A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 2
... tion and subtrac- tion . 1st . Symbols , which are general in form , are equally gene- ral in representation and value . 2nd . The rules of the operations of addition and subtraction in Arithmetical Algebra , when applied to symbols ...
... tion and subtrac- tion . 1st . Symbols , which are general in form , are equally gene- ral in representation and value . 2nd . The rules of the operations of addition and subtraction in Arithmetical Algebra , when applied to symbols ...
Page 7
... tion of three Algebra , directs us to change the signs of the terms of the cases of subtrahend and to write them , when so changed , in the same in the tran- line with the terms of the minuend , incorporating , by a proper Arithmeti ...
... tion of three Algebra , directs us to change the signs of the terms of the cases of subtrahend and to write them , when so changed , in the same in the tran- line with the terms of the minuend , incorporating , by a proper Arithmeti ...
Page 9
... tion from addition to subtraction and conversely . of positive and nega- tive sym- bols . 556. The signs plus and minus , when prefixed to symbols The signs denoting quantities of the same kind , cannot denote modifica- used inde ...
... tion from addition to subtraction and conversely . of positive and nega- tive sym- bols . 556. The signs plus and minus , when prefixed to symbols The signs denoting quantities of the same kind , cannot denote modifica- used inde ...
Page 10
George Peacock. Possible and impos- sible quan- tities . Interpreta- tion of the - in the case of tions of magnitude , but only such affections or qualities of the magnitudes represented , as are convertible by the operations of addition ...
George Peacock. Possible and impos- sible quan- tities . Interpreta- tion of the - in the case of tions of magnitude , but only such affections or qualities of the magnitudes represented , as are convertible by the operations of addition ...
Page 15
... tion is ap- nitudes whose affections and magnitudes can be symbolized or magnitudes expressed by the lines themselves . Thus forces in opposite be ex- directions , such as a force which pushes and a force pulls , or a force which ...
... tion is ap- nitudes whose affections and magnitudes can be symbolized or magnitudes expressed by the lines themselves . Thus forces in opposite be ex- directions , such as a force which pushes and a force pulls , or a force which ...
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.