An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesH. Howe, 1827 - 332 σελίδες |
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Σελίδα 179
... varying one or both of the terms between which the comparison is made . It must be kept in mind that , when a direct ratio is expressed by a fraction , the antecedent of the couplet is al- ways the numerator , and the consequent , the ...
... varying one or both of the terms between which the comparison is made . It must be kept in mind that , when a direct ratio is expressed by a fraction , the antecedent of the couplet is al- ways the numerator , and the consequent , the ...
Σελίδα 191
... varying a proportion , the equality of the ratios must be preserved . And this is effected , either by keeping the ratios the same , while the terms are altered ; or by increasing or diminishing , one of the ratios as much as the other ...
... varying a proportion , the equality of the ratios must be preserved . And this is effected , either by keeping the ratios the same , while the terms are altered ; or by increasing or diminishing , one of the ratios as much as the other ...
Σελίδα 207
... varying becomes a , then B becomes b . This is expressed more concisely , by saying that A varies as B , or A is as B. Thus the wages of a laboring man vary as the time of his service . We say that the interest of money which is loaned ...
... varying becomes a , then B becomes b . This is expressed more concisely , by saying that A varies as B , or A is as B. Thus the wages of a laboring man vary as the time of his service . We say that the interest of money which is loaned ...
Σελίδα 208
... varies as the product of the princi- pal and time . If the time be doubled , and the principal doubled , the interest will be four times as great . 409. One quantity is said to vary directly as a second , and inversely as a third , when ...
... varies as the product of the princi- pal and time . If the time be doubled , and the principal doubled , the interest will be four times as great . 409. One quantity is said to vary directly as a second , and inversely as a third , when ...
Σελίδα 209
... varies as another , the quotient of the one divided by the other is constant . In other words , if the numerator of a fraction varies as the denominator , the value remains the same . If A a :: B : b , that is , if A B. Then : A.a. B.b. ...
... varies as another , the quotient of the one divided by the other is constant . In other words , if the numerator of a fraction varies as the denominator , the value remains the same . If A a :: B : b , that is , if A B. Then : A.a. B.b. ...
Συχνά εμφανιζόμενοι όροι και φράσεις
12 rods abscissa added algebraic antecedent applied arithmetical become binomial calculation called co-efficients common difference Completing the square compound quantity consequent contained cube root cubic equation curve diminished Divide the number dividend division divisor dollars equa Euclid exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multiplicand multiplied or divided negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tities Transposing triangle twice unit unknown quantity varies
Δημοφιλή αποσπάσματα
Σελίδα 190 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Σελίδα 124 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Σελίδα 188 - : b : : mx : y, For the product of the means is, in both cases, the same. And if na : b : : x : y, then a : b : : x :ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities...
Σελίδα 87 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.
Σελίδα 137 - In the same manner, it may be proved, that the last term of the square of any binomial quantity, is equal to the square of half the co-elficient of the root of the first term.
Σελίδα 295 - The operation consists in repeating the multiplicand, as many times as there are units in the multiplier.
Σελίδα 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 49 - As the value of a fraction is the quotient of the numerator divided by the denominator, it is evident, from Art.
Σελίδα 233 - 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.