Mathematics: Compiled from the Best Authors, and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 1W. Hilliard, 1808 - Mathematics |
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Page 14
... equal to the sum of all its parts . " All , that requires explaining , is the method of placing the numbers , and carrying for the tens , both which are evident from the nature of notation . For any other disposition of the num bers ...
... equal to the sum of all its parts . " All , that requires explaining , is the method of placing the numbers , and carrying for the tens , both which are evident from the nature of notation . For any other disposition of the num bers ...
Page 16
... equal to the excess of nines , contained in the sum of all the numbers ; the parts being equal to the whole . This rule was first given by Dr. WALLIS in his Arithmetic , published A. D. 1657 , and is a very simple , easy method ; though ...
... equal to the excess of nines , contained in the sum of all the numbers ; the parts being equal to the whole . This rule was first given by Dr. WALLIS in his Arithmetic , published A. D. 1657 , and is a very simple , easy method ; though ...
Page 17
... equal to the whole , so must the sum of the dif rences of all the similar parts be equal to the difference of the wholes , or given numbers . 2. When any figure of the greater number is less than its correspondent figure in the less ...
... equal to the whole , so must the sum of the dif rences of all the similar parts be equal to the difference of the wholes , or given numbers . 2. When any figure of the greater number is less than its correspondent figure in the less ...
Page 18
... equal to the greater , the work is right . EXAMPLES . ( 1 ) . ( 2 ) ( 3 ) From 3287625 From 5327467 From 1234567 Take 2343756 Take 1008438 Take 345678 Rem . 943869 Remain . 4319029 Remain . 888889 Proof 3287625 Proof 5327467 Proof ...
... equal to the greater , the work is right . EXAMPLES . ( 1 ) . ( 2 ) ( 3 ) From 3287625 From 5327467 From 1234567 Take 2343756 Take 1008438 Take 345678 Rem . 943869 Remain . 4319029 Remain . 888889 Proof 3287625 Proof 5327467 Proof ...
Page 22
... equal to the former , the product is right . . ( 1 ) Multiply 23456787454 by 7 EXAMPLES . ( 2 ) Multiply 32745654473 164197512178 Product . by 234 130982617892 98236963419 65491308946 Product 7662483146682 of nines in their product be equal ...
... equal to the former , the product is right . . ( 1 ) Multiply 23456787454 by 7 EXAMPLES . ( 2 ) Multiply 32745654473 164197512178 Product . by 234 130982617892 98236963419 65491308946 Product 7662483146682 of nines in their product be equal ...
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Common terms and phrases
affirmative amount of 11 angle annuity annum arithmetical Bisect carats cent centre chord circle circumference coefficient common denominator completing the square compound interest compound quantity consequently cube root debt decimal denoted diameter difference Divide dividend division divisor draw equal equation EXAMPLES exponent figure fourth gallons geometrical progression geometrical series give given number greater greatest common measure half improper fraction infinite series less number logarithm manner Multiply negative NOTE nth root number of combinations number of terms number of things payment perpendicular polygon present worth PROBLEM proportion quadratic equation quotient radius ratio Reduce remainder repetend required to find right line RULE sides simple interest sine square root subtract Suppose surd taken tangent third unknown quantity vulgar fraction Whence whole number yards
Popular passages
Page 175 - RULE.* — Multiply each payment by the time at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the true time required.
Page 140 - 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 255 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 198 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Page 149 - To the remainder bring down the first figure in the next period, and call it the dividend. 4. Involve the root to the next inferior power to that which is given, and multiply it by the number denoting the given power, for a divisor.
Page 315 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 124 - As the sum of the several products, Is to the whole gain or loss ; So is each man's particular product, To his particular share of the gain or loss.
Page 139 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 120 - When it is required to find how many of the first sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the last.
Page 132 - When one of the ingredients is limited to a certain quantity. RULE. Take the difference between each price and the mean rate, as before ; then,