A Course of Mathematics ...: Designed for the Use of the Officers and Cadets of the Royal Military College, Volume 2C. Glendinning, 1806 - Mathematics |
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Page 45
... substituted for z in the first , gives ... 7x +16+ < = 52 7x 2 16 7x 7x or + 521636 2 16 Whence 56x + 7x = 36 × 16 = 576 or 63x576 and x = 9 7x Now put 94 for x , and we have z = 16 + 7 = 16 + 794 = 20 the value of z . 4. Given a2 ...
... substituted for z in the first , gives ... 7x +16+ < = 52 7x 2 16 7x 7x or + 521636 2 16 Whence 56x + 7x = 36 × 16 = 576 or 63x576 and x = 9 7x Now put 94 for x , and we have z = 16 + 7 = 16 + 794 = 20 the value of z . 4. Given a2 ...
Page 49
... substitution , or repeating the process : For it is evident from Ex . 2. ( Art . 79. ) that the expressions for x and x will have the same denominator as this for y . And since the coefficients of m , n , and p , in the expression ( B ) ...
... substitution , or repeating the process : For it is evident from Ex . 2. ( Art . 79. ) that the expressions for x and x will have the same denominator as this for y . And since the coefficients of m , n , and p , in the expression ( B ) ...
Page 69
... substituted for x in the fraction b 2a + x b gives x = b ab 4a2 + b the second approxi- 2a + 2a ab mation ; therefore the root a + x = α + = 3 4a2 + b ( a2 + b ) 3 . Again . Let the cube root of a3 + b he required ; ( b being supposed ...
... substituted for x in the fraction b 2a + x b gives x = b ab 4a2 + b the second approxi- 2a + 2a ab mation ; therefore the root a + x = α + = 3 4a2 + b ( a2 + b ) 3 . Again . Let the cube root of a3 + b he required ; ( b being supposed ...
Page 70
... substituted for a2 + b , a3 + b , & c . we have a2 + 3 ( a2 + b ) 3a2 + a2 + b 2a3 + 4 ( a3 + b ) 4a3 + 2 ( a3 + b ) xa = a2 + 3N 3a2 + N x a = r . 2a3 + 4N xα = x a = r . 4a3 + 2N 3a4 + 5 ( a + b ) 3a4 + 5N 5a ++ 3 ( a + b ) xa = x a ...
... substituted for a2 + b , a3 + b , & c . we have a2 + 3 ( a2 + b ) 3a2 + a2 + b 2a3 + 4 ( a3 + b ) 4a3 + 2 ( a3 + b ) xa = a2 + 3N 3a2 + N x a = r . 2a3 + 4N xα = x a = r . 4a3 + 2N 3a4 + 5 ( a + b ) 3a4 + 5N 5a ++ 3 ( a + b ) xa = x a ...
Page 81
... substituted for the letters , the square becomes a binomial : thus , let 5a , and 3 = b , then ( 53 ) 28 + / 60 , where the rational part 8 is the sum of the squares of the two surds , and the irrational part √60 , twice their product ...
... substituted for the letters , the square becomes a binomial : thus , let 5a , and 3 = b , then ( 53 ) 28 + / 60 , where the rational part 8 is the sum of the squares of the two surds , and the irrational part √60 , twice their product ...
Other editions - View all
A Course of Mathematics, Vol. 1: Designed for the Use of the Officers and ... Isaac Dalby No preview available - 2018 |
A Course of Mathematics ...: Designed for the Use of the Officers and Cadets ... Isaac Dalby No preview available - 2016 |
Common terms and phrases
Arith arithmetical progression axis bisect body center of gravity center of oscillation center of percussion circle coefficients column completing the square consequently Corol cube cubic curve cylinder denominator denote depth descending described diameter difference direction distance divided divisor ellipse equal equation equilibrio example expression feet per second fluid force fraction fulcrum Geom given gives horizontal inches infinite lever logarithms motion multiplied nearly number of terms ordinate ounces parabola parallel pendulum perpendicular plane pressure proportional quadratic equation quotient radius ratio rectangle reduced respectively right angles SCHOLIUM shot sides sine specific gravity square root subtangent subtracted Suppose surds surface tangent theorem triangle velocity vertex vertical vulgar fraction weight whence whole number
Popular passages
Page 238 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 55 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.
Page 67 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 66 - Subtract the power from the given quantity, and divide the first term of the remainder by the...
Page 302 - Every body continues in its state of rest, or uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Page 116 - How much gold of 15, of 17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine ? Ans.
Page 134 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 23 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 39 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.