A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 8
... respect to the values or signs of the symbols involved , in virtue of the assumptions made in Art . 546. Thus each other . Art . 21 and note . Thus if b was greater than a , but less than a + c , the operation , or rather succession of ...
... respect to the values or signs of the symbols involved , in virtue of the assumptions made in Art . 546. Thus each other . Art . 21 and note . Thus if b was greater than a , but less than a + c , the operation , or rather succession of ...
Page 12
... respect to magnitude only , is , in both cases , correctly expressed by c : it follows , therefore , that the signs + and - applied to the distance c , under such circumstances , when con- sidered with reference to each other , will ...
... respect to magnitude only , is , in both cases , correctly expressed by c : it follows , therefore , that the signs + and - applied to the distance c , under such circumstances , when con- sidered with reference to each other , will ...
Page 15
... respecting the symbolization of the affections principle of symboliza- and magnitudes of lines , will be equally applicable to those mag - able to tion is ap- nitudes whose affections and magnitudes can be symbolized or magnitudes ...
... respecting the symbolization of the affections principle of symboliza- and magnitudes of lines , will be equally applicable to those mag - able to tion is ap- nitudes whose affections and magnitudes can be symbolized or magnitudes ...
Page 17
... respect to Symbolical addition and subtraction , sumptions are equally applicable , and for the same reasons , to Symbolical in symbo- multiplication and division : they are as follows : 1st . Symbols which are general in form , are ...
... respect to Symbolical addition and subtraction , sumptions are equally applicable , and for the same reasons , to Symbolical in symbo- multiplication and division : they are as follows : 1st . Symbols which are general in form , are ...
Page 19
... , 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 Arithmetical Algebra ( Art . 50 ) . Examples . 573. The following are examples : ( 1 19.
... , 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 Arithmetical Algebra ( Art . 50 ) . Examples . 573. The following are examples : ( 1 19.
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.