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 6
... continued exercise . Mathematical stu- dies are peculiarly fitted for this discipline of the mind . They are calculated to form it to habits of fixed attention ; of sa- gacity , in detecting sophistry ; of caution , in the admission of ...
... continued exercise . Mathematical stu- dies are peculiarly fitted for this discipline of the mind . They are calculated to form it to habits of fixed attention ; of sa- gacity , in detecting sophistry ; of caution , in the admission of ...
Σελίδα 187
... continued proportion . The consequent of each pre- ceding ratio is , then , the antecedent of the following one.- Continued proportion is also called progression , as will be seen in a following section . Thus the numbers 10 , 8 , 6 , 4 ...
... continued proportion . The consequent of each pre- ceding ratio is , then , the antecedent of the following one.- Continued proportion is also called progression , as will be seen in a following section . Thus the numbers 10 , 8 , 6 , 4 ...
Σελίδα 200
... continued proportion , all the CONTINUED PROPORTION . a : b :: b : c :: c : d :: d : e , the ratio of a : b is the same , as that of b : c , of c : d , or of d : e . The ratio of the first of these quantities to the last , is equal to ...
... continued proportion , all the CONTINUED PROPORTION . a : b :: b : c :: c : d :: d : e , the ratio of a : b is the same , as that of b : c , of c : d , or of d : e . The ratio of the first of these quantities to the last , is equal to ...
Σελίδα 201
... continued proportion , the number of couplets , and of course the number of ratios , is one less than the number of quantities . Thus the five pro- portional quantities a , b , c , d , e , form four couplets containing four ratios ; and ...
... continued proportion , the number of couplets , and of course the number of ratios , is one less than the number of quantities . Thus the five pro- portional quantities a , b , c , d , e , form four couplets containing four ratios ; and ...
Σελίδα 213
... continued arithmetical proportion . ( Art . 372. ) Such a series is also called a progression , which is only another name for continu- ed proportion . It is evident , that the proportion will not be destroyed , if the order of the ...
... continued arithmetical proportion . ( Art . 372. ) Such a series is also called a progression , which is only another name for continu- ed proportion . It is evident , that the proportion will not be destroyed , if the order of the ...
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.