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 páginas |
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Página 143
... completing the square , the known and unknown quantities must be brought on opposite sides of the equation by transposition ; and the highest power of the unknown quantity must have the affirmative sign , and be cleared of fractions ...
... completing the square , the known and unknown quantities must be brought on opposite sides of the equation by transposition ; and the highest power of the unknown quantity must have the affirmative sign , and be cleared of fractions ...
Página 144
... completing of the square . The other steps are similar to those by which pure equations are reduced . For the purpose of rendering the completing of the square familiar , there will be an advantage in beginning with exam- ples in which ...
... completing of the square . The other steps are similar to those by which pure equations are reduced . For the purpose of rendering the completing of the square familiar , there will be an advantage in beginning with exam- ples in which ...
Página 145
... Completing the square , Extracting and transp . x2 - x = h - d x3¬x + 1 = 1 + h - d x = ± ( ÷ + h − d ) } . of this is 1 . " 5. Reduce the equation Completing the square , Extracting and transp . 6. Reduce the equation Completing the ...
... Completing the square , Extracting and transp . x2 - x = h - d x3¬x + 1 = 1 + h - d x = ± ( ÷ + h − d ) } . of this is 1 . " 5. Reduce the equation Completing the square , Extracting and transp . 6. Reduce the equation Completing the ...
Página 146
... Completing the square , Extracting and transp . Here the fraction co - efficient of x is 1 Ђ Ꮖ 1 b - b - -- x = 7h 1 I ' b +442 462 + 7 / 1 26- + ( 1/1/12 + 7h ) 3 . xx . ( Art . 158. ) Therefore the 307. In these and similar instances ...
... Completing the square , Extracting and transp . Here the fraction co - efficient of x is 1 Ђ Ꮖ 1 b - b - -- x = 7h 1 I ' b +442 462 + 7 / 1 26- + ( 1/1/12 + 7h ) 3 . xx . ( Art . 158. ) Therefore the 307. In these and similar instances ...
Página 147
... Completing the square , Extracting and transp . a + 5x - 3b = 3x - x2 2 + 2x = 3b - a x2 + 2x + 1 = 1 + 36- 2. Reduce the equation * = 1 ± √1 + 36 — α , 36 • A 2x + 2 x + 2x = 72-8x - 16 Clearing of fractions , Transp . and uniting ...
... Completing the square , Extracting and transp . a + 5x - 3b = 3x - x2 2 + 2x = 3b - a x2 + 2x + 1 = 1 + 36- 2. Reduce the equation * = 1 ± √1 + 36 — α , 36 • A 2x + 2 x + 2x = 72-8x - 16 Clearing of fractions , Transp . and uniting ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Página 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.
Página 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.
Página 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Página 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Página 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.
Página 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.
Página 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...