3-28-46 PREFACE. 54896 THE compiler does not pretend to any thing original in the following work, and if the question were asked, why another Arithmetic should be published while so many are already in use? he would reply, that the deficiency of rules in some Arithmetics and the obscurity in others, seem to render difficult for the learner to make any considerable progress without much oral instruction. To remed this; the compiler has endeavoured to adapt the rules to the understanding of the learner, and he confidently believes, that a scholar of common capacity may, by a careful attention to the rules, and the questions of which a solution ist given, gain a competent knowledge of Arithmetic, with but very little assistance from his teacher. Many rules that seem to be more calculated to grai ify curiosity than to be useful, have been omitted in this work, and nothing is admitted but what seems to be absolutely necessary for every person to un derstand. The work, with its many errors, is presented to the public, not doubting but if it has any merits it will share the patronage of the candid; if it has none, it will be rejected by them.-All the errors that have been noticed,have been corrected in an Errata.—There are, undoubtedly, many more, that have not come to light. Any person, who may discover any errors and will kindly point them out, or suggest any practicable improvement in the Arithmetical Catechism, shall receive the thanks of the COMPILER. ARITHMETICAL CHARACTERS. Signifies equal to. As 1 cwt. 112 lb. that is, 1 cwt Signifies Plus or more. The sign of Addition, as to 14. Signifies Minus or less. The sign of Subtraction; as 10-6-4, that is, from 10 subtract 6, remainder equal to 4, or 10 minus 6 equal to 4. Is the sign of Multiplication; as, 8×8=64. That is, 8 multiplied by 8 is euqal to 64. Is the sign of Division; as 6488; that is 64 divided by 8 the quotient is equal to 8. :::: Proportion: as, 3 6:9: 18; that is, as 3 is to 6 so is 9 to 18. 3 Frefixed to any number, signifies that the square Prefixed to any number, signifies that the cube PAGE 14—21. Practical Question for 1775 read 1776. 37-24 example, for 14 ez. read 11 oz. 33-2d do. for 16 dr. read 10 dr. 3 line from the bottom,for 9roods read 4roods 43-for 23 ft. make 1 yd., read 27 ft. make 1 yd. 45-21 example, for A. bbl. read B. bbl. ARITHMETIC. 1. QUESTION. What is Arithmetic? ANSWER. The art or science which treats of num bers; and is of two kinds, theoretical and practical. 2. Q. What is Theoretical Arithmetic? A. It is that which explains the nature and quality of numbers, and demonstrates the reason of practical operations. 3. Q. What is Practical Arithmetic ? A. It is that which shews the method of working by numbers, so as to be most useful and expeditious for business. 4. Q. On entering upon the study of Arithmetic, what is the first thing that requires attention? A. Notation or Numeration. 5. Q. What is Notation? A. The art of expressing numbers by certain characters or figures; of which there are two methods. The Roman method by letters, and the Arabic method by figures. 6. Q. Which is the method of general use? A. The Arabic method. 7. Q. By how many figures are numbers expressed? A. Ten, viz. 1, 2, 3, 4, 5, 8, 7, 89 9, 0 One, two, three, four, five, six, seven, eight, nine,cypher. called digits. NUMERATION. 1. Q. What does Numeration teach? A. It teaches to read in words, any sum or number proposed in figures. 2. Q. How do you express in words, numbers proposed in figures? A. To the simple value of each figure, join the name of its place, beginning at the left hand and reading towards the right. NUMERATION TABLE. 3 Billions. Co Hund. of Thousands of Millions ∞ Tens. Units 0 1 3. What is the use of the words at the head of the table? A. They shew the signification of the figures against which they stand. 4. 3294, 234567, 301009009.• How do you write or express in figures, numbers which are given in words? A. Write down the figures as their values are expressed, beginning at the right hand or place of units, and supply any deficiency in the order with cyphers. EXAMPLES. Write down in proper figures the following humbers. Seventeen, Three hundred and twenty-one, Eight thousand four hundred and six, Sixty thousand six hundred and sixty, Three hundred and nine thousand five hundred and four, Forty-four millions and forty, Nine hundred and seven millions nine hundred and seventy, Nine billions nine millions nine thousand nine hundred and nine. Sixteen thousand, Sixteen hundred, Sixteen. One hundred & four thousand Forty. 5. Q. What are the fundamental rules of Arithmetic ? A. Addition, Subtraction, Multiplication, and Di vision. |