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 7
... extracting the cube root , or inscribing a circle in a square . This is called solving a problem . A theo- rem is something to be proved . A problem is some- thing to be done . 16. When that which is required to be done , is so easy ...
... extracting the cube root , or inscribing a circle in a square . This is called solving a problem . A theo- rem is something to be proved . A problem is some- thing to be done . 16. When that which is required to be done , is so easy ...
Σελίδα 138
... EXTRACTING the ROOT of both sides , a root of the same name as the power . Ex . 1. Reduce the equation By transposition By evolution 6 + x2 - 8 = 7 x2 = 7 + 8-6 = 9 x = ± √9 = ± 3 . The signs and V are both placed before 9 , be- cause ...
... EXTRACTING the ROOT of both sides , a root of the same name as the power . Ex . 1. Reduce the equation By transposition By evolution 6 + x2 - 8 = 7 x2 = 7 + 8-6 = 9 x = ± √9 = ± 3 . The signs and V are both placed before 9 , be- cause ...
Σελίδα 140
... extracting an even root of a quantity , the solution does not determine whether the answer is positive or negative . [ Art . 297. ] But what is thus left ambiguous by the algebraic process , is frequently settled by the statement of the ...
... extracting an even root of a quantity , the solution does not determine whether the answer is positive or negative . [ Art . 297. ] But what is thus left ambiguous by the algebraic process , is frequently settled by the statement of the ...
Σελίδα 142
... extracting the root of both sides of the equation . An affected quadratic may be solved in the same way , if the member which contains the unknown quantity is an exact square . Thus the equation x2 + 2ax + a2 = b + h . may be reduced by ...
... extracting the root of both sides of the equation . An affected quadratic may be solved in the same way , if the member which contains the unknown quantity is an exact square . Thus the equation x2 + 2ax + a2 = b + h . may be reduced by ...
Σελίδα 143
... square is completed , the equation is reduced , by extracting the square root of both sides , and transposing the known part of the binomial root . [ Art . 303. ] The quantity which is added to one side of the QUADRATIC EQUATIONS . 143.
... square is completed , the equation is reduced , by extracting the square root of both sides , and transposing the known part of the binomial root . [ Art . 303. ] The quantity which is added to one side of the QUADRATIC EQUATIONS . 143.
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Συχνά εμφανιζόμενοι όροι και φράσεις
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...