The Explication of Some Marks, used in this compendium. Two parallel lines are the marks of Equality ; as 12 oz=1 lb. signifies that 12 ounces are equal to 1 pound. 4+2=6: i. e. 4 more 2, are equal to 6. 2=2 : i. e. 4 less 2, are equal to 2. A line between two points, or between four points, is the sign of division ; as 4-2 or 4;2=2 :i. e. 4 divided by 2, are equal to 2. The reversed paren) (thesis denotes division also; as 2)4(2 : i. e. 4 divid ed by 2, is equal to 2. *34Numbers placed in a fraction-like manner, do like wise denote division; the lower heing the divisorg. and the upper number the divideod. :: Four points, set in the middle of four numbers, de note them to be proportioned to one another, by the rule of three; as 2..4::8..16: that is, as two is to 4, so is 8 to 16. N. B. Some Masters instead of points use long strokes to keep the terms separate, but it is wrong to do so: for the two points between the first and second terms, and also between the third and the fourth, shew that the two first and the two last terms are in the same proportion. And whereas four points are put between ihe second and third terms, they serve to disjoint them, and shew that the second and third, and first and fourth terms, are not in the same direct proportion to each other as are those before mentioned. OF NOTATION. Q. WHAT is Notation? A. It is the Art of expressing Numbers by certain Characters or Figures. Q. What is the use of Notation ? A. Notation teaches us to read and write Numbers by their true V e. Q. How many sorts of Characters or Figures are Numbers usually expressed by. A. Two, viz. the Arabic Figures and the Latin Letters. Q. How are the Arabie Figures expressed ? Ă. The Arabic Figures are thus expressed ; One 1, Two 2, Three 3, Four 4, Five 5, Six 6, Seven 7, Eight 8, Nine 9, Nought or Cipher o. And this is the Notation, or reading and writing, of every single Figure. Q. How far may the use of these Figures be extended? Ă. These ten Characters, or figures, may be used to express all manner of Numbers, from the least to the greatest that can be conceived; even without end. Q. How many Figures are sufficient to express most ordinary concerns ? A. Nine ; and, therefore, the table of Notation commonly extends no further than to nine places. Q. Why does it consist of nine places rather than of eight or ten ? A. Because they make up three eren Periods. X. A Period is a quantity expressed by three Figures, whereof the first to the right-hand signifies so many units or single things; the second so many tens; and the third so many hundreds. Q. Why are three figures called a Period? Å. Because if the number be increased above three places, there is still the same periodical return of the value of those places, and every third figare to the lefthand, will always be bundreds, if it be ever so far extended. Q. Is an Unit, or one, a number? X. An Unit is a number, because it may properly answer the question how many ? Q. Give an example or two. Å. How many Gods do we believe? The answer is One. How many Sundays in the compass of a week? Answ. One, PART IV.-QUESTIONS Pagej A short Collection of pleam sant and diverting foregoing rules is Questions Page 184 PART V.-OF DUODECIMALS. ADDITION Subtraction, 185 Multiplication 178 194 The Explication of Some Marks, 'used in this compendium. Two parallel lines are the marks of Equality ; as 12 oz=1 lb. signifies that 12 ounces are equal to 1 pound. +Saint George's cross signifies more, or addition, as 4+2=6: i. e. 4 more 2, are equal to 6. A strait line signifies less, or substraetion; as 4 2=2 :i. e. 4 less 2, are equal to 2. x Saiut Andrew's cross, denotes multiplication, as 4X2=8. i. e. 4 multiplied by 2, are equal to 8. A line between two points, or between four points, is the sign of division ; as 4+2 or 4-2=2: i. e. 4 divided by 2, are equal to 2. The reversed paren) (thesis denotes division also; as 2)4(2:i. e. 4 dividl ed by 2, is equal to 2. 179 Numbers placed in a fraction-like manner, do like wise denote division; the lower being the divisor, and the upper number the dividend. :: Four points, set in the middle of four numbers, dea. note them to be proportioned to one another, by the rule of three ; as 2..4::83.16: that is, as two is to 4, so is 8 to 16. N. B. Some Masters instead of points use long strokes to keep the terms separate, but it is wrong to do so : for the two points between the first and second terms, and also between the third and the fourth, shew that the two first and the two last terms are in the same proportion. And whereas four points are put between ihe second and third terms, they serve to disjoint them, and shew that the second and third, and first and fourth terms, are not in the same direct proportion to each other as are those before mentioned. OF NOTATION. A. It is the Art of expressing Numbers by certain Characters or Figures. Q. What is the use of Notation? A. Notation teaches us to read and write Numbers by their true Value. Q. How many sorts of Characters or Figures are Numbers usually expressed by. A. Two, viz. the Arabic Figures and the Latin Letters. Q. How are the Arabic Figures expressed ? A. T'he Arabic Figures are thus expressed; One 1, Two 2, Three 3. Four 4, Five 5, Six 6, Seven 7, Eight 8, Nine 9, Nought or Cipher 0. And this is the Notation, or reading and writing, of every single Figure. Q. How far may the use of these Figures be extended ? Ā. These ten Characters, or f'igures, may be used to express all manner of Numbers, from the least to the greatest that can be conceived; even without end. Q. How many Figures are sufficient to express most ordinary concerns ? A. Nine ; and, therefore, the table of Notation commonly extends no further than to nine places. Q. Why does it consist of nine places rather than of eight or ten? A. Because they make up three even Periods. A. A Period is a quantity expressed by three Figures, whereof the first to the right-hand signifies so many units or single things ; the second so many tens; and the third so many hundreds. Q. Why are three figures called a Period? Å. Because if the nnmber be increased above three places, there is still the same periodical return of the value of those places, and every third figure to the lefthand, will always be bundreds, if it be ever so far extended. Q. Is an Unit, or one, a number? X. An Unit is a number, because it may properly answer the question how many ? Q. Give an example or two. Ā. How many Gods 'do we believe? The answer is One. How many Surdays in the compass of a week.t Answ. One, Q. In what nature or proportion of value, do Numbers increase from the Unit's place to the left hand ? 1. By Ten. Q. If two figures are given to be read together, low must they be valued ? A. The first figure towards the right hand is Units, and the next to that is so many tens as 89, eighty-nine. Where 9 is in the place of units, and 8 is in the place of tens ; for eight teus are properly called eighty. Q. If three figures or a whole period be given, how is it to be valued ! 1. Beginning at the last figure on the right hand, I value them units, tens, hundreds ; as 789, seven hundred and eighty-nine Note 1. As 'every third figure from the place of units, bears the name of hundreds : so for any great sum to be distinguished into periods, (as in the following tables) will be of good use to the learner, in the easier valuing and expressing that sum. 2. There is also another sort of periods, which some distinguish thus, viz. millions, millions of millions, &c. and others thus, viz. millions, billions, trillions, &c. each period consisting of 6 places, but as periods of this kind seldom or never occur in business, it is sufficient only to mention them in this place without saying any thing further about them. TABLE II. TABLE I. 9 4 8 9 8 9 9 6 5 98 9 3 4.72 9 7 8 9 4 8 9 1 S 7 8 9 7 8 9 7 31 2 3 6 9 7 8 9 7 8 9 1 2 7 1 4 8 89 89 8 9 1 9 2 1 6 4 8 9 7 8 9 7 8 9 5 7 3 1 2 9 8 4 2 Note. See the notation of Numbers by Latin Letters, in the New Guide to the English Tongue, p E8. B |