* Feb. 21, For 1 4 lb. Sugar, at $.09, $ 1.26 Cr. Feb 1, By Cash, $24.66 $2.00 4 days labor, at $1.50, $6.00 8.00 Bal. duc T. G., March 3, Received Payment, $16.66 Theodore Gay. (k.) The mere sending of a bill to a person, except at his request, or at the time of sending the articles for which the bill is made out, is equivalent to a request that the money due on it should be paid. (7.) A bill is said to be against the person who the one who is to receive the money due on it. preceding bills is against Humphrey Barrett, and Dodge. owes, and in favor of Thus the first of the in favor of Geo. W. 100. Examples for Practice. - Due Bills. Make out the proper bills for each of the following examples: : 1. L. H. Holmes is a dry goods dealer, residing in Bridgewater. Oct. 7, 1854, he sold to E. C. Hewett, for cash, 3 yds. of broadcloth at $3.62, 3 yds. of doeskin at $1.68, 1 cravat for $1.50, 1 vest for $6.00, 1 pair of gloves for $1.00, and 1 pair of boots for $4.50. 2. A. B. Curry & Son, of Providence, sold to Geo. A. Richards, June 13, 1855, the following articles, viz.: 35 *This entry is repeated so as to make the form of the bill more apparent lbs. live geese feathers, at 50 cents per pound; 12 common chairs, at $.42 each; 6 cane seat, at $1.00 each; 6 mahogany spring seat, at $3.00 each; 3 common bedsteads, at $3.00 each; 2 cottage bedsteads, at $5.00 each; 2 best hair mattresses, 25 lb. each, at $.50 per lb.; 2 palm leaf mattresses at $4 each, 2 husk at $5.00 each, 2 straw at $2.50 each, 1 sofa, $35; 1 pair tete-a-tetes, $75; 1 gilt mirror, $75; 1 marble centre table, $42; 1 secretary, $45; 1 painted chamber set, $45; 1 enamelled chamber set, $125.00; 3 common bureaus at $8.00 each; 1 marble toilet bureau, $42.00; 1 extension dining table, $45.00; 12 oak dining chairs at $3.50; 1 timepiece, $8.00; and 1 whatnot, $25.00. 3. John Smith sold to David Brown the following articles, viz.: Oct. 7, 1854, 13 bushels of potatoes at $.56, 19 bu. corn at $.97, and 3 bbl. of apples at $2.42; Nov. 1, 4 tons of hay at $19, and 3 tons at $18.50; Dec. 17, 40 bushels of potatoes at $.67, 34 bu. of corn at $.98, and 21 bbl. of apples at $2.75 per barrel. Jan. 1, 1855, the account was settled by a due bill. NOTE. A due bill is not a promise to pay a debt, but merely an acknowledgment that it is due. It is intended to cut off after disputes as to the debt for which it is given, by furnishing the creditor additional means of establishing the justice of his claim. Every due bill, or written promise to pay money, should contain the words "value received," to show that the person who signs it has received an equivalent for it. Indeed, it is a principle in law, that no claim is valid unless it is based on some service rendered, or consideration given, to the person against whom it is made, or on his account. To illustrate the form of a due bill, we will suppose that John Smith owes James Brown $25, and that he gives him a due bill for the amount, as follows: $25. Boston, Jan. 1, 1855. Due to James Brown twenty-five dollars, for value received. John Smith. The receipt, when a due bill is given, might be, “Received payment by due bill," or, "Settled by due bill." 4. May 7, 1855, Hill & Saunders, of Boston, sold to James Drew, 1 cask linseed oil, 24 gal., at $1.50 per gal.; 1 bag Java coffee, 122 lbs., at 16 cents per lb.; 1 hhd. of N. O. molasses, 127 gals., at 34 cents per gal.; 1 chest tea, 84 lb., at 48 cents per lb.; 1 bag pepper, 24 lbs., at 11 cents per lb.; 1 box N. O. sugar, 278 lbs., at 6 cents per lb. 5. April 21, 1855, French & Simmons, of New York, sold to Clark & Hubbard, 1 piece super. broadcloth, 26 yds., at $3.75 per yd.; 1 piece fancy cassimere, 31 yds., at $1.34 per yd.; 1 piece black cassimere, 23 yds., at $1.62 per yd.; 6 pieces English prints, 29, 31, 30, 33, 29, and 31 yds., or 183 yds., at $.12 per yd.; 3 pieces Merrimack prints, 28, 32, 31 yds., or 91 yds., at $.09 per yd. ; 2 pieces Scotch gingham, 42 and 41 yds., or 83 yds., at $.17 per yd.; 1 piece sarsenet cambric, 32 yds., at $.28 per yd.; 3 dozen