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 180
... varying one or both of the terms between which the com- parison is made . It must be kept in mind that , when a di- rect ratio is expressed by a fraction , the antecedent of the couplet is always the numerator , and the consequent , the ...
... varying one or both of the terms between which the com- parison is made . It must be kept in mind that , when a di- rect ratio is expressed by a fraction , the antecedent of the couplet is always the numerator , and the consequent , the ...
Σελίδα 190
... varying a proportion , the equality of the ratios must be preserved . And this is effected , either by keeping the ratios the same , † Euclid 16. 5- * See Note G. while the terms are altered ; or by increasing or 190 ALGEBRA .
... varying a proportion , the equality of the ratios must be preserved . And this is effected , either by keeping the ratios the same , † Euclid 16. 5- * See Note G. while the terms are altered ; or by increasing or 190 ALGEBRA .
Σελίδα 204
... varying becomes a , then B becomes b . This is expressed more concisely , by saying that A varies as B , A is as B. Thus the wages of a labouring man vary as the time of his service . We say that the interest of money which is loaned ...
... varying becomes a , then B becomes b . This is expressed more concisely , by saying that A varies as B , A is as B. Thus the wages of a labouring man vary as the time of his service . We say that the interest of money which is loaned ...
Σελίδα 205
... varies as B , that is , that A : a :: B : b . The expression AB may be called a general proportion . 406. One quantity is said to vary directly as another , when the one increases as the other increases , or is diminished as the other ...
... varies as B , that is , that A : a :: B : b . The expression AB may be called a general proportion . 406. One quantity is said to vary directly as another , when the one increases as the other increases , or is diminished as the other ...
Σελίδα 206
... varies as the product of the prin- cipal and time . If the time be doubled , and the principal doubled , the interest will be four times as great . 409. One quantity is said to vary directly as a second , and inversely as a third , when ...
... varies as the product of the prin- cipal and time . If the time be doubled , and the principal doubled , the interest will be four times as great . 409. One quantity is said to vary directly as a second , and inversely as a third , when ...
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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...