The elements of algebraParker, 1845 - 287 σελίδες |
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Σελίδα 145
... varying and dependent quantities bear to each other the conclusions are more readily obtained by expressing only two terms in each proportion , than by retaining the four . But though , in considering the variation of such quantities 10 ...
... varying and dependent quantities bear to each other the conclusions are more readily obtained by expressing only two terms in each proportion , than by retaining the four . But though , in considering the variation of such quantities 10 ...
Σελίδα 146
... vary directly as B. N. B. When it is simply stated that one quantity varies ' as another it is always meant that the one ' varies directly ' as the other . Ex . 1. If a man agrees to work for a certain sum per hour , the amount of his ...
... vary directly as B. N. B. When it is simply stated that one quantity varies ' as another it is always meant that the one ' varies directly ' as the other . Ex . 1. If a man agrees to work for a certain sum per hour , the amount of his ...
Σελίδα 147
... vary as two others jointly , if , when the former is changed in any manner , the product of the other two be changed in the same proportion . Thus A varies as B and C jointly , ( A ∞ BC ) , when A cannot be changed to a , but the ...
... vary as two others jointly , if , when the former is changed in any manner , the product of the other two be changed in the same proportion . Thus A varies as B and C jointly , ( A ∞ BC ) , when A cannot be changed to a , but the ...
Σελίδα 148
... vary as another , it will also vary as any multiple , or part , of the other . Let A & B , and m be any constant quantity , then because A : a :: Bb , A a :: mB : mb , or A : a :: B b : ( Art . 249 ) ; that m m B is , A ∞ mB , or 269 ...
... vary as another , it will also vary as any multiple , or part , of the other . Let A & B , and m be any constant quantity , then because A : a :: Bb , A a :: mB : mb , or A : a :: B b : ( Art . 249 ) ; that m m B is , A ∞ mB , or 269 ...
Σελίδα 149
... vary as another , any power or root of the former will vary as the same power or root of the latter . Let A vary as B , then A : a :: B : b , and by Art . 253 , A ” : a ” :: Bb " ; that is , A " ∞ B " , where n is whole or fractional ...
... vary as another , any power or root of the former will vary as the same power or root of the latter . Let A vary as B , then A : a :: B : b , and by Art . 253 , A ” : a ” :: Bb " ; that is , A " ∞ B " , where n is whole or fractional ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c a²x² algebraical quantities annuity Arithmetical Progression Binomial Theorem coefficient common denominator compound interest continued fraction cube root difference digits divided divisible divisor equal equation expressed extracting the square factors Find the G. C. M. find the number Find the square Find the value given greater Greatest Common Measure Hence Least Common Multiple less lowest terms Mult multiplied negative number of combinations number of terms numerator and denominator positive integers Present Value prime number probability proposed quantity prove quadratic quadratic equation quotient ratio reduced remainder represent rule shew shillings square root subtracted supposition surd unknown quantities vulgar fraction whole number
Δημοφιλή αποσπάσματα
Σελίδα 286 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 139 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 77 - Divide this quantity, omitting the last figure, by twice the part of the root already found, and annex the result to the root and also to the divisor, then multiply the divisor as it now stands by the part of the root last obtained for the subtrahend.
Σελίδα 107 - A laborer agreed to serve for 36 days on condition that for every day he worked he should receive $1.25, and for every day he was absent he should forfeit 50 cents.
Σελίδα 4 - RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator: then reduce the new fraction to its lowest terms.
Σελίδα 132 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Σελίδα civ - The hold of a vessel partly full of water (which is uniformly increased by a leak) is furnished with two pumps worked by A and B, of whom A takes three strokes to two of .B's ; but four of .B's throw out as much water as five of A's. Now...
Σελίδα 31 - The sign of equality, called equal, or equal to, signifies that the quantities between which it is placed are equal to each other.
Σελίδα 112 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Σελίδα 3 - If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction is not altered.