## Tracts on the Resolution of Affected Algebräick Equations by Dr. Halley's, Mr. Raphson's, and Sir Isaac Newton's, Methods of Approximation |

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absolute term affected equations affirmative roots alfo Algebra besore binomial co-efficient compound quantity 14,937 conjecture conse consequently cubick equation degree of exactness difference equa equation x equation x3 equations by approximation fifth root given number Halley Halley's method increase investigation Isaac Newton Lagny latter least root left-hand side less little greater magnitude method of approximation method of resolving nearly equal Newton's method nomial quantity number of figures obtained order to discover original equation places of figures proposed equation 14,937 quadratick equation quadrinomial quantity quan quently quotient Raphson's method real and affirmative resolution Scholium second near value shewn sifth sigures simple equation Sir Isaac Newton's sirst square substitution subtracting suppose supposition terms that involve Theresore third near value three numbers tion tity trinomial quantity true value unknown quantity value of x Vieta Wallis

### Popular passages

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