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 sider |
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Resultat 1-5 av 22
Side viii
... Progression , 213 XV . Mathematical Infinity , 226 XVI . Division by Compound Divisors , 233 XVII . Involution of Compound Quantities , by the Binomial Theorem , 242 XVIII . Evolution of Compound Quantities , 253 XIX . Infinite Series ...
... Progression , 213 XV . Mathematical Infinity , 226 XVI . Division by Compound Divisors , 233 XVII . Involution of Compound Quantities , by the Binomial Theorem , 242 XVIII . Evolution of Compound Quantities , 253 XIX . Infinite Series ...
Side 187
... progression , as will be seen in a following section . Thus the numbers 10 , 8 , 6 , 4 , 2 , are in continued arithme- tical proportion . For.10-8-8-6-6-4-4-2 . The numbers 64 , 32 , 16 , 8 , 4 , are in continued geometri- cal ...
... progression , as will be seen in a following section . Thus the numbers 10 , 8 , 6 , 4 , 2 , are in continued arithme- tical proportion . For.10-8-8-6-6-4-4-2 . The numbers 64 , 32 , 16 , 8 , 4 , are in continued geometri- cal ...
Side 213
... PROGRESSION . ART . 422. QUANTITIES which decrease by a common difference , as the numbers 10 , 8 , 6 , 4 , 2 , are in continued arithmetical ... progression , when ARITHMETICAL PROGRESSION . 213 Arithmetical and Geometrical Progression,
... PROGRESSION . ART . 422. QUANTITIES which decrease by a common difference , as the numbers 10 , 8 , 6 , 4 , 2 , are in continued arithmetical ... progression , when ARITHMETICAL PROGRESSION . 213 Arithmetical and Geometrical Progression,
Side 214
... progression , when they increase or decrease by a common difference.- When they increase , they form what is called an ascending series , as 3 , 5 , 7 , 9 , 11 , & c . When they decrease , they form a descending series , as 11 , 9 , 7 ...
... progression , when they increase or decrease by a common difference.- When they increase , they form what is called an ascending series , as 3 , 5 , 7 , 9 , 11 , & c . When they decrease , they form a descending series , as 11 , 9 , 7 ...
Side 215
... progression , the last term is equal to the first , the product of the common difference into the number of terms less one . Any other term may be found in the same way . For the series may be made to stop at any term , and that may be ...
... progression , the last term is equal to the first , the product of the common difference into the number of terms less one . Any other term may be found in the same way . For the series may be made to stop at any term , and that may be ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Side 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...
Side 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.
Side 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.
Side 295 - The operation consists in repeating the multiplicand, as many times as there are units in the multiplier.
Side 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 49 - As the value of a fraction is the quotient of the numerator divided by the denominator, it is evident, from Art.
Side 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.