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 83
... Half of this is And subtracting double the required number , leaves ...... x + 5 x + 5 2 x + 5 -2x 2 Which , by the ... half the difference added to , and subtracted from half the sum , will be the greater and less , respectively . 4 ...
... Half of this is And subtracting double the required number , leaves ...... x + 5 x + 5 2 x + 5 -2x 2 Which , by the ... half the difference added to , and subtracted from half the sum , will be the greater and less , respectively . 4 ...
Page 85
... half the second ; what is the length of the column ? Let the length of the third be Then that of the second will be .......... x 216+ 216+ 2 216 + x 2 = x The first and half the second together is ...... 216+ Which , by the quest . is ...
... half the second ; what is the length of the column ? Let the length of the third be Then that of the second will be .......... x 216+ 216+ 2 216 + x 2 = x The first and half the second together is ...... 216+ Which , by the quest . is ...
Page 96
... half 2r the coefficient of x in the middle term , is r the root of r2 the third term . Therefore the third term of the square of which x2 + ax are the two first terms , will be a2 the square of half the coefficient a ; the whole square ...
... half 2r the coefficient of x in the middle term , is r the root of r2 the third term . Therefore the third term of the square of which x2 + ax are the two first terms , will be a2 the square of half the coefficient a ; the whole square ...
Page 97
... half the coefficient a ) to each side of the equation , we get x2 ax + 4a2 = c + 4a2 and extracting the roots , .... xa = √ ( c + 4a2 ) whence xa + √ ( c + 4a2 ) ++ ) which is the affirmative root . But in this case , a -- x is also ...
... half the coefficient a ) to each side of the equation , we get x2 ax + 4a2 = c + 4a2 and extracting the roots , .... xa = √ ( c + 4a2 ) whence xa + √ ( c + 4a2 ) ++ ) which is the affirmative root . But in this case , a -- x is also ...
Page 98
... half 6 is 9 ; Whence 12 And by evolution , Therefore x = 3 ± 912 and or values of x . - 6x + 972 +9 = 81 , X- -3 = √81 = 9 . 6 , the positive , and negative roots , # 3. Given x2 - - 12x35 . To find x , Completing the square gives x2 ...
... half 6 is 9 ; Whence 12 And by evolution , Therefore x = 3 ± 912 and or values of x . - 6x + 972 +9 = 81 , X- -3 = √81 = 9 . 6 , the positive , and negative roots , # 3. Given x2 - - 12x35 . To find x , Completing the square gives x2 ...
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.