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 6
... remaining brackets and arrange the terms , when reduced , in alphabetical order ( Arts . 20 and 21. ) ( 14 ) a- [ a + b− { a + b + c − ( a + b + c + d ) } ] - = a - a − b + { a + b + c− ( a + b + c + d ) } = = = -b + a + b + c− ( a ...
... remaining brackets and arrange the terms , when reduced , in alphabetical order ( Arts . 20 and 21. ) ( 14 ) a- [ a + b− { a + b + c − ( a + b + c + d ) } ] - = a - a − b + { a + b + c− ( a + b + c + d ) } = = = -b + a + b + c− ( a ...
Page 48
... remaining part of the operation , and arranging the result accord- ing to powers of a , we get ( c - d ) a2 + 6 ( bc - bd ) a +9 ( b2c - b2d ) ( bc - bd + c - cd ) a - 3 ( b'd - b3c - bc2 + cbd ) * In the next place , we find by trial ...
... remaining part of the operation , and arranging the result accord- ing to powers of a , we get ( c - d ) a2 + 6 ( bc - bd ) a +9 ( b2c - b2d ) ( bc - bd + c - cd ) a - 3 ( b'd - b3c - bc2 + cbd ) * In the next place , we find by trial ...
Page 68
... remaining term of the square by double the prị- mary term of the root , making the quotient the second term of the root : add this second term , with its proper sign , to double the primary , to form the divisor : multiply the last term ...
... remaining term of the square by double the prị- mary term of the root , making the quotient the second term of the root : add this second term , with its proper sign , to double the primary , to form the divisor : multiply the last term ...
Page 93
... remaining side , angles , and also their areas equal to each other : and the demonstration , and therefore the The values of x are 12 ( DP ) , or − 4 ( DP ' ) . B P ' C A D P If we change the signs of a , b , c , and therefore the ...
... remaining side , angles , and also their areas equal to each other : and the demonstration , and therefore the The values of x are 12 ( DP ) , or − 4 ( DP ' ) . B P ' C A D P If we change the signs of a , b , c , and therefore the ...
Page 222
... and if the movement be further continued in con- formity with the same conditions , the point or stellated , A B C will for ever circulate in the same figure : but if , all the other A 17 D E 144 " B assumptions remaining , 222.
... and if the movement be further continued in con- formity with the same conditions , the point or stellated , A B C will for ever circulate in the same figure : but if , all the other A 17 D E 144 " B assumptions remaining , 222.
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.