A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 13
... proposed * . may be modified in same con- 560. The same problem may be variously modified in form , The same without altering the essential conditions upon which its solution problem by the principles of Symbolical Algebra depends ...
... proposed * . may be modified in same con- 560. The same problem may be variously modified in form , The same without altering the essential conditions upon which its solution problem by the principles of Symbolical Algebra depends ...
Page 14
... proposed in Art . 558 we suppose the traveller to move from A to B upon the curved or zigzag line ACB through a distance equal to a and then return upon the same path from B to C through a distance equal to b , his final distance from A ...
... proposed in Art . 558 we suppose the traveller to move from A to B upon the curved or zigzag line ACB through a distance equal to a and then return upon the same path from B to C through a distance equal to b , his final distance from A ...
Page 26
... proposed divisor : in the first case , we get a terminable quotient , which multiplied into the divisor , repro- duces the dividend : but in the second , there is no terminable quotient which multiplied into the divisor , will reproduce ...
... proposed divisor : in the first case , we get a terminable quotient , which multiplied into the divisor , repro- duces the dividend : but in the second , there is no terminable quotient which multiplied into the divisor , will reproduce ...
Page 36
... proposed to reduce to its most common divisor is simple form : for we have already shewn ( Arts . 75 and 578. ) required , may be as- that any factor common to the numerator and denominator of form a frac- a fraction may be obliterated ...
... proposed to reduce to its most common divisor is simple form : for we have already shewn ( Arts . 75 and 578. ) required , may be as- that any factor common to the numerator and denominator of form a frac- a fraction may be obliterated ...
Page 77
... roots , and will generally indicate that the problem in which they originate , is incapable of solution in the sense in which it was proposed . x2 - px - q = 0 ( 5 ) CHAPTER XIX On the general theory and solution of quadratic equations.
... roots , and will generally indicate that the problem in which they originate , is incapable of solution in the sense in which it was proposed . x2 - px - q = 0 ( 5 ) CHAPTER XIX On the general theory and solution of quadratic equations.
Common terms and phrases
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
Popular passages
Page 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.
Page 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 235 - The logarithm of a product is the sum of the logarithms of its factors.
Page 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 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.
Page 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Page 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Page 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Page 395 - ... and it is in this sense, and in this sense only, that...
Page 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.