A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page xi
... manner as of the un- digital numbers and geometrical lines , the limitations of value to limited which they are subject in Arithmetical Algebra : for they are the symbols equally competent to represent quantities of all kinds , and of ...
... manner as of the un- digital numbers and geometrical lines , the limitations of value to limited which they are subject in Arithmetical Algebra : for they are the symbols equally competent to represent quantities of all kinds , and of ...
Page 34
... manner , one line may represent a time t , and another line any other time t ' , if they bear to each other the proportion of t to t ' : but the magnitudes v and t admit of no comparison with each other , and therefore the line which ...
... manner , one line may represent a time t , and another line any other time t ' , if they bear to each other the proportion of t to t ' : but the magnitudes v and t admit of no comparison with each other , and therefore the line which ...
Page 36
... manner that the processes for finding the greatest common measure and the multiples least common multiple of two or more numbers are involved of algebra- ical expres- in the corresponding reductions of numerical fractions ( Arts . 98 ...
... manner that the processes for finding the greatest common measure and the multiples least common multiple of two or more numbers are involved of algebra- ical expres- in the corresponding reductions of numerical fractions ( Arts . 98 ...
Page 37
... manner , the fraction 791 a2 + 452 ab + 1017b2 1469a + 1243b is reducible to the more simple form 7a2 + 4ab + 9b * 13a + 11b the common divisor being 113 . of monono- factors . 607. In the second place , there may exist a simple symbol ...
... manner , the fraction 791 a2 + 452 ab + 1017b2 1469a + 1243b is reducible to the more simple form 7a2 + 4ab + 9b * 13a + 11b the common divisor being 113 . of monono- factors . 607. In the second place , there may exist a simple symbol ...
Page 40
... manner , we have Aa = axd and Bb = byd , when ax and by have no common divisor , and where neither a nor b can obliterate d or a factor of d . LEMMA 4. The highest common divisor of Aa and Bb is the highest common divisor of A and B ...
... manner , we have Aa = axd and Bb = byd , when ax and by have no common divisor , and where neither a nor b can obliterate d or a factor of d . LEMMA 4. The highest common divisor of Aa and Bb is the highest common divisor of A and B ...
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.