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 1
... common Arithmetic we employ the numeral figures only , but in Algebra it is usual to represent quantities of every kind , both known and unknown , by letters of the Alphabet ; and in this consists its peculiar excellence , because the ...
... common Arithmetic we employ the numeral figures only , but in Algebra it is usual to represent quantities of every kind , both known and unknown , by letters of the Alphabet ; and in this consists its peculiar excellence , because the ...
Page 6
... common multiple of 3 , a , b , c . 25. Given quantities are those whose values are known . 26. Unknown quantities are those whose values are un- known , or required . N. B. By quantities , in these Definitions , we under- stand such ...
... common multiple of 3 , a , b , c . 25. Given quantities are those whose values are known . 26. Unknown quantities are those whose values are un- known , or required . N. B. By quantities , in these Definitions , we under- stand such ...
Page 7
... common to each term . Thus , suppose the sum of the affirmative quantities 2a , 5a , 7a , a , and 3a is required : 2a 5a 7a a За Sum 18a Here it is evident , whatever be the value of a , that the sum 2a + 5a + 7a + a + 3a is 18a ; where ...
... common to each term . Thus , suppose the sum of the affirmative quantities 2a , 5a , 7a , a , and 3a is required : 2a 5a 7a a За Sum 18a Here it is evident , whatever be the value of a , that the sum 2a + 5a + 7a + a + 3a is 18a ; where ...
Page 8
... common quantity . Let the sum of 2ab quired : ab , 4ab 2ab , Tab - 5ab , and ab- ab , be re- 2ab ab 4ab 2ab Tab ab . -- 5ab ab 14ab9ab5ab the sum . Now 1495 , therefore , the sum is + 5ab or 5ab . Let a = = 2 , b = 1 : Then 2ab ab _____ ...
... common quantity . Let the sum of 2ab quired : ab , 4ab 2ab , Tab - 5ab , and ab- ab , be re- 2ab ab 4ab 2ab Tab ab . -- 5ab ab 14ab9ab5ab the sum . Now 1495 , therefore , the sum is + 5ab or 5ab . Let a = = 2 , b = 1 : Then 2ab ab _____ ...
Page 11
... common arithme- tic , if those to be subtracted are the least : Thus , from take - rem . - 7x + 3z - 4y 5x + z- Зу 2x + 2z - y Other Examples . bx + 3cx 5 √ ax - 3x2 −√ ax + Qz2 6 √ ax - 52 2 From take diff . 2ax - - dx + 2x — 3gx ...
... common arithme- tic , if those to be subtracted are the least : Thus , from take - rem . - 7x + 3z - 4y 5x + z- Зу 2x + 2z - y Other Examples . bx + 3cx 5 √ ax - 3x2 −√ ax + Qz2 6 √ ax - 52 2 From take diff . 2ax - - dx + 2x — 3gx ...
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.