12. A schoolmafter being asked how many scholars he had, anfwered: If I had as many, and as many, and as many, I fhould have 99; how many had he? 13. When I wrote this, if to my age you add, ,,(thereof) with 3 more, The number 25 will then be had ; Ingenious Tyro's, pray my age explore. 14. What number is that, which added to its+its+ +3, makes 108? 15. Admit there is 2121. 14 s. 7 d. to be divided amongst a captain, four men, and a boy; the captain to have a share and half; the men each a fhare, and the boy of a share; what ought each perfon to have? 9 1 = 2 = 2 capt. ÷ = 24 men, and boy, 6 Then 2+244 6 2 + =35=2121. 145. 7d. = 51055d, 3551055(306330-8752%= 35) 51055 (3 =8752=361. 8 s. 43 d. 35 1. s. d. 16. There is a ciftern with three unequal cocks, containing 60 gallons of water; and if the greatest cock be opened, it will be empty in one hour; and if the fecond cock be opened, it will be empty in two hours; if the third be opened, it will be empty in three hours: now I demand in what time it will be empty, if all run together? The firft empties 1 ciftern in an The fecond 2 hour = 9 उ 2 their fum all 11\60/360 17. A gentleman has an orchard of fruit trees, one-half of the trees bearing apples, one-fourth pears, one-fixth plums, and one-fifty of them bearing cherries; how many fruit trees in all grow in the said orchard? 18. Five perfons difcourfing about their ages, faid the fecond to the firft, my age is the double of your's; and faid the third to the firit, my age is as much, and as much as your's; then faid the fourth to the second and third, my age is as much as both yours added together; but faid the fifth, my age is three times as much as the age of the firft, and the fum of all our ages make just 168 years; what was the age of each? T SECT. I. - NOTATION. HE word decimal is derived from decem (ten) and denotes the nature of its numbers; because the integer, or whole thing, whether it be coin, weight, measure, time, &c. is fuppofed to be divided into ten equal parts, and every one of those parts into ten other equal parts, &c. ad infinitum. The integer being thus divided by imagination into 10, 100, 1000, 10000, &c. is the denominator to the decimal fraction : 17 5 Thus, T, THOS, 10000, &c. Thefe denominators are feldom or never fet down, but only the numerators; and when the numerators do not confift of fo many places as the denominator hath cyphers, the faid places in the numerator must be fupplied by cyphers prefixed on the left-hand. So is wrote .3, T is .05, is .017, and is .0051, &c. 17 3 10 Alfo mixed numbers are expreffed thus, viz. 8.7 is 8 and 7 tenths, 59.017 is 59 and 17 thousandths, or parts of a thousand, &c. Cyphers at the end, namely at the right-hand of a decimal, do neither augment or diminish its value; for 5, .50, .500, 5000, and 50000, are decimals having the fame value, being each equal to, as may be found by abbreviation of vulgar fractions. Cyphers prefixed to decimals, decrease their value in a tenfold proportion, by removing them further from the integer. Thus .55 tenth parts. .05 5 parts of an hundred. .0055 parts of a thousand. .00055 parts of ten thousand. .000055 parts of an hundred thoufand, &c. In whole numbers, the first place above (that is, on the left-hand of) the place of units, fignifies tens of units; but in fractions, the first place beneath (that is, on the right-hand of) the place of units, denotes tenth-parts of 1, or unity, and is called the firft place of decimal parts, or place of primes; likewife the fecond place above the place of units, fignifies hundreds of units; but the fecond place beneath the place of units, expreffes hundredth parts of unity, and is called the second place of decimals, or place of seconds; fo that as the value of the places in integers afcend in a tenfold proportion from the place of units towards the lefthand, fo the value of the places of decimals defcend in a tenfold proportion beneath the place of units towards the right-hand. A TA It may be obferved by the foregoing table, that the places of integers, or whole numbers, are separated from the decimal parts by a point, that the numbers on the left-hand of the point expreffes 872365 integers, or units; and that the number on the right-hand of the point fhews .82353785 parts of 1 (or an integer) fuppofed to be divided into 100000000 equal parts. Hence, if the feparating point, in any mixed or fractional number, be moved one place towards the left-hand, then every figure, and confequently the whole expreffion, is but a tenth part of what it was before; that is, it is divided by 10; if it be moved two places, it is divided by 100; if three places, by 1000, &c. But if the feparating point be moved towards the right-hand, then the whole expreffion is multiplied by 10, 100, 1000, &c. according as it is moved one, two, or three places. There are several ways of reading or expreffing a decimal, as fuppofing the decimal parts in the table were to be read in words, viz. .82353785. First, They may be reduced to, and exprefs as vulgar 82353785 fractions, viz. 100000000 Secondly, By calling them primes, feconds, &c. according to their distance from the feparating point, viz. 8 primes, 2 feconds, 3 thirds, 5 fourths, 3 fifths, 7 fixths, 8 fevenths, and 5 eighths. Thirdly, Thus 82 millions, 353 thousand, 785 eights. Fourthly, Or thus, 8, 2, 3, 5, 3, 7, 8, 5 of a decimal. SECT, |