An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesHowe & Deforest, 1814 - 303 σελίδες |
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Σελίδα 6
... instances . The proper field for the display of mathematical genius , is in the region of invention . But what is requisite for an elementary work , is to collect , arrange , and illustrate , materials already provided . However humble ...
... instances . The proper field for the display of mathematical genius , is in the region of invention . But what is requisite for an elementary work , is to collect , arrange , and illustrate , materials already provided . However humble ...
Σελίδα 7
... instances , it is necessary to resort to indirect demonstration ; which is a method of establishing a proposition , by proving that to suppose it not true , would lead to an absurdity . This is frequently called reductio ad absur- dum ...
... instances , it is necessary to resort to indirect demonstration ; which is a method of establishing a proposition , by proving that to suppose it not true , would lead to an absurdity . This is frequently called reductio ad absur- dum ...
Σελίδα 7
... instance , three terms must be given , to enable us to find a fourth . → These three terms are the data , upon which the cal- culation is founded . If we are required to find the number of acres , in a circular island ten miles in cir ...
... instance , three terms must be given , to enable us to find a fourth . → These three terms are the data , upon which the cal- culation is founded . If we are required to find the number of acres , in a circular island ten miles in cir ...
Σελίδα 7
... instances , a proposition and its converse are both true ; as in the preceding example . But this is not always the case . A circle is a figure bounded by a curve ; but a figure bounded by a curve is not of course a circle . 20. The ...
... instances , a proposition and its converse are both true ; as in the preceding example . But this is not always the case . A circle is a figure bounded by a curve ; but a figure bounded by a curve is not of course a circle . 20. The ...
Σελίδα 21
... instance , the profits of trade are the subject of calculation , and the gain is considered positive ; the loss will be negative ; because the latter must be sub- tracted from the former , to determine the clear profit . If the sums of ...
... instance , the profits of trade are the subject of calculation , and the gain is considered positive ; the loss will be negative ; because the latter must be sub- tracted from the former , to determine the clear profit . If the sums of ...
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12 rods abscissa added algebraic antecedent applied arithmetic become binomial calculation called Clearing of fractions co-efficients Completing the square compound quantity consequent cube root cubic equation curve demonstration denominator diminished dividend division divisor dollars equa equal quantities errour Euclid exponents expressed Extracting and transp factors fourth geometrical geometrical progression given quantity greater Hence inches infinite series inverted involution last term less letters manner mathematics Mult multiplicand negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive prefixed principle Prob Prod proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule SECTION sides square root substituted subtracted subtrahend supposed supposition theorem third tion tity Transposing transposition triangle twice uniting terms unknown quantity varies vulgar fraction whole
Δημοφιλή αποσπάσματα
Σελίδα 214 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 188 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Σελίδα 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Σελίδα 227 - 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.
Σελίδα 189 - If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS OF BOTH COUPLETS, MAY BE INVERTED, WITHOUT DESTROYING THE PROPORTION.
Σελίδα 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Σελίδα 187 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
Σελίδα 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.
Σελίδα 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...