A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα 9
... satisfy but as the rules for performing these operations and arithmeti- cal algebra , the results obtained are or may be made identical in those must be as- two sciences in all cases which are equally within their pro- vince , it is ...
... satisfy but as the rules for performing these operations and arithmeti- cal algebra , the results obtained are or may be made identical in those must be as- two sciences in all cases which are equally within their pro- vince , it is ...
Σελίδα 10
... satisfy . It remains to shew that there exist large classes of magnitudes which possess qualities which can be correctly symbolized by the signs + and - , and that consequently the terms negative and impossible + are not coextensive in ...
... satisfy . It remains to shew that there exist large classes of magnitudes which possess qualities which can be correctly symbolized by the signs + and - , and that consequently the terms negative and impossible + are not coextensive in ...
Σελίδα 12
... satisfy : thus in the case which we have posite lines , sym- directions , been considering , it is opposition of direction , and opposition of and oppo- direction alone which these signs can correctly express : for if tions only . we ...
... satisfy : thus in the case which we have posite lines , sym- directions , been considering , it is opposition of direction , and opposition of and oppo- direction alone which these signs can correctly express : for if tions only . we ...
Σελίδα 30
... satisfy the first condition ( Art . 591 ) , because if we replace a and b by the numbers 5 and 4 , then ab is re- placed by their product or 20 , the units in the factors being equal lines , and those in the product being the squares ...
... satisfy the first condition ( Art . 591 ) , because if we replace a and b by the numbers 5 and 4 , then ab is re- placed by their product or 20 , the units in the factors being equal lines , and those in the product being the squares ...
Σελίδα 55
... satisfy bd ' the required condition : and inasmuch as it is assumed that the form of this product , whatever it may be , is independent of the specific values of the symbols involved ( Art . 546 ) , it follows that ab cd ' a which is ...
... satisfy bd ' the required condition : and inasmuch as it is assumed that the form of this product , whatever it may be , is independent of the specific values of the symbols involved ( Art . 546 ) , it follows that ab cd ' a which is ...
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.