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 17
... means , that ab is to cd ; as the sum of α and m , to the sum of b and n . ― 45. Algebraic quantities are said to be alike , when they are expressed by the same letters , and are of the same power and unlike , when the letters are ...
... means , that ab is to cd ; as the sum of α and m , to the sum of b and n . ― 45. Algebraic quantities are said to be alike , when they are expressed by the same letters , and are of the same power and unlike , when the letters are ...
Σελίδα 24
... means 6 degrees above 0 ; and 06 , 6 degrees below 0 . * NOTE . The expression " less than nothing " may not be wholly improper ; if it is intended to be understood , not lite- rally , but merely as a convenient phrase adopted for the ...
... means 6 degrees above 0 ; and 06 , 6 degrees below 0 . * NOTE . The expression " less than nothing " may not be wholly improper ; if it is intended to be understood , not lite- rally , but merely as a convenient phrase adopted for the ...
Σελίδα 26
... means a complete list of the self - evident propositions , which are furnished by the mathematics . It is not necessary to enumerate them all . Those have been se- lected , to which we shall have the most frequent occasion to refer ...
... means a complete list of the self - evident propositions , which are furnished by the mathematics . It is not necessary to enumerate them all . Those have been se- lected , to which we shall have the most frequent occasion to refer ...
Σελίδα 78
... means of equations . An equation is a proposition , expressing in algebraic charac- ters , the equality between one quantity or set of quantities and another . Thus x + ab + c , is an equation , in which the sum of x and a , is equal to ...
... means of equations . An equation is a proposition , expressing in algebraic charac- ters , the equality between one quantity or set of quantities and another . Thus x + ab + c , is an equation , in which the sum of x and a , is equal to ...
Σελίδα 85
... means of a proportion . To show how this may be reduced to an equation , it will be ne- cessary to anticipate the subject of a future section , so far as to admit the principle , that " when four quantities are in ge- ometrical ...
... means of a proportion . To show how this may be reduced to an equation , it will be ne- cessary to anticipate the subject of a future section , so far as to admit the principle , that " when four quantities are in ge- ometrical ...
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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...