A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα iii
... reduce its principles and their applications to a complete and regular system , all whose parts were connected with ... reduction of such principles , as those which I have ventured a to put forward , to an elementary form , in.
... reduce its principles and their applications to a complete and regular system , all whose parts were connected with ... reduction of such principles , as those which I have ventured a to put forward , to an elementary form , in.
Σελίδα vii
... reduction of algebraical expressions to their most simple 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 ...
... reduction of algebraical expressions to their most simple 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 ...
Σελίδα x
George Peacock. CHAPTER XLIII . On the solution and reduction of recurring equations CHAPTER XLIV . On the solution of simultaneous equations , and the theory of elimination ... PAGE 361 366 CHAPTER XLV . On the algebraical solution of ...
George Peacock. CHAPTER XLIII . On the solution and reduction of recurring equations CHAPTER XLIV . On the solution of simultaneous equations , and the theory of elimination ... PAGE 361 366 CHAPTER XLV . On the algebraical solution of ...
Σελίδα 6
... reduce to their most simple 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 + ...
... reduce to their most simple 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 + ...
Σελίδα 21
... reduced to the equivalent form − a * + 2 ( b2 + c2 ) a3 — bˆ + 2b3c2 — cˆ . The same result may be equally arranged under the equivalent forms and -b ' + 2 ( a2 + c " ) b3 — a1 + 2a2c2 - c1 - - c * + 2 ( a2 + b2 ) c2 - a * + 2 a2 b2- b ...
... reduced to the equivalent form − a * + 2 ( b2 + c2 ) a3 — bˆ + 2b3c2 — cˆ . The same result may be equally arranged under the equivalent forms and -b ' + 2 ( a2 + c " ) b3 — a1 + 2a2c2 - c1 - - c * + 2 ( a2 + b2 ) c2 - a * + 2 a2 b2- 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.