To express the value of words of number by figures. RULE. Place a figure representing the word in the place which the word reprefents, and where a word is wanting place a cipher, (in its stead; as for tens, hundreds, &c.) this number affix the fign or denomination in which the fum is given. EXAMPLES. What figures are equivalent to fix thoufand-eighty four th h. eighty-four,hths. Dollars & fifty five hundredths? A. 6 0 8 4, 5 5% Express two hundred pounds and thirty four fortieths by figures. A. 2003 £, here both units and tens are wanting, fo 0 0 fupply their defect. Exprefs eleven thousand eleven hundred and eleven by figures. A. 11000, 1100 & 11, 12111. kept in motion, will in a certain time move a certain distance or length, these [viz. time and distance] determine the velocity or swiftness of motion; so the distance, time and motion of any thing in action may be compared with that of any other; as the velocity of sound, of falling bodies, with that of the motion of the earth, planets, &c. • NUMERATION, is the art or act of numbering ; and · Teaches to express numbers by words or characters;' it teaches the different value of figures by their different places, and to read or write any sum or number by these ten characters, 0, 1, 2, 3, 4, 5, 6, 7, 8,9' To express any number by words or characters is the act of numbering; and to know how to express any number by words and characters is the art of numbering; so the act or art of expressing any number or value in any form is numeration; whether the number be great. er or less than what is esteemed an intiger or unit, whether it be of quantity or quality, and whether the ratio be decimal, duodecimal, or any other; therefore the tables of money, weight, &c. seem more naturally to fall under this head than any other; though the different values are more commonly distinguished different names than different places; as . s. d. instead of pounds, tenths, hundredths, &c. From the preceeding quotations it appears that the expressing of numbers in any form is numeration; as one hundred may be expressed by 100, by 10 tens, by 10 E. &c. 1 by zo s, by 20 times 12 pence, &c. the diameter of a circle by,31831 of the cir. &c. 10 tenths by 1, by,1 of ten &c. PART 2d. DECIMAL ARITHMETIC, Is that by which operations are performed with figures whofe values are determined by their distance from unity or the decimal point. SIMPLE ADDITION, Is the collecting or adding together of two or more fimple numbers, to fhow their value in one fum. RULE. Place all the given numbers fo that units may ftand under units or the decimal points under each other; then, begin with the firft right hand column, and add one figure to another, to their fum add the next figure, &c. when the column is added up, place the right hand figure of its fum under the column and add the reft to the fecond column, which add up as before, &c. thus proceed to the laft column, under which place its whole fum ; and place a decimal point in the fum total under those above; this fum will be of the given denomination, & equal in value to all its parts. (See DEM. OF RULES.) PROGF. Add each column downward, or draw a line between any two of the given numbers and add the fum of thofe below the line to those above, and this fum will be equal to the fum total; or add two or more of the given figures together, then add the figures of this fum together, to which add one or more of the given figures, add the figures of this fum together, &c. until all the given figures are exhaufted, fet down the remainder, add the fum total together in the fame manner, and if the work be right its remainder will be like that of the given numbers; or neglect the nines or three in the given number and in the fum total and if the work be right the remainders will be alike. EXAMPLES. Addition and Subtraction Table. Arithmetical Progreffion or Proportion‹ * 4 6 1 2 3 6 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 7 8 9|10|11|12|13|14|15|16|17|18|19|20|21|22] 2 8 9 10 11 12 13 14 15 16 17 18 19 20|21|22|23| 3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 4 10 11 12 13 +15 16 17 18 19 20 21 22 23 24 25 5 8910111213141516171819202122232425,26 6 7 9|10|11|12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 7 To learn the Table for addition. Begin at the left upper corner; fay, 2 and 2 are 4, 3 and 2 are 5, 4 and 2 are 6, &c. then 2 and 3 are 5, 3 and 3 are 6, 4 and 3 are 7, &c. and for fubtraction; (it is unneceffary to go farther than 10 from 19, 9 remains,) fay 2 from 4 and 2 remains, 3 from 5—2, 4 from 6-2, &c. or 2 from 4-2, 2 from 5-3, 2 from 6-4, &c. then, 3 from 5-2, 3 from 6-3, &c. * The numbers, in the table increasing by the addition of an equal number, are in arithmetical progression; and the relation or proportion they bear to each other is arithmetical; i.e. the second number 2 is as much more than the first 1, as the 3d is more than the 2d; and each of the second numbers is as much less than each of the fourth opposit, as each of the third is less than each of the fifth; and 4.. 7::5,.8; and 2 + 3.. 4 + 5 :: 6 † 7..8 +9 ; and 4..3:: 2..1 arithmetically.The common difference or number 4d or d is called the arithmetical ratio. If two arithmetical series, the one ascending; as, 1, 2, 3, 4, 5, the other descending; as 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, whose ratios are equal, be 4d together, their sums, will be severally equal; as, 1, 2, 3, 4, (The numbers which form the 8,7, 6, 5, series are called the terms, the first and last are called Lextremes, the rest, means. 9, 9, 9, 9, In large numbers place a dot opposit each ten, add the r to the next figure & one for each dot to the next column. 2 2121b 23 1924 d. 94 42 7,4, 9 4+ 2,5 3 1 2lb Add 22 Eagles, 33 $, 44d, 55 c, 66 m, together. 22 Add 4. 40. 10d. to 30. 3. 4d. A. 34 43. 14d, What is the value of 44 £. 4d. and 7£ 1% 3d ? Add 275 S. to 1204,7 cts. Σ A 51. 18. 7d. A. 2870,47 dimes. What is the motion of the earth's equator each hour? 69251.31 A.= The fum of the diurnal 1035,64 and annual 68215,67 miles. [Table 13.] SIMPLE SUBTRACTION, IS the taking or fubtracting of one fimple number from another to find their difference: The largest given number, is called the minuend, the lefs, the Jubtrahend, and their difference, the remainder. RULE. Place the lefs given number under the greater, fo that units may ftand under units, or the decimal points under each other; then, find how many the upper right hand figure exceeds the lower; place this fum or difference underneath; but if the lower figure is the largest subtract it from ten and add this difference to the upper figure, or add ten to the upper figure and fubtract the lower from this fum, fet down the difference, and add one to the next lower figure or diminish the upper figure one, and subtract as before; then, place a point under those above, and the difference or answer will be in the given denomination. Such a figure as will increase the lower figure to the upper is always the true difference. (See DEMONSTRATION OF RULES.) PROOF. Add the difference to the fubtrahend and their fum will be equal to the minuend, or fubtract it from the minuend and the difference will be equal to the fubtrahend; or add all the figures together |