A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 89
... ratio , will lead likewise to some one of the equations which we have just been considering * . trical pro- ( 4 ) To find a point in a given chord of a circle produced A geome- from whence the tangent drawn to the circle shall be equal ...
... ratio , will lead likewise to some one of the equations which we have just been considering * . trical pro- ( 4 ) To find a point in a given chord of a circle produced A geome- from whence the tangent drawn to the circle shall be equal ...
Page 91
... ratio to the rect- angle under its distances from the third and fourth . Let A , B , C and D be the given points , and let P be the point required : let AD = a , BD = b : ABCD P CD : = c and DP = a , the lines being estimated from A ...
... ratio to the rect- angle under its distances from the third and fourth . Let A , B , C and D be the given points , and let P be the point required : let AD = a , BD = b : ABCD P CD : = c and DP = a , the lines being estimated from A ...
Page 93
... under two , of them , may bear a given ratio either to the rectangle formed by a given line and another of these inter- cepted lines , or to the rectangle formed by two of them . " The sepa- rate cases of Geome- try are compre- hended 93.
... under two , of them , may bear a given ratio either to the rectangle formed by a given line and another of these inter- cepted lines , or to the rectangle formed by two of them . " The sepa- rate cases of Geome- try are compre- hended 93.
Page 115
... 76 x 1 x 2 x 3 x 4 x 5 x 6 : a I " a index is 1 the 4th term of ( √√x — √a ) , where = x2 u = - " a2 1 x 2 3 1 × 5 × 9 a 2 43 × 1 × 2 × 3 • u3 = .1171875 x 13 I 8 The limits of the in- 690. The inverse ratio of 115.
... 76 x 1 x 2 x 3 x 4 x 5 x 6 : a I " a index is 1 the 4th term of ( √√x — √a ) , where = x2 u = - " a2 1 x 2 3 1 × 5 × 9 a 2 43 × 1 × 2 × 3 • u3 = .1171875 x 13 I 8 The limits of the in- 690. The inverse ratio of 115.
Page 116
... ratio are n and − 1 , and that , when the series does not terminate , it perpetually approximates to the latter . The limits of the in- - 691. In a similar manner it will appear that the inverse verse ratio ratio of any two consecutive ...
... ratio are n and − 1 , and that , when the series does not terminate , it perpetually approximates to the latter . The limits of the in- - 691. In a similar manner it will appear that the inverse verse ratio ratio of any two consecutive ...
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.