A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 9
... appears , therefore , that in the case of negative symbols , the operation of addition is no longer associated with the fun- damental idea of increase , nor that of subtraction with that of decrease : and thus a change of sign from plus ...
... appears , therefore , that in the case of negative symbols , the operation of addition is no longer associated with the fun- damental idea of increase , nor that of subtraction with that of decrease : and thus a change of sign from plus ...
Page 15
... amount : and it consequently appears that the sub- traction of a debt , in the language of Symbolical Algebra , is not its obliteration or removal , but the change of its affection or character , from money or property owed to money or 15.
... amount : and it consequently appears that the sub- traction of a debt , in the language of Symbolical Algebra , is not its obliteration or removal , but the change of its affection or character , from money or property owed to money or 15.
Page 19
... appear most symmetrical or most convenient . " " If the sign of the mononomial multiplier be negative , the signs of all the terms of the multiplicand will be changed : in every other respect the rule agrees with that which is given in ...
... appear most symmetrical or most convenient . " " If the sign of the mononomial multiplier be negative , the signs of all the terms of the multiplicand will be changed : in every other respect the rule agrees with that which is given in ...
Page 62
... appears that Ja × √a = a , where Ja denotes the square root of a ( Art . 223 ) : we conclude , therefore , that a is identical in meaning with Ja , inasmuch as when multiplied into itself , it produces the same result * . 637. What is ...
... appears that Ja × √a = a , where Ja denotes the square root of a ( Art . 223 ) : we conclude , therefore , that a is identical in meaning with Ja , inasmuch as when multiplied into itself , it produces the same result * . 637. What is ...
Page 64
... appears that ao = 1 , a Proof that ( a ) " = a ** , Examples of the re- duction of expres- sions in which in- dices occur . whatever be the value of a . 642. If n be a whole number , it may be easily shewn that ( a ) " = a . For , in ...
... appears that ao = 1 , a Proof that ( a ) " = a ** , Examples of the re- duction of expres- sions in which in- dices occur . whatever be the value of a . 642. If n be a whole number , it may be easily shewn that ( a ) " = a . For , in ...
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.