Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/500

 4*8 A R I T H M E T I C K. Examp. 2. In working by the inverted method, for the repeating 0 in the multiplier, take of the multiplicand. The Divide 97 1 6 = 97.125 refuit wants very little of the true anfwer. by 2 3 =2.25 and the quot by x8 6 =18.5 Examp, 2. 18.5) 2.25)97.125(43.10(24 Multiply 18 6 by 2 4, and 2 3 continually. 900 • * 370 12 712 616 4.0 18 6—18.5 2.3' 2 4= 2.3* 18.5 675 555 2 3 = 2.25 375 225 *61 1806 2?33 1500 1350 2 4 43.10 2.25 i 50 Sexagesimals. 21583' Decimal praftice might likewife be ufed to good pur86333 pofe in the arithmetic of fexagefimals, as it would fhorten 863533 and facilitate the operations. Sexagefimals, ftrittly fpeaking, are degrees, minutes, feconds, thirds, 6^. where each degree is divided into 12 ^/". 97 60 minutes, and each minute into 60 fecpnds, <foc.; but under this title is alfo ufually comprehended the divifion 1.500 of a fign into 30 degrees. They are commonly marked 12 as under. Signs, deg. min. fee. thirds. 7 24 36 54 48 <bc. Sexagefimals properly belong to aftronomy, being ufed IL Divifion. in computations of motion and time, where the degree of motion, and hour of time, are equally divided into Examp, 1. 60 minutes. The preference of the decimal method to that of the fexagefimal will appear from the following Divide 452 8 11=452.7430^ f example of addition done both ways. by 18 s = i8.4I0= *|^ Sexagefimally. Decimally. Signs. ° * 5. 18.4*0)4527.430/5 10 20 47 17 = 10.69293,518, 1841 452.7430/ 7 18 50 40= 7.62814,814, 9 25 30 28 = 9.85018,518, 16575)407468.750(24.583 11 10 40 50= 11.35601,851, 33150 12 3 x5 49 7 = 3•52728,703, 75968 7.000 From the above example it is obvious, that even in 66300 addition the decimal operation is more fimple and eafy than the fexagefimal, efpecially if care be taken to ufe 96687 no more decimal places than what are abfolutely nocef82875 ' fary. Anf. 24 7 But in multiplication and divifion the advantage of the decimal method is ftill greater; for in the fexagefimaf 132600 way the operation is extremely tedious; whereas, by working decimally, it is performed in the fame manner, 55250 and with the fame eafe, as in duodecimals. 49725. Vulgar Fractions. Decimal practice may fometimes be profitably ufed in the
 * 38125
 * 5525