A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα 2
... value . 2nd . The rules of the operations of addition and subtraction in Arithmetical Algebra , when applied to ... values , from zero upwards , we may likewise include zero in their number : upon this assumption , the ex- pressions ...
... value . 2nd . The rules of the operations of addition and subtraction in Arithmetical Algebra , when applied to ... values , from zero upwards , we may likewise include zero in their number : upon this assumption , the ex- pressions ...
Σελίδα 7
... values of the symbols and adopting also as the subject matter of ing of the operations our operations or of our reasonings , whatever quantities or forms of themselves , symbolical expression may result from this extension : but , inas ...
... values of the symbols and adopting also as the subject matter of ing of the operations our operations or of our reasonings , whatever quantities or forms of themselves , symbolical expression may result from this extension : but , inas ...
Σελίδα 61
... value , are general in form , we are authorized ciple of to conclude by " the principle of the permanence of equivalent nence of ... values of m and n . Principle of indices . Interpreta- tion of a . Meaning CHAPTER XVI The theory of indices.
... value , are general in form , we are authorized ciple of to conclude by " the principle of the permanence of equivalent nence of ... values of m and n . Principle of indices . Interpreta- tion of a . Meaning CHAPTER XVI The theory of indices.
Σελίδα 67
... value , cal Alge- bra . though different in the arrangement of their terms . If the relation of the values of the symbols x and a be known , the Rule for the extraction of the square root of these expressions , which is given in ...
... value , cal Alge- bra . though different in the arrangement of their terms . If the relation of the values of the symbols x and a be known , the Rule for the extraction of the square root of these expressions , which is given in ...
Σελίδα 68
... values of x and a is unknown , but that xa is always the root of a2 - 2 ax + a2 , and a - r the root of a2 −2 ax + x2 : and it is only when the relation of values of x and a is unknown , that there is nothing to guide us in the ...
... values of x and a is unknown , but that xa is always the root of a2 - 2 ax + a2 , and a - r the root of a2 −2 ax + x2 : and it is only when the relation of values of x and a is unknown , that there is nothing to guide us in the ...
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.