An Elementary Treatise on Algebra: Theoretical and Practical |
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Page ix
... extracting the square root of bino- mial surds , 360 VI . Calculation of imaginary quantities , 365 CHAPTER VIII . On Pure Equations , 370 SECT . I. Solution of pure equations of the first degree by involution , II . Solution of pure ...
... extracting the square root of bino- mial surds , 360 VI . Calculation of imaginary quantities , 365 CHAPTER VIII . On Pure Equations , 370 SECT . I. Solution of pure equations of the first degree by involution , II . Solution of pure ...
Page 316
... root a ; for ( a ) 2m + 1 is equal 297. Evolution , or the rule for extracting the root of any algebraic Quantity whatever , is divided into the four following Cases . 1 CASE I. To find any root of a simple algebraic 316 EVOLUTION .
... root a ; for ( a ) 2m + 1 is equal 297. Evolution , or the rule for extracting the root of any algebraic Quantity whatever , is divided into the four following Cases . 1 CASE I. To find any root of a simple algebraic 316 EVOLUTION .
Page 330
... extracting the cube root of numbers may be understood by comparing the pro- cess for extracting the cube root of ( a + b + c ) 3 , ( Art . 300 ) , with the following operations , in which is de- duced the cube root of the number ...
... extracting the cube root of numbers may be understood by comparing the pro- cess for extracting the cube root of ( a + b + c ) 3 , ( Art . 300 ) , with the following operations , in which is de- duced the cube root of the number ...
Page 332
... extracting the cube root of numbers . RULE . 310. Point off every third figure , beginning with the units ; find the greatest cube number contained in the first period , and place the cube root of it in the quotient . Subtract its cube ...
... extracting the cube root of numbers . RULE . 310. Point off every third figure , beginning with the units ; find the greatest cube number contained in the first period , and place the cube root of it in the quotient . Subtract its cube ...
Page 360
... EXTRACTING THE SQUARE ROOT of BINOMIAL SURDS . 363. The square root of a quantity cannot be partly rational and partly a quadratic surd . If possible , let √n = a + m ; then by squaring both sides , n = a3 + 2a / m + m , and 2a / mn ...
... EXTRACTING THE SQUARE ROOT of BINOMIAL SURDS . 363. The square root of a quantity cannot be partly rational and partly a quadratic surd . If possible , let √n = a + m ; then by squaring both sides , n = a3 + 2a / m + m , and 2a / mn ...
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Common terms and phrases
a²+ab+b² added adfected algebraic quantities becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root difference digits divi dividend division enunciation equa equal example exponent expressed extracting the root factors find the values formula fourth gives greater greatest common divisor greatest common measure Hence least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative observed operation positive preceding Prob problem proportion proposed equation quadratic equations quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations solution square root substituting subtracted third tion tity transposition travelled unity unknown quantity values of x whence whole number
Popular passages
Page iv - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Page 498 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Page 57 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 162 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples...
Page 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 503 - THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to CF.
Page 496 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Page 318 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 7 - NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...