A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα 2
... become 0 + b and 0 - b , or + b and -- b , or b and - b respectively , when a becomes equal to zero : this is another mode of deriving the conclusion in the text . 547. Proceeding upon the assumptions made in the last Rule 2.
... become 0 + b and 0 - b , or + b and -- b , or b and - b respectively , when a becomes equal to zero : this is another mode of deriving the conclusion in the text . 547. Proceeding upon the assumptions made in the last Rule 2.
Σελίδα 18
... become successively equal to zero : thus , if we suppose b = 0 and d = 0 , the product ( 1 ) in question becomes 1st . ( a - 0 ) ( c− 0 ) = a c − a × 0 - 0 × c + 0 x 0 , or a × b = ab , obliterating the terms which involve zero . If ...
... become successively equal to zero : thus , if we suppose b = 0 and d = 0 , the product ( 1 ) in question becomes 1st . ( a - 0 ) ( c− 0 ) = a c − a × 0 - 0 × c + 0 x 0 , or a × b = ab , obliterating the terms which involve zero . If ...
Σελίδα 23
... becomes obviously interminable . " : This is the same rule which is followed in Arithmetical Alge- bra , ( Art . 84 ) , and the examples which are given in illustration of it ( Art 86 ) , are examples also of Symbolical Division . 582 ...
... becomes obviously interminable . " : This is the same rule which is followed in Arithmetical Alge- bra , ( Art . 84 ) , and the examples which are given in illustration of it ( Art 86 ) , are examples also of Symbolical Division . 582 ...
Σελίδα 27
... become indefinitely small or zero . ( Art . 166 ) . tients in 585. In Arithmetical Algebra , we adopt or we assume a ... becomes divergent , when the operation in which it originates ceases cal to to belong to Arithmetical Algebra . tion ...
... become indefinitely small or zero . ( Art . 166 ) . tients in 585. In Arithmetical Algebra , we adopt or we assume a ... becomes divergent , when the operation in which it originates ceases cal to to belong to Arithmetical Algebra . tion ...
Σελίδα 28
... become zero ( 0 ) or infinity ( ) , according as a is less or greater than a , or in other words , according as the series is a result both of Arithmetical and Symbolical Algebra , or of the latter science only and if we were at liberty ...
... become zero ( 0 ) or infinity ( ) , according as a is less or greater than a , or in other words , according as the series is a result both of Arithmetical and Symbolical Algebra , or of the latter science only and if we were at liberty ...
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.