaac Newton's, Methods of Approximation (Google eBook)

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J.Davis and sold by J. White, 1800 - Equations - 479 pages
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Page 351 - Clairaut, in that Part of his Elements of Algebra in which he endeavours to prove the Rules of Multiplication laid down by Writers on Algebra concerning Negative Quantities.
Page 247 - equation has as many roots as there are units in the index of the higheft power of the
Page 294 - Roots of any Equations Generally., and that without any
Page 359 - equation has as many roots as there are units in the index of the
Page 287 - OBSERVATIONS ON MR. RAPHSON's METHOD OF RESOLVING AFFECTED EQUATIONS OF ALL DEGREES
Page 3 - yet, do the bufinefs: for it does at leaft Quintuple the given Figures in the Root; neither is ■ the Calculus very large or
Page 26 - by one Multiplication and two Divifions, which otherwife would require three Multiplications and one Divifion. Let us take now one Example of this Method, from the Root (of the
Page 20 - of a, the Sign of se (and confequently of the prevailing Parts in the compofition of it) will always be contrary to the Sign of the difference b. Whence
Page 309 - 155.*.? = 10,000. But that this may appear the more clearly, I will now repeat the foregoing refolution of this equation in the ftyle and manner of Mr. Raphfon, by omitting the feveral reafonings fet forth in the foregoing articles, and making ufe of a Canon, or Theorem, for the purpofe of computing the
Page 357 - Root of an Equation that has more than One real and affirmative Root. [Reprinted from the Third Volume of the

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