The entire separation of mental and written exercises, and the placing of them in different volumes, as adopted in several popular works, the author deems objectionable, as it is calculated to make two distinct impressions of one and the same process, and therefore less likely to lead to a full understanding of the principles involved. In this work the mental and written exercises are placed together under one rule, and questions are appended by which the learner may examine and teach himself. The principles of mensuration, embracing artificers' work, have been introduced, and it is believed treated of, at sufficient length to prove of lasting value to the future mechanic, who, as a schoolboy, may master these pages. In the hope that it may not be found wanting in the points above set forth, this work is now submitted to the examination of the public. The first 104 pages of this work, embracing the rules preceding FRACTIONS, together with four pages of miscellaneous oral exercises, and twelve pages of miscellaneous written exercises, are published as THE FIRST PART OF THE UNITED STATES ARITHMETIC. The vast number of pupils engaged in studying the elementary rules of Arithmetic, who never progress to the more advanced rules, and the greater length of time generally devoted to the former than the latter, by those who study the whole of the subject, satisfactorily prove that such a division will subserve economy; and therefore, it is presumed, will meet the approval of teachers and directors of schools. Philadelphia, February, 1845. A KEY to the United States Arithmetic, designed for the use of teachers, has been published. Cylinder, - Pyramid, CHARACTERS USED IN THIS WORK. This sign denotes addition; and is read plus, as 4+7; that is, 4 added to 7, which is equal to 11. - This sign denotes subtraction; and is read minus, as 9-4; that is, from 9 take 4, or 9 minus 4, which is equal to 5. × The sign of multiplication; and is read multiplied by, as 5×3; that is, 5 multiplied by 3, which is equal to 15. The sign of division; and is read divided by, as 6÷2; that is, 6 is to be divided by 2, which is equal to 3. The sign of equality; and is read equal to, as 2+4 =6; that is, 2 added to 4, are equal to 6. is to so is: The sign of proportion; thus, 3 : 4 : 68; that is, as 3 is to 4 so is 6 to 8. 42, 43, 44. Signs of involution; denoting that 4 is to be squared, cubed, or raised to the 4th power. |