A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 85.
Σελίδα vii
... equivalent forms CHAPTER XV . Formal statement of the principle of the permanence of equiva- lent forms . CHAPTER XVI . The theory of indices ..... CHAPTER XVII . PAGE 1 17 36 52 59 61 On the extraction of square roots in Symbolical ...
... equivalent forms CHAPTER XV . Formal statement of the principle of the permanence of equiva- lent forms . CHAPTER XVI . The theory of indices ..... CHAPTER XVII . PAGE 1 17 36 52 59 61 On the extraction of square roots in Symbolical ...
Σελίδα 2
... equivalent expression b + c in one case , and by b - c in the other : in the first case , we get a − b = b + c − b = b − b + c ( Art . 22 ) , b = b - c - b = 0 + c ( Art . 16 ) = + c = c : and in the second a - - - = b − b − c = 0 ...
... equivalent expression b + c in one case , and by b - c in the other : in the first case , we get a − b = b + c − b = b − b + c ( Art . 22 ) , b = b - c - b = 0 + c ( Art . 16 ) = + c = c : and in the second a - - - = b − b − c = 0 ...
Σελίδα 3
... equivalent to that which would arise from the subtraction of 3a from 5a : or , in other words , the addition of 3a to 5a in Symbolical Algebra , is equivalent to the subtraction of 3a from 5a in Arithmetical Algebra . ( 4 ) Add together ...
... equivalent to that which would arise from the subtraction of 3a from 5a : or , in other words , the addition of 3a to 5a in Symbolical Algebra , is equivalent to the subtraction of 3a from 5a in Arithmetical Algebra . ( 4 ) Add together ...
Σελίδα 5
... equivalent to the sum of a and b . ( 2 ) 7a ( 3 ) -7a 3 a 4a ( 4 ) 7 a ( 5 ) 7 a - 3a 3 a 3 a - 4 a 10 a - 10a In these examples , the minuend and subtrahend are written underneath each other , as in common Arithmetic : the results are ...
... equivalent to the sum of a and b . ( 2 ) 7a ( 3 ) -7a 3 a 4a ( 4 ) 7 a ( 5 ) 7 a - 3a 3 a 3 a - 4 a 10 a - 10a In these examples , the minuend and subtrahend are written underneath each other , as in common Arithmetic : the results are ...
Σελίδα 6
... equivalent form the terms which are ex- ternal to those which remain : we then remove the remaining brackets and arrange the terms , when reduced , in alphabetical order ( Arts . 20 and 21. ) ( 14 ) a- [ a + b− { a + b + c − ( a + b + ...
... equivalent form the terms which are ex- ternal to those which remain : we then remove the remaining brackets and arrange the terms , when reduced , in alphabetical order ( Arts . 20 and 21. ) ( 14 ) a- [ a + b− { a + b + c − ( a + b + ...
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.