A Treatise on the Elements of AlgebraR. Watts and sold by T. Cadell, 1821 - 227 σελίδες |
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Σελίδα 19
... Example , the dividend is arranged according to the powers of a , the first term of the divisor . we proceed by the following steps ; Having done this , 1. a is contained in a3 , a ' times ; put this in the quotient . 11. Multiply a - b ...
... Example , the dividend is arranged according to the powers of a , the first term of the divisor . we proceed by the following steps ; Having done this , 1. a is contained in a3 , a ' times ; put this in the quotient . 11. Multiply a - b ...
Σελίδα 28
... ( with their proper signs ) " the remaining terms of the numerator with the denominator " under them , and the result will be the mixed quantity re- " quired . " EXAMPLE 1 . a2 + ab + b2 Reduce a Ex . 1 . 28 ALGEBRAIC FRACTIONS .
... ( with their proper signs ) " the remaining terms of the numerator with the denominator " under them , and the result will be the mixed quantity re- " quired . " EXAMPLE 1 . a2 + ab + b2 Reduce a Ex . 1 . 28 ALGEBRAIC FRACTIONS .
Σελίδα 29
Bewick Bridge. EXAMPLE 1 . a2 + ab + b2 Reduce a a + ab Here a Ꮡ to a mixed quantity . = a + b is the integral part , and is the fractional part ; - a b2 a + b + is the ... EXAMPLE 1 . 4 a Reduce and 1a Ex . 1 . ALGEBRAIC FRACTIONS . 29.
Bewick Bridge. EXAMPLE 1 . a2 + ab + b2 Reduce a a + ab Here a Ꮡ to a mixed quantity . = a + b is the integral part , and is the fractional part ; - a b2 a + b + is the ... EXAMPLE 1 . 4 a Reduce and 1a Ex . 1 . ALGEBRAIC FRACTIONS . 29.
Σελίδα 30
Bewick Bridge. 2x 5x EXAMPLE 1 . 4 a Reduce and 1a , 3. ს " 2x xbx5 = 10bx 5 to a common denominator . 5x X3 X5 = 75x new numerators ; 4 ax3xb12ab 3 xbx5 = 15b common denominator ; Hence the frac- tions required are 10bx 75x 12 ab ...
Bewick Bridge. 2x 5x EXAMPLE 1 . 4 a Reduce and 1a , 3. ს " 2x xbx5 = 10bx 5 to a common denominator . 5x X3 X5 = 75x new numerators ; 4 ax3xb12ab 3 xbx5 = 15b common denominator ; Hence the frac- tions required are 10bx 75x 12 ab ...
Σελίδα 31
... EXAMPLE 1 . 14x + 7ax + 21x2 Reduce to its lowest terms . 35x2 The coefficient of every term of the numerator and denominator of this fraction is divisible by 7 , and the letter also enters into every term ; therefore 7x will divide ...
... EXAMPLE 1 . 14x + 7ax + 21x2 Reduce to its lowest terms . 35x2 The coefficient of every term of the numerator and denominator of this fraction is divisible by 7 , and the letter also enters into every term ; therefore 7x will divide ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic algebraic quantities ANSW arithmetic arithmetic series binomial chord circle coefficients Conic Sections consequently cosine cotan cubic equation curvature curve denominator diameter divided divisor Ellipse equa equal equation A)=0 equation whose roots EXAMPLE expressed Find the sum Find the value Formula fraction geometric geometric progression given equation greater greatest common measure Hence Hyperbola impossible roots last term latus-rectum least common multiple limiting equation logarithm manner multiplied negative roots nth root number of terms Parabola parallel perpendicular plane positive powers PROPERTY quadratic equation quadratic surd quotient radius ratio right angles rule secant second term shewn side simple equations sine and cosine square root substituted Subtract surd tangent THEOR Theorem triangle unknown quantities whole number
Δημοφιλή αποσπάσματα
Σελίδα 38 - MOMENTUM, from moveo, to move ; the product of the numbers which represent the quantity of matter and the Velocity of a body, is called its momentum or quantity of motion. MUCILAGINOUS ; resembling mucilage or gum. MULTIPLE, from multiplico, to render manifold ; a quantity is said to be a multiple of another when it contains that other quantity a certain number of times without a remainder. N.
Σελίδα 103 - Prob. 7. Two persons draw prizes in a lottery, the difference of which is 120 dollars, and the greater is to the less, as the less to 10. What are the prizes 1 Prob.
Σελίδα 58 - Thus, in the case of 53361 (whose square root is a number consisting of three figures) ; since the square of the figure standing in the hundred's place cannot be found either in the last period...
Σελίδα 123 - If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth. (Alg. 364.) Thus, if a : b : : c : d, then |=|, and"=^.
Σελίδα 129 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 58 - For the square of tens can give no figure in the first right hand period ; the square of hundreds can give no figure in the first two periods on the right ; and the square of the highest figure in the root can give no figure except in the first period on the left.
Σελίδα 1 - Notation. 1. Quantities whose values are known or determined, are generally expressed by the first letters of the Alphabet, a, b, c, d, &c. ; and unknown or undetermined quantities are commonly represented by the last letters of the Alphabet, x, y, z, &c.
Σελίδα 90 - The sum of those digits is 5 ; and if 9 be added to the number itself, the digits will be inverted.
Σελίδα 128 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...