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 viii
... 253 XIX . Infinite Series , 259 XX . Composition and Resolution of the higher Equations , 278 XXI . Application of Algebra to Geometry . XXII . Equations of Curves , 292 308 INTRODUCTORY OBSERVATIONS ON THE MATHEMATICS IN GENERAL . ART .
... 253 XIX . Infinite Series , 259 XX . Composition and Resolution of the higher Equations , 278 XXI . Application of Algebra to Geometry . XXII . Equations of Curves , 292 308 INTRODUCTORY OBSERVATIONS ON THE MATHEMATICS IN GENERAL . ART .
Σελίδα 4
... the equality of the sides inferred . In many instances , a proposition and its converse are both true ; as in the prece- ding example . But this is not always the case . A circle is a figure bounded by a curve ; but a figure 4 MATHEMATICS .
... the equality of the sides inferred . In many instances , a proposition and its converse are both true ; as in the prece- ding example . But this is not always the case . A circle is a figure bounded by a curve ; but a figure 4 MATHEMATICS .
Σελίδα 5
... curve ; but a figure bounded by a curve is not of course a circle . : : 0. The practical applications of the mathematics , in the common concerns of business , in the useful arts , and in the various branches of physical science , are ...
... curve ; but a figure bounded by a curve is not of course a circle . : : 0. The practical applications of the mathematics , in the common concerns of business , in the useful arts , and in the various branches of physical science , are ...
Σελίδα 307
... = half the base , y = half the perpendicular , and a and equal the two given lines ; Then x = 462 -a2 15 of y = √ 4a2 = b2 + 2 - * • 15 * See Note X SECTION XXII . EQUATIONS OF CURVES . ART . 526. GEOMETRICAL PROBLEMS . 307.
... = half the base , y = half the perpendicular , and a and equal the two given lines ; Then x = 462 -a2 15 of y = √ 4a2 = b2 + 2 - * • 15 * See Note X SECTION XXII . EQUATIONS OF CURVES . ART . 526. GEOMETRICAL PROBLEMS . 307.
Σελίδα 308
... curve drawn on a plane , are determined , by taking the distance of each from two right lines perpendicular to each other . Let the lines AF and AG ( Fig . 16. ) be perpendicular to each other . Also , let the lines DB , D'B ' , D " B ...
... curve drawn on a plane , are determined , by taking the distance of each from two right lines perpendicular to each other . Let the lines AF and AG ( Fig . 16. ) be perpendicular to each other . Also , let the lines DB , D'B ' , D " 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.