A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
From inside the book
Results 1-5 of 41
Page ix
... limits of the values of series proceeding according to ascending or descending powers of a symbol , which is capable of indefinite diminution or increase CHAPTER XXXVII . ........ On the series and exponential expressions for the sine ...
... limits of the values of series proceeding according to ascending or descending powers of a symbol , which is capable of indefinite diminution or increase CHAPTER XXXVII . ........ On the series and exponential expressions for the sine ...
Page 9
... limits , possess precisely the same meaning : it is only when the results of these rules are not common to Arithmetical Algebra , that it will be found necessary to resort to an interpretation of their meaning , upon principles which we ...
... limits , possess precisely the same meaning : it is only when the results of these rules are not common to Arithmetical Algebra , that it will be found necessary to resort to an interpretation of their meaning , upon principles which we ...
Page 11
... limits of Arithmetical Algebra : but if we suppose the traveller to return farther northwards than he went , in the first instance , south- wards , or AB to be less than BC , then his distance C B AC to the north of the point of ...
... limits of Arithmetical Algebra : but if we suppose the traveller to return farther northwards than he went , in the first instance , south- wards , or AB to be less than BC , then his distance C B AC to the north of the point of ...
Page 37
... limit to the number of such divisors , inasmuch as every as factors . algebraical expression can be divided by any mononomial , with- out producing an indefinite quotient . Thus , we may divide a2 - ax x and 1 + and a2 + ax severally by 37.
... limit to the number of such divisors , inasmuch as every as factors . algebraical expression can be divided by any mononomial , with- out producing an indefinite quotient . Thus , we may divide a2 - ax x and 1 + and a2 + ax severally by 37.
Page 45
... limits of the real roots of numerical equations : the process , however , becomes extremely laborious , even for equations of the 4th or 5th degrees , in consequence of the rapidity with which the numerical coefficients increase . Other ...
... limits of the real roots of numerical equations : the process , however , becomes extremely laborious , even for equations of the 4th or 5th degrees , in consequence of the rapidity with which the numerical coefficients increase . Other ...
Common terms and phrases
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
Popular passages
Page 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.
Page 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 235 - The logarithm of a product is the sum of the logarithms of its factors.
Page 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 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.
Page 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Page 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Page 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Page 395 - ... and it is in this sense, and in this sense only, that...
Page 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.