A New System of Arithmetick Theorical and Practical: Wherein the Science of Numbers is Demonstrated in a Regular Course Frm Its First Principles, Thro' All the Parts and Branches Thereof; Either Known to the Ancients, Or Owing to the Improvements of the Moderns ...

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J. Osborn, 1730 - Algebra - 627 pages
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Page 256 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 194 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
Page 194 - The difference of the squares of two numbers is equal to the product of their sum and difference.
Page 25 - The number to be multiplied is called the multiplicand, the number by which it is multiplied the multiplier, and the result the product.
Page 575 - Simple interest is that | which is paid for the principal, or sum lent, at a certain rate or allowance made by law, or agreement of parties, whereby so much aa 5J.
Page 223 - Multiply ú the sum of the extremes by the number of terms, and the product will be the answer 10.
Page 583 - Divide the given amount by the amount o/$l, at the given rate per cent., for the given time. REMARK. — This rule is deduced from the fact that the amount of different principals for the same time and at the same rate per cent., are to each other as those principals. BANK DISCOUNT. Bank Discount is the sum paid to a bank for...
Page 213 - IN ARITHMETICAL PROPORTION THE SUM OF THE EXTREMES is EQUAL TO THE SUM OF THE MEANS. 24. GEOMETRICAL' PROPORTION is AN EQUALITY OF GEOMETRICAL RATIOS, AND ARITHMETICAL PROPORTION AN EQUALITY OF ARITHMETICAL RATIOS.
Page 40 - But, before we explain the way of using these rods, there is another thing to be known, viz. that the figures on every rod are written in an order different from that in the table. Thus, the little square space, or division, in which the several products of every column are written, is divided into two parts, by a line across from the upper angle on the right to the lower on the left ; and if the product is a digit, it is set in the lower division ; if it has two places, the first is set in the lower,...
Page 64 - III. (1266), it was enacted that 32 grains of wheat taken out of the middle of the ear, and well dried, should weigh a pennyweight, of which 20 should make au ounce, of which 12 should make a pound.