cotton hose at $1.87 per doz.; and 2 lbs. Marshall's linen thread at $1.75 per lb. 6. Geo. Stevens, of Worcester, sold to Daniel Barnard, Sept. 15, 1854, 28 bu. of potatoes at $.87; Oct. 1, 43 bu. of potatoes at $.65; Oct. 7, 7 tons of hay at $19.50, 4 tons at $18.37, and 2 tons at $17.25; and Nov. 3, 23 bbl. of apples at $1.75, and 19 bbl. at $1.94. Mr. Barnard paid Mr. Stevens, Oct. 5, 1854, $20, Oct. 17, $13.50; and Nov. 20, he sold him 14 lb. sugar at 7 cents, 12 lb. at 9 cents, 8 lb. at 11 cents, 7 lb. coffee at 15 cents, 4 lb. tea at 54 cents, 3 lb. at 47 cents, 4 lb. chocolate at 19 cents, and 1 bag salt for $1.25. Jan. 1, 1855, Mr. Stevens made out his bill. SECTION IX. PROPERTIES OF NUMBERS, TESTS OF DIVISIBILITY, FACTORS, MULTIPLES, DIVISORS. 101. Definitions. (a.) A FACTOR of any given number is such a number as taken an entire number of times will produce the given number; or, the FACTORS of a number are the numbers which multiplied together will produce it. Thus, 2 is a factor of 4, 6, 8, &c. ; 3 is a factor of 6, 9, 12, 15, &c. (b.) A DIVISOR of a number is any number which will exactly divide it. NOTE. Every divisor of a number must be a factor of it, and every factor of a number a divisor of it. The terms factor and divisor, as here used, are only applied to entire numbers. (c.) A PRIME NUMBER is one which has no other factors besides itself and unity. Thus, 1, 2, 3, 5, 7, 11, 13, 17, &c., are prime numbers. (d.) A COMPOSITE NUMBER is one which has other factors besides itself and unity. Thus, 4, 6, 8, 9, 10, 12, 14, 15, 16, &c., are composite numbers. (e.) Any entire number of times a given number is a MULTIPLE of it; or, a MULTIPLE of a number is any number which can be exactly divided by it. Thus, 12 is a multiple of 1, 2, 3, 4, 6, and 12, because it is an exact number of times each of them, or because it can be divided by each without a remainder. (f.) Two numbers are PRIME TO EACH OTHER when they have no common factor. For example, 4 and 9 are prime to each, as are 8 and 15, 24 and 35, &c. Again, 6 and 9 are not prime to each other, because they have the common factor 3; 8 and 12 are not prime to each other, because they have the common factor 4, &c. NOTE. It is obvious from the foregoing, that every number is a factor of all its multiples, and a multiple of all its factors. 102. Demonstration of Principles. Proposition First.- If one of two numbers is a factor of another, it must be a factor of any number of times that other number. For to find any number of times a given number, we have only to multiply the number by some new factor, without striking out any of the former ones. Illustrations. Since 2 is a factor of 12, it must be a factor of any number of times 12, as 24, 36, 48, &c. Since 7 is a factor of 14, it must be a multiple of any number of times 14, as 28, 42, 56, &c. Proposition Second. If each of two numbers is a multiple of a third number, their sum and their difference must also be multiples of that third number. For, adding an exact number of times a given number to, or subtracting it from, an exact number of times the same number, must give an exact number of times that number. 3 times 9, or 27, Illustrations. 8 times 9, or 72, +3 times 9, or 27, = 11 times 9, or 99. So 8 times 9, or 72, = 5 times 9, or 45. Again. Both 12 and 20 are multiples of 4, and so is their sum, 32, and their difference, 8. Both 42 and 28 are multiples of 7, and so is their sum, 70, and their difference, 14. Proposition Third. If one of two numbers is a multiple of a third number, and the other is not, neither their sum nor their difference will be a multiple of that third number. For both the sum and the difference of an entire, and a fractional, number of times a given number, must equal a fractional number of times that given number. Illustrations. 8 times 6, or 48, + 21 times 6, or 15, = or 63. - 101 times 6, 8 times 6, or 48, 21 times 6, or 15, = 51 times 6, or 33. 7 times 9, or 66, — 4 times 9, or 36, = 3 times 9, or 30. 7 times 9, or 66, + 4 times 9, or 36, = 11 times 9, or 102. |