The Arithmetical Expositor, Or, A Treatise on the Theory and Practice of Arithmetic: Suited to the Commerce of the United States : in Two Parts, Volume 1

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Kimber and Sharpless, 1824 - Arithmetic

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Page 2 - An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the time therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and...
Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 2 - An Act supplementary to an Act, entitled, " An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts, and Books, to the Authors and Proprietors of such Copies during the times therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
Page 8 - Hence, the first term, ratio, and number of terms being given, to find the sum of the series, RULE. Raise the ratio to a power whose index is one less than the number of terms, from which subtract 1, and divide the remainder by the ratio less 1 ; the quotient is the sum of a series with 1 for the first term; then multiply this quotient by the first term of any required series ; the product will be its amount.
Page 5 - If we have four numbers, 2, 4, 8, and 10, of which the difference between the first and second is equal to the difference between the third and fourth, these numbers are said to be in arithmetical proportion. The first term 2 is called an antecedent, and the second term 4, with which it is compared, a consequent. The number 8 is also called an antecedent, and the number 10, with which it is compared, a consequent.
Page 64 - That is, the first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one.
Page 43 - ... be. RULE. Take a series proceeding from and increasing by a unit, up to the number to be combined ; and another series of as many places decreasing by a unit, from the number out of which the combinations are to be made, multiply...
Page 7 - If the extremes be 10 and 70, and the number of terms 21 ; what is the common difference, and the sum of the series ? Ans. th
Page 70 - There will dx also be n — m constants in the resulting equation ; and as we can choose at pleasure the m constants we eliminate, we can form as many resulting equations containing n — m constants, as the number of combinations that can be formed out of n things taken »г at a time ; that is, n (n — 1) ... (n — m + 1) [m.
Page 8 - Multiply the last term by the ratio, and divide the difference between this product and the first term by the difference between the ratio and one.

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