A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα vii
... multiples of two or more algebraical expres- sions CHAPTER XIV . On the reduction of algebraical expressions to their most simple equivalent forms CHAPTER XV . Formal statement of the principle of the permanence of equiva- lent forms ...
... multiples of two or more algebraical expres- sions CHAPTER XIV . On the reduction of algebraical expressions to their most simple equivalent forms CHAPTER XV . Formal statement of the principle of the permanence of equiva- lent forms ...
Σελίδα 36
... multiples least common multiple of two or more numbers are involved of algebra- ical expres- in the corresponding reductions of numerical fractions ( Arts . 98 and 116 ) : we use the terms highest and lowest , with respect to 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 and 116 ) : we use the terms highest and lowest , with respect to the ...
Σελίδα 42
... multiple ( the lowest when discoverable ) of their required several denominators : the factor , thus introduced , whether sim- fractional ple or compound , may be obliterated , when convenient or neces- sary , at the conclusion of the ...
... multiple ( the lowest when discoverable ) of their required several denominators : the factor , thus introduced , whether sim- fractional ple or compound , may be obliterated , when convenient or neces- sary , at the conclusion of the ...
Σελίδα 45
... multiple of 27 and 15 . ( 5 ) x + 2x2 + 9 x2 + 2x + 3 7x311x + 15x + 9 7x + 3 the common divisor is x2- 2x + 3 . ( 6 ) 12x2 + 55x + 63 = = 4x + 9 : : 63 x3 - 36x2-343x + 196 21 x3 — 61 x + 28 the common divisor is 3x + 7 : the first ...
... multiple of 27 and 15 . ( 5 ) x + 2x2 + 9 x2 + 2x + 3 7x311x + 15x + 9 7x + 3 the common divisor is x2- 2x + 3 . ( 6 ) 12x2 + 55x + 63 = = 4x + 9 : : 63 x3 - 36x2-343x + 196 21 x3 — 61 x + 28 the common divisor is 3x + 7 : the first ...
Σελίδα 50
... multiple of it , and the lowest or most simple common multiple of two or more such expressions is The lowest required in the reduction of two or more algebraical fractions to their most simple equivalent forms , in the same manner as ...
... multiple of it , and the lowest or most simple common multiple of two or more such expressions is The lowest required in the reduction of two or more algebraical fractions to their most simple equivalent forms , in the same manner as ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 235 - The logarithm of a product is the sum of the logarithms of its factors.
Σελίδα 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Σελίδα 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.
Σελίδα 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Σελίδα 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Σελίδα 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Σελίδα 395 - ... and it is in this sense, and in this sense only, that...
Σελίδα 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.