A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
From inside the book
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Page 3
... use of the sign throughout , instead of the sign + . - ( 5 ) За -5a + 7a ( 6 ) -- 3x2 I2 - 7x2 ( 7 ) - abc 12abc 13 abc - 20 abc Examples . - - 4 a - 4x3 - 9x2 4abc Rule for Subtraction In these examples , the coefficients of 3.
... use of the sign throughout , instead of the sign + . - ( 5 ) За -5a + 7a ( 6 ) -- 3x2 I2 - 7x2 ( 7 ) - abc 12abc 13 abc - 20 abc Examples . - - 4 a - 4x3 - 9x2 4abc Rule for Subtraction In these examples , the coefficients of 3.
Page 4
George Peacock. Rule for Subtraction In these examples , the coefficients of the like terms , which have the same sign , are added together , and to the difference of the sums , preceded by the sign of the greater , is subjoined the ...
George Peacock. Rule for Subtraction In these examples , the coefficients of the like terms , which have the same sign , are added together , and to the difference of the sums , preceded by the sign of the greater , is subjoined the ...
Page 6
... coefficients ( Art . 25 ) , of like and unlike terms ( Art . 28 ) , metical of indices and powers ( Arts . 38 and 39 ) , and the methods of Algebra , the defini- denoting the ordinary operations ( Art . 9 ) . tions deter- mine the rules ...
... coefficients ( Art . 25 ) , of like and unlike terms ( Art . 28 ) , metical of indices and powers ( Arts . 38 and 39 ) , and the methods of Algebra , the defini- denoting the ordinary operations ( Art . 9 ) . tions deter- mine the rules ...
Page 18
... coefficient is the product of the coefficients of the several factors ( Art . 37 ) : if the coefficient be 1 , ( Art . 30 ) , it is generally suppressed , as not necessary to be exhibited . " " Its literal part is found by writing the ...
... coefficient is the product of the coefficients of the several factors ( Art . 37 ) : if the coefficient be 1 , ( Art . 30 ) , it is generally suppressed , as not necessary to be exhibited . " " Its literal part is found by writing the ...
Page 21
... coefficient of the quotient is found by dividing the coefficient of the dividend by that of the divisor . " " The literal part of the quotient is found by obliterating the symbols or their powers , which are common to the dividend and ...
... coefficient of the quotient is found by dividing the coefficient of the dividend by that of the divisor . " " The literal part of the quotient is found by obliterating the symbols or their powers , which are common to the dividend and ...
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.