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 11
... gives the same result as adding an equal positive one . 38. When the quantities are alike , and have numeral coeffi- cients , the operation may be performed as in common arithme- tic , if those to be subtracted are the least : Thus ...
... gives the same result as adding an equal positive one . 38. When the quantities are alike , and have numeral coeffi- cients , the operation may be performed as in common arithme- tic , if those to be subtracted are the least : Thus ...
Page 14
... gives ab - be - da + dc ( 36 ) ; the same result as by the rule . Therefore , cxd is + dc ; and consequently like signs give plus ( + ) in the product . Other Examples . 5xy - ab + z 3a3 + 2x3 y3 4a 14 Зах Product 20axy —4a2b + 4az 35z ...
... gives ab - be - da + dc ( 36 ) ; the same result as by the rule . Therefore , cxd is + dc ; and consequently like signs give plus ( + ) in the product . Other Examples . 5xy - ab + z 3a3 + 2x3 y3 4a 14 Зах Product 20axy —4a2b + 4az 35z ...
Page 16
... give plus in the quotient , and unlike signs minus . Thus ab divided by + b gives + a ; for a x b is ab the dividend . Also ab divided by b gives + a ; because · bx a is vidend . ab the di- --- But when ab is divided by -b , the ...
... give plus in the quotient , and unlike signs minus . Thus ab divided by + b gives + a ; for a x b is ab the dividend . Also ab divided by b gives + a ; because · bx a is vidend . ab the di- --- But when ab is divided by -b , the ...
Page 17
... gives a 5 2 or a3 the quotient ; For a2 x a3a5 ( 45 ) . Or denoting the quotient by the fraction , and reducing it to its low- est terms , a2 X = a3 the quotient . 4-3 Also a x3 is x = x'x the quotient . 772 m 3 And divided by x3 is x m ...
... gives a 5 2 or a3 the quotient ; For a2 x a3a5 ( 45 ) . Or denoting the quotient by the fraction , and reducing it to its low- est terms , a2 X = a3 the quotient . 4-3 Also a x3 is x = x'x the quotient . 772 m 3 And divided by x3 is x m ...
Page 20
... gives x5 + x4 , which subtracted from a3 + 1 the dividend and x4 + 1 remains , the second dividend , - - Next , x is contained x3 times inx4 , therefore - x3 is the second term in the quotient ; and ( x + 1 ) × —x3 gives x4x3 , which ...
... gives x5 + x4 , which subtracted from a3 + 1 the dividend and x4 + 1 remains , the second dividend , - - Next , x is contained x3 times inx4 , therefore - x3 is the second term in the quotient ; and ( x + 1 ) × —x3 gives x4x3 , which ...
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.