## The First Part of the United States Arithmetic Designed for Schools |

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The First Part of the United States Arithmetic: Designed for Schools William Vogdes No preview available - 2016 |

### Common terms and phrases

1hhd 6fur acres added addition amount Arithmetic bales barrels Bought bushels called carry cents cloth compound containing cords cost denominations difference Divide dividend division divisor dollars dozen earth elapsed equal EXAMPLES excess EXERCISES expressed feet figures five flour four fourth gained gallons give given grains greater half hand hogsheads hundred imports inches land length less lower means measure merchant method miles millions mills months multiplicand multiplier nines operation ounces paid pair person Philadelphia piece population pounds prime factors proceed Proof purchased quantity quarters quotient receive Reduce remainder Resolve RULE School silver sold square square miles stand subtraction sugar Supposing tens thing third thousand tons United weeks weight whole wine worth write yards York

### Popular passages

Page 61 - TABLE. 4 nails, (na.) or 9 inches, make 1 quarter, marked qr. 4 quarters, or 36 inches, - 1 yard, - - - - yd. 3 quarters, ------ 1 ell Flemish, - - E. Fl 5 quarters, ------ 1 ell English, - - EE 6 quarters, ------ 1 ell French, - - E. Fr 27.

Page 47 - Multiply the last remainder by the preceding divisor, or last but one, and to the product add the preceding remainder ; multiply this sum by the next preceding divisor, and to the product add the next preceding remainder ; and so on, till you have gone backward through all the divisors and remainders to the first.

Page 15 - ... any number divided by 9, will leave the same remainder as the sum of its figures, or digits, divided by 9, which may be thus demonstrated.

Page 62 - LIQUID MEASURE 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt...

Page 54 - Scale: 4 farthings (far.) = 1 penny (d.); 12 pence = 1 shilling (s.) ; 20 shillings — 1 pound (£). 156.

Page 34 - The reason of this method is obvious ; for any number multiplied by the component parts of another, must give the same product as if it were multiplied by that number...

Page 63 - ... ..1 gallon, gal 36 gallons " .1 barrel, bar. 54 gallons

Page 40 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers. Let a denote the base of the system ; also, let m and n be any two numbers, and x and y their logarithms. Then, by the definition of logarithms, we have ax=m, (1.) a?in.

Page 91 - Carry the integers, thus found, to the product of the next higher denomination, with which proceed as before ; and so on, through all the denominations -to the highest; then this product, together with the several remainders, taken as one number, will be the whole amount required.

Page 49 - Divide the number by any prime number which will divide it without any remainder ; then divide the quotient in the same way, and so continue until a quotient is obtained which is a prime. Then will the successive divisors, together with the last quotient, be the prime factors required.