ARITHMETICAL INSTRUCTOR. ARITHMETIC.* 1. The object of Arithmetic is, to represent numbers in a concise and distinct manner by characters, and to simplify, by means of such characters, the methods of calculation. 2. Arithmetic may be called an art, when it merely teaches the methods of performing the practical operations to which numbers are subjected. * According to Ash's English Dictionary, Arithmetic is derived from the Greek, (Arithmos, number, and Metreo, to measure,) the science of numbers, the art of computa tion. Samuel Webber, in his Mathematics, says, that number is the abstract ratio of one quantity to another of the same kind, taken for unity; and that Arithmetic, as a science, is the theory of numbers, and as an art, the method of practical operations in numbers. The Abbot Demolieres says, that quantity discrete is called number, of which the most simple is unity, or one; and that science which treats of number or quantity discrete is called Arithmetic. B 3. It may be called a science, when it demonstrates the various properties and relations of num bers. 4 4. The nature of Arithmetical operations is, to find from numbers given, others which are required. 5. There are five principal rules in Arithmetic, viz. Notation, Addition, Subtraction, Multiplication, and Division. 6. To these belong Numeration, which is the method of expressing any number in words. NOTATION. 1. Notation of numbers is, the proper method of writing them. 2. Numbers are usually expressed by certain Arabic characters, called figures, and the Roman letters. 3. The Arabic figures are thus expressed, viz. 1, one; 2, two; 3, three; 4, four; 5, five; 6, six; 7, seven; 8, eight; 9, nine; 0, cypher. 4. These ten characters, being properly disposed, will conveniently express any number, however great. 5. The Roman letters will, also, express any number, without limitation; but are chiefly used to mark dates, and the chapters and sections of books. 6. The following letters are used to express numbers, viz. NUMERATION.* Units. Tens. Hundreds of thousands of millions. Hundreds of thousands. Thousands. F Billions. 1 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 2 3 4 3 2 1 Hundreds of thousands of billions. Tens of thousands of billions. ∞ Hundreds of billions. Hundreds of thousands of trillions. Tens of thousands of trillions. Thousands of trillions. Hundreds of trillions. Tens of trillions. Trillions. Quadrillions. 360 10530 6200000 370492000 Three hundred and sixty, Ten thousand five hundred and thirty, Six millions two hundred thousand, Three hundred and seventy millions four hundred and ninety-two thousand, It is required to write down in proper figures the numbers expressed by the following words, viz. Twenty-nine. One hundred and nineteen. Any number of figures whatever, may be accurately numerated, by dividing them into periods of six figures each, as in the above scheme, repeating millions of millions, for billions, millions of millions of millions for trillions, &c. as often as the figures 2, 3, 4, &c. placed underneath, in the above scheme, designates. Three thousand and nine. Ten thousand and nineteen. Six hundred thousand three hundred. Nine hundred millions, three hundred thousand three hundred and three. Seventy-five billions. One hundred quadrillions. It is required to write down in proper words the following numbers, viz. The diameters of our Moon," Mercury, Georgian Sidus,. The diameter of the sun, Jupiter, and Georgian Sidus, in miles by the numbers oppo. site to each, viz. by the numbers oppo- Are Are expressed in miles site to each, viz. expressed 2180. 2600. 7906. 7970. 4444. 81000. 67000 35000. 763000. 240000. 125000000. 426000000.. 780000000. 1565000000.. Archimedes said, “give me a place to stand, and I shall remove the Earth." The probable weight which Archimedes would have had to raise, is expressed by the following number of pounds, viz. 400 000 000 000 000 000 000 000. How many? |