A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 18
... successively equal to zero : thus , if we suppose b = 0 and d = 0 , the product ( 1 ) in question becomes 1st . ( a - 0 ) ( c− 0 ) = a c − a × 0 - 0 × c + 0 x 0 , or a × b = ab , obliterating the terms which involve zero . If we ...
... successively equal to zero : thus , if we suppose b = 0 and d = 0 , the product ( 1 ) in question becomes 1st . ( a - 0 ) ( c− 0 ) = a c − a × 0 - 0 × c + 0 x 0 , or a × b = ab , obliterating the terms which involve zero . If we ...
Page 19
... successive term of the polynomial , and arrange the pro- Case 2 . ducts of the several terms in the result , preceded by their proper signs , in any order which may appear most symmetrical or most convenient . " " If the sign of the ...
... successive term of the polynomial , and arrange the pro- Case 2 . ducts of the several terms in the result , preceded by their proper signs , in any order which may appear most symmetrical or most convenient . " " If the sign of the ...
Page 20
... successively every term of one factor into every term of the other , add the several partial products together , and arrange the terms of the result in any order which may be considered most convenient , without regard to the sign of ...
... successively every term of one factor into every term of the other , add the several partial products together , and arrange the terms of the result in any order which may be considered most convenient , without regard to the sign of ...
Page 22
... successively by the rule in Case 1 ( Art . 578 ) , every term of the dividend by the divisor , and the several results connected with their proper signs form the quotient . ” ( Art . 81 ) . 580. The following are examples : ( 1 ) Divide ...
... successively by the rule in Case 1 ( Art . 578 ) , every term of the dividend by the divisor , and the several results connected with their proper signs form the quotient . ” ( Art . 81 ) . 580. The following are examples : ( 1 ) Divide ...
Page 24
... successive remainders are mononomials and the successive subtrahends are binomials : it follows there- fore , that the remainders can never disappear , however far the operation is continued , and the series which forms the quotient is ...
... successive remainders are mononomials and the successive subtrahends are binomials : it follows there- fore , that the remainders can never disappear , however far the operation is continued , and the series which forms the quotient is ...
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.