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 iv
... prob- ability which occur in the concerns of life . So far as it is desirable to form a taste for mathematical studies , it is important that the books by which the student is first introduced to an acquaintance with these subjects ...
... prob- ability which occur in the concerns of life . So far as it is desirable to form a taste for mathematical studies , it is important that the books by which the student is first introduced to an acquaintance with these subjects ...
Σελίδα 4
... prob- A theorem is something to be proved . A problem is something to be done . 16. When that which is required to be done , is so easy , as to be obvious to every one , without an explanation , it is call- · ed a postulate . Of this ...
... prob- A theorem is something to be proved . A problem is something to be done . 16. When that which is required to be done , is so easy , as to be obvious to every one , without an explanation , it is call- · ed a postulate . Of this ...
Σελίδα 19
... must be continually intro- duced or implied , in demonstrations and the solutions of prob- lems , they are placed together , for the convenience of refer- ence . 63. Axiom 1. If the same quantity or equal quantities NEGATIVES . 19.
... must be continually intro- duced or implied , in demonstrations and the solutions of prob- lems , they are placed together , for the convenience of refer- ence . 63. Axiom 1. If the same quantity or equal quantities NEGATIVES . 19.
Σελίδα 76
... Prob . 2. What number is that , to which , if its half be ad- ded , and from the sum 20 be subtracted , the remainder will be a fourth part of the number itself ? In stating questions of this kind , where fractions are con- cerned , it ...
... Prob . 2. What number is that , to which , if its half be ad- ded , and from the sum 20 be subtracted , the remainder will be a fourth part of the number itself ? In stating questions of this kind , where fractions are con- cerned , it ...
Σελίδα 77
... Prob . 4. Divide 48 into two such parts , that if the less be divided by 4 , and the greater by 6 , the sum of the quotients will be 9 . Here , if x be put for the smaller part , the greater will be 48 - x . X 48 -x By the conditions of ...
... Prob . 4. Divide 48 into two such parts , that if the less be divided by 4 , and the greater by 6 , the sum of the quotients will be 9 . Here , if x be put for the smaller part , the greater will be 48 - x . X 48 -x By the conditions of ...
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.