EXPLANATION of the CHARACTERS made use of in this BOOK. X Signs. Names. Significations. Minus, or less, The sign of Subtraction, as 6 - 2 is 4. 12. The Signs of Proportionals, as 2:4:: 6:12. :: Sois, Extraction The Square Root of 9=3 is 3/9=3, and of the Roots, } the Cube Root of 8=2 is 8=2. 6 --4x9=18; signifies, that 6, less 4, multiplied by 9=18. N. B. 82 denotes that S is to be squared. 93 denotes that 9 is to be cubed. ber 4. } The Twelve SIGNS of the ZODIAC. * Libra, the Balance. ve Capricornus, the Goat. 2 Leo, the Lion. Aquarius, the Water-bearer. mm Virgo, the Virgin. * Pisces, the Fishes. TUTOR'S GUIDE; BEING A COMPLETE SYSTEM OF ARITHMETIC. BOOK I. Arithmetic in Whole and Compound Numbers. INTRODUCTION. ARITHMETIC is the science or knowledge of Numbers, which is either Unit, or a multitude of Units. Unit is any thing considered as one, or 1. Digits, or Figures, are the marks by which Numbers are denoted or expressed, and are the nine following, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9: with these there is used the mark 0, called a Cipher, which of itself stands for nothing; but being annexed to the right-hand of a Digit, alters its value; thus, 40 signifies forty, and 400 stands for four hundred, &c. (See the following Table.) Integers, or whole Numbers, are such as express a Number or multitude of things, whereof each is considered as an Unit. Thus, 6 Pounds, 12 Yards, 140 Miles, &c. each of which is called an Integer, or whole Number. Compound Numbers are such as consist of different denominations, as Pounds, Shillings, Pence, and Farthings; or Hundreds, Quarters, Pounds, Ounces, &c. Thus 47). 12s. 6 d. or 4C. 2qrs. 141b. &c. A Fraction, or broken Number, is always less than Unit, as & represents three quarters of any thing or Unit, and g is six eighths of Unit, or 1, &c. Arithmetic, with regard to art and science, consists both in Theory and Practice. Theory considers the nature and quality of Numbers, and demonstrates the reason of practical operations. The Practice is that which shows the method of working by Numbers, so as to be the most useful and expeditious for B TRACTION. business, and has five principal or fundamental Rules for the operation ; viz. 1. NUMERATION, or Notation. 2. Addition. , 3. Sub 4. MULTIPLICATION. 5. Division. Sect. I. NUMERATION TEACHETH to read or express the true value of any Number when written down; and consequently to write down any proposed Number, according to its true value; and this consisteth of two parts: 1. The due order of placing down Figures. 2. The true value of each Figure in its place; both of which are plainly exhibited in the following TABLE. EXAMPLES. Write down the Value of the following Numbers in Words at length, viz. (1) 94 (6) 6040390 (2) 762 (7) 47639121 (3) 3024 790401950 (4) 37460 9) 79041955 (5) 142613 In Figures, express (1) Seventy-seven. (2) Four hundred and ninety. (3) Six thousand and fifty-five. (4) Seventeen thousand seven hundred and nine. (5) Eight hundred thousand and two. (6) Seven millions forty-four thousand and seventy-four. (7) Six hundred and ninety-four millions four hundred thousand and sixty. NOTATION by Roman Numerical Letters. One, five, ten, fifty, hundred, five hundred, thousand. I, V, X, L, C, D, M. When a lesser numerical letter stands before a greater, it must be taken from it; as, I before V or X; and X before L, or C, &c. Thus, four, nine, forty, ninety, &c. IV, IX, XL, XC. When a lesser numerical letter stands after a greater, it is to be added to it. Thus, six, eleven, sixty, one hundred and ten. СХ. A Line drawn over any number less than a thousand signifies so many thousands; as LX, is sixty thousand; C, is C one hundred thousand; M, is one Million, &c. Write down in common Figures the following Numbers, expressed in numerical letters, viz. XIX, CC, DC, DLX. MI, MDCCL, LXX, CX, MD, and MDC. Write down in numerical letters the following Numbers, expressed in common Figures, viz. 29, 104, 419, 1741, 2007, 17678, 10004, and 67 4084. II. ADDITION of INTEGERS TEACHETH to add sundry Numbers together into one Sum, called the Total, RULE. 1. Place all the Numbers of a like name under one another; that is, units under units, tens under tens, hundreds under hundreds, &c. 2. Begin with the Units, and singly collect the Sum of each a |