The Elements of Algebra: Designed for the Use of Common Schools, Also Serving as an Introduction to the "Treatise on Algebra"H.H. Hawley & Company, 1848 - 251 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 176
... product , we have ( 4 + x ) ( 4 — x ) = 16 — x2 . Now , since x is positive for all real values of x , it follows that the product 16 - x2 is always less than 16 ; that is , no two real numbers whose sum is 8 , can be found such that ...
... product , we have ( 4 + x ) ( 4 — x ) = 16 — x2 . Now , since x is positive for all real values of x , it follows that the product 16 - x2 is always less than 16 ; that is , no two real numbers whose sum is 8 , can be found such that ...
Σελίδα 218
... products are positive , and three are negative . II . The letters forming the different products of this common denominator being always arranged in alpha- betical order X , Y , Z , we remark that the subscript num- bers of the first ...
... products are positive , and three are negative . II . The letters forming the different products of this common denominator being always arranged in alpha- betical order X , Y , Z , we remark that the subscript num- bers of the first ...
Σελίδα 219
... negative sign . ( See Art . 17. ) In the present case the products formed by pass- ing obliquely downwards , are taken positive . In this sort of checker - board movement , we must ob- serve that when we run out at the bottom of any ...
... negative sign . ( See Art . 17. ) In the present case the products formed by pass- ing obliquely downwards , are taken positive . In this sort of checker - board movement , we must ob- serve that when we run out at the bottom of any ...
Σελίδα 220
... positive product X2Y3Z1 . Again , commencing with X3 , we pass to Y1 , and thence obliquely downwards to Z2 , and find the positive product X3Y1Z2 . Now , for the negative products we inake similar move- ments obliquely upwards . Thus ...
... positive product X2Y3Z1 . Again , commencing with X3 , we pass to Y1 , and thence obliquely downwards to Z2 , and find the positive product X3Y1Z2 . Now , for the negative products we inake similar move- ments obliquely upwards . Thus ...
Σελίδα 221
... POSITIVE PRODUCTS . 2X5X3-30 3 × 2 × 4 24 4X3X7-84 138 -135 NEGATIVE PRODUCTS . 2 × 2 × 7 = -28 3x3x3 = -27 4X5X480 -135 3 common denominator . We have for the numerator of x the following operation : NEGATIVE PRODUCTS . POSITIVE ...
... POSITIVE PRODUCTS . 2X5X3-30 3 × 2 × 4 24 4X3X7-84 138 -135 NEGATIVE PRODUCTS . 2 × 2 × 7 = -28 3x3x3 = -27 4X5X480 -135 3 common denominator . We have for the numerator of x the following operation : NEGATIVE PRODUCTS . POSITIVE ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
added algebraic algebraic quantities antecedent arithmetical progression bx-ab change the signs Clear the equation cleared of fractions coefficient common denominator Consequently decimal denote digits Divide the number divisor equal equation of fractions EXAMPLES exponent expression Extracting the square favorable Find a number find the values find x formula four quantities fourth geometrical geometrical progression gives Hence inequality least common multiple left-hand term letters metical mixed quantity NEGATIVE PRODUCTS negative quantities nth root number of combinations number of permutations number of terms number sought numerator and denominator obtain OPERATION placed polynomial POSITIVE PRODUCTS pression proportion quadratic equation quotient rate per cent reciprocal Reduce remainder repetend Rule under Art second term simple chance simple equations solved square root subscript numbers substituted subtract things taken third tions Transposing and uniting twice uniting terms unknown quantity values of x VULGAR FRACTIONS
Δημοφιλή αποσπάσματα
Σελίδα 54 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator.
Σελίδα 77 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
Σελίδα 69 - What number is that whose third part exceeds its fourth part by 16 ? Let x= the number required, Then its — part will be —x, and its — part —a;.
Σελίδα 181 - 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 99 - Then divide the first term of the remainder by the first term of the divisor...
Σελίδα 38 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Σελίδα 44 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Σελίδα 134 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Σελίδα 10 - It denotes that the quantities between which it is placed, are to be multiplied together.
Σελίδα 47 - To reduce an improper fraction to a whole or mixed number, — RULE : Divide the numerator by the denominator ; the quotient will be the whole or mixed number. EXAMPLES FOR PRACTICE.