A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the Higher Parts Usually Taught in Colleges : Containing Moreover, the New Method of Cubic and Higher Equations, as Well as the Development and Application of the More Recently Discovered Theorem of SturmO. Hutchinson, 1842 - 360 σελίδες |
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Σελίδα 23
... observing to place the negative sign before the parenthesis . ab - 6xy + 3 am― ( 4ab + 3xy + am ) Thus , denotes ... observe to change the signs of the terms thus enclosed . In this way we can transform the expression a2b + xy — 7 am ...
... observing to place the negative sign before the parenthesis . ab - 6xy + 3 am― ( 4ab + 3xy + am ) Thus , denotes ... observe to change the signs of the terms thus enclosed . In this way we can transform the expression a2b + xy — 7 am ...
Σελίδα 24
... observe that this is the same as to multiply -b by a , hence we must re- peat -b as many times as there are units in a repeating a minus quantity once , twice , thrice , or any number of times can not change it to a positive quantity ...
... observe that this is the same as to multiply -b by a , hence we must re- peat -b as many times as there are units in a repeating a minus quantity once , twice , thrice , or any number of times can not change it to a positive quantity ...
Σελίδα 25
... observe that 3a2b = 3aab 4a3b2-4aaabb Hence , the product will be 3aabX4aaabb = 12aaaaabbb = 12a5b3 . Here we ... observing to prefix the sign + when both factors have like signs ; and the sign have contrary signs . II . Write the ...
... observe that 3a2b = 3aab 4a3b2-4aaabb Hence , the product will be 3aabX4aaabb = 12aaaaabbb = 12a5b3 . Here we ... observing to prefix the sign + when both factors have like signs ; and the sign have contrary signs . II . Write the ...
Σελίδα 26
... the terms of the multiplicand , successively by each term of the multiplier , and observe the same rules , for the signs and exponents , as in Case I. II . When there arise several partial products alike , 26 MULTIPLICATION .
... the terms of the multiplicand , successively by each term of the multiplier , and observe the same rules , for the signs and exponents , as in Case I. II . When there arise several partial products alike , 26 MULTIPLICATION .
Σελίδα 31
... observing to prefix to the quotient the sign + when the signs of the dividend and divisor are alike ; and the sign when they are contrary . II . Subtract the exponents of the letters in the divisor from the exponents in the ...
... observing to prefix to the quotient the sign + when the signs of the dividend and divisor are alike ; and the sign when they are contrary . II . Subtract the exponents of the letters in the divisor from the exponents in the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ algebraic annuity arithmetical progression assume becomes BINOMIAL THEOREM cleared of fractions common logarithms consequently cube root cubic equation D₁ degree denote dividend equa Equating the coefficients exponent expression Extracting the square factors figure Find a root find the value formula four quantities fourth geometrical progression given gives greatest common divisor greatest common measure Hence imaginary roots infinite series left-hand member m₂ method multinomial theorem multiply Napierian Nlog nth root nth term number of terms numerator and denominator obtain OPERATION polynomial proportion quadratic equation quotient real roots recurring equation Reduce remainder Required the sum result right-hand member root of equation Rule under Art scale of relation second term square root STURM'S THEOREM Subtracting suppose surd Taking the logarithm third three roots tion transposing and uniting uniting terms unknown quantity values substituted
Δημοφιλή αποσπάσματα
Σελίδα 199 - If we have a : c : : a' : c', a : c : : a" : c", a : c : : a'
Σελίδα 34 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
Σελίδα 67 - A farmer had two flocks of sheep, each containing the same number. Having sold from one of these 39, and from the other 93, he finds twice as many remaining in the one as in the other. How many did each flock originally contain 1 Prob.
Σελίδα 195 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 116 - Divide it by twice the root just found, and add the quotient both to the root and to the divisor. Multiply the divisor thus increased, into the term last placed in the root, and subtract the product from the dividend.
Σελίδα 48 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Σελίδα 176 - A person being asked his age, answered, " My mother was 20 years old when I was born, and her age multiplied by mine, exceeds our united ages by 2500.
Σελίδα 95 - Substitution. water. How much gold, and how much silver, did this crown contain ? Ans. 14,77... Ibs. of gold, and 5,22.. .Ibs. of silver. 151. Problem. To solve any number of equations of the...
Σελίδα 205 - Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then...
Σελίδα 61 - Any term may be transposed from one side of an equation to the other by changing its sign.