A Treatise on the Elements of AlgebraR. Watts and sold by T. Cadell, 1821 - 227 σελίδες |
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Σελίδα 9
... lesser of these sums from " the greater ; to this difference , annex the sign of the greater together with the common letter or letters , and the " result will be the sum required . " 66 and con- If the aggregate of the positive terms ...
... lesser of these sums from " the greater ; to this difference , annex the sign of the greater together with the common letter or letters , and the " result will be the sum required . " 66 and con- If the aggregate of the positive terms ...
Σελίδα 24
... lesser , and let their sum be represented by s and their difference by d , Then a + b = s and a - b - d .. by Addition , 2 a = s + d and a = + by tracted from -rx , the result is -rx - tx ; and , as this means that the sum of rx and tx ...
... lesser , and let their sum be represented by s and their difference by d , Then a + b = s and a - b - d .. by Addition , 2 a = s + d and a = + by tracted from -rx , the result is -rx - tx ; and , as this means that the sum of rx and tx ...
Σελίδα 25
... lesser , by subtracting half the given " difference from half the given sum . " 29. Let a , b , s , d have the same relation as before , then s = a + b d = a - b Hence , by Multiplication , s × d = a2— b2 ( See Ex.2 . CASE III . p.14 ...
... lesser , by subtracting half the given " difference from half the given sum . " 29. Let a , b , s , d have the same relation as before , then s = a + b d = a - b Hence , by Multiplication , s × d = a2— b2 ( See Ex.2 . CASE III . p.14 ...
Σελίδα 40
... lesser , and the preceding divisor by " the last remainder , till nothing remains ; the last divisor is " the greatest common measure . ” To find the greatest common measure of three numbers , a , b , c ; let d be the greatest common ...
... lesser , and the preceding divisor by " the last remainder , till nothing remains ; the last divisor is " the greatest common measure . ” To find the greatest common measure of three numbers , a , b , c ; let d be the greatest common ...
Σελίδα 80
... lesser part . II . The greater part must exceed the lesser by 9 . A 111. But It . But it is evident that the greater and 80 SIMPLE EQUATIONS . The solution of questions producing simple equations -
... lesser part . II . The greater part must exceed the lesser by 9 . A 111. But It . But it is evident that the greater and 80 SIMPLE EQUATIONS . The solution of questions producing simple equations -
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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...