## The First Part of the United States Arithmetic Designed for SchoolsE.C. & J. Biddle, 1857 - 112 pages |

### Other editions - View all

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

### Common terms and phrases

1cwt 1hhd 2fur 5fur 6fur 7fur acres bales barrels of flour bushels cents ciphers composite number cords cost cubic difference divided by 9 dividend division divisor dollars dozen drachms dry measure elapsed ells equal excess of 9s excess of nines feet furlongs gallons given numbers greater Grenada half eagles hogsheads hundred inches integers John Sobieski less number method of proof millions mills minuend MISCELLANEOUS EXERCISES multiplicand multiplier number of examples number of square Ohhd ounces paid pair Pennsylvania PETER HAINES Philadelphia piece pints population Port wine pounds prime factors prime number purchased quantity quarts quotient quotient figure reams receive remainder Repeat the table RULE School sold square miles subtraction sugar Thousand 321 tons troy weight United States Arithmetic Vogdes weight whole number yards of cloth

### 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.