Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 13
... less than d . 3 ° . The signs of proportion , :::: . The single colon stands for , is to ; the double colon for , as . Thus , the expression , a : b :: C : d , is read , a is to b , as c is to d . The double colon is equivalent to the ...
... less than d . 3 ° . The signs of proportion , :::: . The single colon stands for , is to ; the double colon for , as . Thus , the expression , a : b :: C : d , is read , a is to b , as c is to d . The double colon is equivalent to the ...
Página 20
... of the positive and negative terms separately ; subtract the less sum from the greater , prefixing the sign of the greater ; to the result annex the common literal part . EXAMPLES . 1. Find the sum of 3ays , -5ay3 20 MANUAL OF ALGEBRA .
... of the positive and negative terms separately ; subtract the less sum from the greater , prefixing the sign of the greater ; to the result annex the common literal part . EXAMPLES . 1. Find the sum of 3ays , -5ay3 20 MANUAL OF ALGEBRA .
Página 24
... less than either . Thus , the sum of Tab and -4a2b , is 3a2b . To distinguish between these cases , the sum of two or more algebraic quantities , is called their algebraic sum . II . SUBTRACTION . Definitions . 21. Subtraction is the ...
... less than either . Thus , the sum of Tab and -4a2b , is 3a2b . To distinguish between these cases , the sum of two or more algebraic quantities , is called their algebraic sum . II . SUBTRACTION . Definitions . 21. Subtraction is the ...
Página 27
... less than the minu- end ; in algebra the difference may be greater than the minuend . Thus , the difference obtained by subtracting - 4a2 from 6a2 is 10a2 . Hence , the difference between two algebraic quantities is called the algebraic ...
... less than the minu- end ; in algebra the difference may be greater than the minuend . Thus , the difference obtained by subtracting - 4a2 from 6a2 is 10a2 . Hence , the difference between two algebraic quantities is called the algebraic ...
Página 38
... less than the exponent of the same letter in the divisor , the exponent of that letter in the quotient will be neg- ative . Thus , by the rule , we have , a2 a2 = a ~ 8 ; but a5 απ = ; 1 ... α = as Hence , we infer that a quantity with ...
... less than the exponent of the same letter in the divisor , the exponent of that letter in the quotient will be neg- ative . Thus , by the rule , we have , a2 a2 = a ~ 8 ; but a5 απ = ; 1 ... α = as Hence , we infer that a quantity with ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference contain contrary signs cube root Davies denominator denote the number distance dividend divisible equa equal roots equation whose roots EXAMPLES exponent expression extracting the square factors Find the cube Find the greatest Find the least Find the square Find the sum following principle following rule geometrical geometrical progression given equation greatest common divisor hence imaginary indicated irreducible fraction least common multiple logarithm Mathematics miles minuend monomial multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quan quotient radical sign ratio real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root Sturm's Theorem substituting subtract third tion tity transposing travels unknown quantity V₁ whole number
Pasajes populares
Página 145 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 239 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Página 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 245 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 42 - ... the first term of the quotient ; multiply the divisor by this term and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Página 239 - In any proportion, the product of the means is equal to the product of the extremes.
Página 245 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Página 41 - 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.
Página 264 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.