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 8
... respectively , and subtract the less from the greater , then prefix the sign of the greater to the difference , and subjoin the common quantity . Let the sum of 2ab quired : ab , 4ab 2ab , Tab - 5ab , and ab- ab , be re- 2ab ab 4ab 2ab ...
... respectively , and subtract the less from the greater , then prefix the sign of the greater to the difference , and subjoin the common quantity . Let the sum of 2ab quired : ab , 4ab 2ab , Tab - 5ab , and ab- ab , be re- 2ab ab 4ab 2ab ...
Page 49
... respectively the same , and have the same signs as those of b , g , and r in the denominator ( these latter being the coefficients of y in the given equations ) , it is manifest from analogy that m , n , and p will have the same respective ...
... respectively the same , and have the same signs as those of b , g , and r in the denominator ( these latter being the coefficients of y in the given equations ) , it is manifest from analogy that m , n , and p will have the same respective ...
Page 54
... respectively , at b we get c + d = b d therefore a + bb :: c + d : d . a c 90. And by subtracting & c . ( instead of the addition ) we shall a ' c ' b . -a have d . = a с whence b - a : a :: d - c ; c Therefore , as the difference of ...
... respectively , at b we get c + d = b d therefore a + bb :: c + d : d . a c 90. And by subtracting & c . ( instead of the addition ) we shall a ' c ' b . -a have d . = a с whence b - a : a :: d - c ; c Therefore , as the difference of ...
Page 56
... respective antecedents , the results , and the an- tecedents will still be proportionals . Let ab :: c : d Then na b :: nc : d ( by the ... respectively proportionals . Suppose ab : cd , Then = с Then And 62 ( 75. Ax . 3 , or 56 ALGEBRA .
... respective antecedents , the results , and the an- tecedents will still be proportionals . Let ab :: c : d Then na b :: nc : d ( by the ... respectively proportionals . Suppose ab : cd , Then = с Then And 62 ( 75. Ax . 3 , or 56 ALGEBRA .
Page 57
... respective diameters : Then da : D2 :: a : A ( Geom . 105. Cor . ) that is , the areas are in the du plicate ratio of their diameters . And taking the square roots of the four terms , d : D :: až : A3 , viz . the diameters are in the ...
... respective diameters : Then da : D2 :: a : A ( Geom . 105. Cor . ) that is , the areas are in the du plicate ratio of their diameters . And taking the square roots of the four terms , d : D :: až : A3 , viz . the diameters are in the ...
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.