A school algebra to quadratic equations1875 |
From inside the book
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Page 8
... rule for the subtraction of like quantities . RULE 3. - Write the terms under each other and change the sign of the quantity to be subtracted . Then ( 1 ) If the signs are alike add the coefficients , prefix the common sign , and affix ...
... rule for the subtraction of like quantities . RULE 3. - Write the terms under each other and change the sign of the quantity to be subtracted . Then ( 1 ) If the signs are alike add the coefficients , prefix the common sign , and affix ...
Page 12
... rule of sub- traction is a - b - c + d . If an expression within brackets ... rules ; but the inside pair must be removed first . This direction must be observed ... signs of its terms changed . Therefore ( a + x ) + ( a - x ) - ( 4a -2x ) ...
... rule of sub- traction is a - b - c + d . If an expression within brackets ... rules ; but the inside pair must be removed first . This direction must be observed ... signs of its terms changed . Therefore ( a + x ) + ( a - x ) - ( 4a -2x ) ...
Page 22
... signs produce + and unlike signs - This rule of signs is very important and ought now to be added to the rule already given for multiplying simple expressions . That rule will then stand thus , Multiply together the numerical ...
... signs produce + and unlike signs - This rule of signs is very important and ought now to be added to the rule already given for multiplying simple expressions . That rule will then stand thus , Multiply together the numerical ...
Page 24
... rule of signs is true in division as well as in multiplication . Like signs give + and unlike signs — . Also we observe that to divide one simple term by another we have the following rule . RULE . - Take away from the dividend all the ...
... rule of signs is true in division as well as in multiplication . Like signs give + and unlike signs — . Also we observe that to divide one simple term by another we have the following rule . RULE . - Take away from the dividend all the ...
Page 26
... rule , and we place the result a2 as the first term of the quotit . Next we multiply every term of the divisor by the x , and then subtract the product from the divi- dend , changing the signs of the quantities to be subtracted . The ...
... rule , and we place the result a2 as the first term of the quotit . Next we multiply every term of the divisor by the x , and then subtract the product from the divi- dend , changing the signs of the quantities to be subtracted . The ...
Common terms and phrases
a+b+c a²-b² a²+ab+b² a²+b² added adfected quadratic Algebra Arithmetic bought cent changing their signs clearing off fractions complete the square compound expressions cost difference Ditto Divide the number dividend division divisor eliminate equa equal equation containing examples exceeds EXERCISE extract the square factors feet Find the numbers florins following rule gallons greatest common measure half-crowns half-guineas Hence least common multiple methods miles per hour minuend number sought numerator and denominator numerical value obtained PROBLEMS proceed quadratic equation quotient remainder Remove the brackets Required the number rule of signs second term sheep shillings simple equations SIMULTANEOUS EQUATIONS Solve the equations Solve the following square root subtracted sugar suppose symbols terms containing third Transpose twice the product unknown quantities write written x+1 x+2 yards
Popular passages
Page 91 - A vintner sold 7 dozen of sherry and 12 dozen of claret for 50/., and finds that he has sold 3 dozen more of sherry for 10/. than he has of claret for 6/. Required the price of each.
Page 28 - I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 28 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 28 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 69 - There is a certain number, consisting of two places of figures, which is equal to four times the sum of its digits ; and if 18 be added to it, the digits will be inverted; what is the number? Ans. 24.
Page 73 - ... 7. A person walking along the road in a fog meets one waggon and overtakes another which is travelling at the same rate as the former. and he observes that between the time of his first seeing and passing the waggons, he walks 20 yds. and 60 yds.
Page 43 - ... start at the same time, from the same place, and travel in opposite directions, what will represent their distance apart at the end of 1 day ? of 2, 3, 4, 5 days ? ART.
Page 44 - Divide the greater number by the less, the divisor by the remainder, and thus continue to divide the last divisor by the last remainder until there is no remainder ; the last divisor will be the greatest common divisor.
Page 34 - Any term may be transposed from one side of an equation to the other by changing its sign.
Page 3 - Quantities having the same sign are said to have like signs ; those having different signs are said to have unlike signs.