A Complete Treatise on Arithmetic, Rational and Practical: Wherein the Properties of Numbers are Clearly Pointed Out: the Theory and Practice of the Science are Deduced from First Principles and Demonstrated in a Familiar Manner; with a Great Variety of Proper Examples in All the Rules, Perfectly Suited to the Man of Business, Academies, Schools, and Students of Every Denomination, Desirousof Becoming Proficients in Accounts ...

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Printed and sold for the author, by J. Jones, 1804 - Arithmetic - 177 pages
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Page 73 - Algebraic operations are based upon definitions, and the following axioms : 1. If equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities, the quotients will be equal. 5.
Page 148 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 147 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 49 - Find the first figure in the root, by the table of powers, which subtract from the given number. 3. Bring down the first figure in the next point to the remainder, and call it the dividend. 4. Involve the root into the next inferior power to that which is given ; multiply it by the given power, and call it the divisor. 5. Find a quotient figure by common division, and annex it to the root ; then involve the whole root into the given power, and call that the subtrahend. 6.
Page 73 - If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Page 132 - Up starts a hare before my two greyhounds. The dogs, being light of foot, did fairly run, Unto her fifteen rods, just twenty-one. The distance that she started up' before Was fourscore sixteen rods just, and no more.
Page 32 - Multiply the divisor by this quotient; subtract the product from the part of the dividend used, and to the remainder bring down the next figure of the dividend.
Page 157 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 43 - To be 100 feet from th' top to th' ground ; Against the wall a ladder stood upright, Of the same length the castle was in height : •A. waggish youngster did the ladder slide (The bottom of it) 10 feet from the side ; ' Now I would know how far the top did fall, By pulling out the ladder from the wall t A 6 ini nearly 26.
Page 103 - Quantities is the least involved, and let the Value of that Quantity be found in each Equation by the Rules already given), looking upon all the Rest as known : let the Values thus found be put equal to each other (for they are equal...

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