ARITHMETIC. ARITHMETIC is the fcience of calculating by numbers; it explains the nature of figures and demonftrates the principles and caufes on which their effects depend. Arithmetic is alfo the art of exprefiing numbers by certain characters and producing different effects from the fame characters or the fame effects from different characters; for which purposes it is effentially divided into three PARTS; viz. Numeration, Simple and Compound Arithmetic; each of the two latter divifions is fubdivided into four principal RULES; viz. Addition, Subtraction, Multiplication and Divifion; and the values of their refults, &c. are feverally afcertained by Numeration, Numeration is the art or act of afcertaining and exprefsing the value of figures or numbers, according to their definite meaning, and local fituation or diftance from the standard wnity in decimal or fimple arithmetic, and according to the divifion of the integer or unit in vulgar or compound arithmetic. Decimal or Simple Numeration is that in which the relative value of every figure is determined by its diftance from units; which is a term uled to fignify the fixed place of the first figure at the right hand of integers or at the left of the decimal point, in which a figure has merely its fimple value; the fecond place is called tens in which a figure has ten times its fimple value; the third hundreds, &c. The firft place at the right of the point is termed tenths, in which a figure has one tenth of its fimple value, ie. tenths of the integer; the fecond place is called hundredths, &c. So each figure increases or decreafes by removal toward the left or right in a ten-fold proportion, and the whole fum may be increased or decreafed ten-fold by removing the point one place to the left or right. The above remarks appear in the following tables.. • Septillions sextillions Quintillions • Quatrillions hunds of thous of bs billions ∞ hunds of thous of ms tens of thous of ms thousands of ms hundreds of ms tens of ms millions thousands bund of E hunds of thousands E of E suan co units tenths hundred thousandths ten thousandths thousandths Chundredths ⚫ millionths ⚫ billionths trillionths, &c 2 76 8 9 10 3 5 6 2 0 9 4 7 6 0 8 4,5 5 0 7 9 6 th of th of th of th of th of th Vulgar or Compound Numeration is the numbering of fractions or irregular parts; in which the relative value of every part is determined by the number of parts the integer or unit is divided and fubdivided into; which parts are called the divifor or denominator; which in English and other divifions is known by divers names; as, twentieths are known by fhillings, 12ths of fhillings (or 20ths) by pence, 16ths and. 12ths by ounces and inches, &c. as 10 ten 10 8 8 20 twentieths of a pound shillings, 12 of a ftinelics or 8 in 161-4 oz In fuch cafes as the preceding it is only neceffary that the dividend or numerator, which is the value of the given fum,, (in thofe parts of the integer,) fhould be expreffed in figures; but a divifor that is not generally known as above fhould be placed under a line with the dividend or given value over it ass or four parts of five. 34 parts of 40, nd four 34 Vulgar Fractions are of three kinds; viz. Regular or proper fractions, i.e. ther the largeft; as, 4, 12, 10. Irregular or improper fractions, i.e. ther not the largeft; as, 21. Compound fractions, i.e. fractions of fractions or parts of fractions; as, of of of a pound= 3 farthings. 12 of feet=10 fq. in. or 44 ft. Compound fractions include all the following, T T 1 10 Tables of English Money, Weights and Measures, in which the proportions are given which one bears to another, and the value of each one compared with another. |