University Algebra: Embracing a Logical Development of the Science with Numerous Graded ExamplesA.S. Barnes, 1889 - 320 páginas |
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Página 22
... Difference . - 22. To demonstrate a rule for Subtraction , let the sum of the terms of the minuend be denoted by m , and the sum of the terms of the subtrahend by s ; from the definition , the remainder must be such a quantity that ...
... Difference . - 22. To demonstrate a rule for Subtraction , let the sum of the terms of the minuend be denoted by m , and the sum of the terms of the subtrahend by s ; from the definition , the remainder must be such a quantity that ...
Página 24
... difference , in Algebra , has a more exten- sive signification than in Arithmetic . In Arithmetic , the difference is always less than the minuend ; whereas , in Algebra , the difference may be greater than the minuend . Thus , the ...
... difference , in Algebra , has a more exten- sive signification than in Arithmetic . In Arithmetic , the difference is always less than the minuend ; whereas , in Algebra , the difference may be greater than the minuend . Thus , the ...
Página 39
... difference of any two quanti ties , is equal to the square of the first , minus twice the product of the first and second , plus the square of the second . 3. The product of the sum and difference of two USEFUL FORMULAS . 39 Useful ...
... difference of any two quanti ties , is equal to the square of the first , minus twice the product of the first and second , plus the square of the second . 3. The product of the sum and difference of two USEFUL FORMULAS . 39 Useful ...
Página 40
... difference of two quantities , is equal to the square of the first , minus the square of the second . first rule , EXAMPLES . 1. Let it be required to find the square of 2a + 3.x. The square of 2a , is 4a2 ; twice the product of 2a and ...
... difference of two quantities , is equal to the square of the first , minus the square of the second . first rule , EXAMPLES . 1. Let it be required to find the square of 2a + 3.x. The square of 2a , is 4a2 ; twice the product of 2a and ...
Página 48
... difference between any two multiples of those quantities . Let P and P ' denote any two quantities , both of which are divisible by D ; and let m and n be any two factors whatever : then will mP and nP ' be any two multiples of P and P ...
... difference between any two multiples of those quantities . Let P and P ' denote any two quantities , both of which are divisible by D ; and let m and n be any two factors whatever : then will mP and nP ' be any two multiples of P and P ...
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Términos y frases comunes
algebraic Arithmetic ax² Binomial Formula Clearing of fractions coefficients common difference containing contrary signs cube root Davies denominator denote the number distance dividend divisible equal roots equation whose roots EXAMPLES exponent expressions Extract the square factors Find the cube Find the fourth Find the greatest Find the square following RULE geometrical progression given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple Let x denote logarithm miles monomial Multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quotient radical sign real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root STURM'S THEOREM Substituting subtract third Transform the equation Transposing travels unknown quantity Whence whole number write X₁
Pasajes populares
Página 258 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 255 - 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.
Página 136 - 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 36 - 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 81 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 231 - If four quantities are in proportion, they will be in proportion by COMPOSITION...
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.