A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα vii
... the fundamental operations of Symbolical Algebra to expressions involving the sign √ - 1 . CHAPTER XIX . 67 74 On the general theory and solution of quadratic equations . 77 CHAPTER XX . On the solution of equations of higher.
... the fundamental operations of Symbolical Algebra to expressions involving the sign √ - 1 . CHAPTER XIX . 67 74 On the general theory and solution of quadratic equations . 77 CHAPTER XX . On the solution of equations of higher.
Σελίδα viii
... quadratic factors . CHAPTER XXI . The binomial theorem and its applications CHAPTER XXIII . On the use of the square and higher roots of 1 as signs of affec- tion .... CHAPTER XXIV . PAGE 96 110 120 On the symbolical properties of ...
... quadratic factors . CHAPTER XXI . The binomial theorem and its applications CHAPTER XXIII . On the use of the square and higher roots of 1 as signs of affec- tion .... CHAPTER XXIV . PAGE 96 110 120 On the symbolical properties of ...
Σελίδα 77
... quadratic or expression q , is equivalent to the solution of the binomial equations . quadratic equation ( Arts . 246 and 377 ) x2 = q , or x2 - q = 0 . For the value of x , determined from this equation is q or the square root of 9 ...
... quadratic or expression q , is equivalent to the solution of the binomial equations . quadratic equation ( Arts . 246 and 377 ) x2 = q , or x2 - q = 0 . For the value of x , determined from this equation is q or the square root of 9 ...
Σελίδα 78
... quadratic equations . x2 + px + q = 0 The three first of these equations have been considered in Art . 384 : the last belongs exclusively to Symbolical Algebra . It is obvious that these four equations are convertible with each other ...
... quadratic equations . x2 + px + q = 0 The three first of these equations have been considered in Art . 384 : the last belongs exclusively to Symbolical Algebra . It is obvious that these four equations are convertible with each other ...
Σελίδα 82
... quadratic tion of qua- equations , and of problems which lead to them , may be con- dratic sidered as supplementary to those which are given in Arts . 389 , and 410 , and 412t . equations . It may be otherwise shewn , that , if a be a ...
... quadratic tion of qua- equations , and of problems which lead to them , may be con- dratic sidered as supplementary to those which are given in Arts . 389 , and 410 , and 412t . equations . It may be otherwise shewn , that , if a be a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ angle of transfer application arith Arithmetical Algebra assumed becomes biquadratic equation Chapter coefficients common divisor considered corresponding cos² cosecant cotangent cube roots cubic equation denote determined divergent series divisor equa equal equisinal equivalent forms examples expression factors figure follows formula fraction geometrical angle given in Art goniometrical angle greater identical inasmuch indeterminate infinity involve last Article less likewise logarithms magnitude and position metical multiple negative nth roots operations period primitive equation primitive line problem proposition quadratic quotient radius ratio replace represent right angles shewn sides similar manner sin² sine and cosine solution square root subtraction successive Symbolical Algebra tangent tion triangle unknown quantities values whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 88 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 235 - The logarithm of a product is the sum of the logarithms of its factors.
Σελίδα 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Σελίδα 455 - Inquiry into the Validity of a Method recently proposed by George B. Jerrard, Esq., for Transforming and Resolving Equations of Elevated Degrees: undertaken at the request of the Association by Professor Sir WR Hamilton.
Σελίδα 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Σελίδα 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Σελίδα 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Σελίδα 395 - ... and it is in this sense, and in this sense only, that...
Σελίδα 262 - Fink not only discovered the law of tangents, but pointed out its principal application; namely, to aid in solving a triangle when two sides and the included angle are given.