Origin of measures of length, of surface, of capacity and of solidity, 136 Calculations in simple and compound numbers compared, THE FRENCH MONEY, WEIGHTS AND MEASURES, New York & Connecticut do. 140 RULE OF THREE by Analysis, 142 FRACTIONS,-general principles, To reduce them to their lowest terms, Prime numbers—measures to determine the measures To find common measures-a greatest com. meas. Multiples--a least com. mult., Multiplication,-a Fraction by a whole number, To multiply a Fraction by a Fraction, FELLOWSHIP,-simple and compound, by analysis and ratio, 159–61 Division,-a Fraction by a Fraction, To reduce whole numbers to Fractions of higher denominations, 167 fractions to do. of lower denom. fractions to whole nnmbers of lower denom. 170 To reduce Vulgar Fractions to Decimals, REPETENDS, OR CIRCULATING DECIMALS, 175 & 78 To reduce whole numbers to decimals of bigher denominations, 176 Contraction for Sterling Money, Contraction in Multiplication, To reduce decimals to whole numbers, of lower denom., 182 Contraction for Sterling Money, Another mode of reducing whole numbers to decimals of higher denom., of} Table, showing comparative values of currencies, TIME, RATE, and int. given, to find PRIN., PRINCIPAL, INT, and time given, to find RATE, Concise rules for finding decimals of time, Prin. Rate, and INT. given, to find TIME, AMT., RATE and TIME given, to find PRIN. DISCOUNT,—by division, and by multiplication, Mode of discounting in banks, 222 Contraction in finding int. by first obtaining it at 12 per cent., 223 To find interest on Sterling Money, PROFIT AND LOSS, when allowance is made for TIME. To calculate present worths at comp. int., Notes WITH ENDORSEMENTS, com. rule, RULE OF THREE, direct and inverse, explained, FELLOWSHIP,—simple, by proportion, CONJOINED PROPORTION, or the CHAIN ROLE, FellowSHIP,-compound, by proportion, CUBE ANNUITIES,--at simple interest, Table of multipliers for finding amounts, To find what annuity a given sum will buy, PERMUTATION.-to find how many permutations can be made of a given number of things, To find how many, when a given number is taken at a time, 281 OBSERVATIONS, &c.-ancient mode of calculating, Roman ABACUS, and Chinese Swan-PAN, Essential and accidental properties of numbers, Notions of Pythagoras and his disciples, ERRATA. In a small part of the impression, p. 82. 3d line in ex. 87, for 65 In & Lxxxix, the rule called the Massachusetts rule is erroneously How many anchors do you see here? Ans. ONE. How many ropes are there, fastened to the anchor ? Now there is a single anchor, and a single rope ; and each of these single things, you tell me, is ONE. Then, what is a single thing called? Hence, A SINGLE THING OF ANY KIND IS CALLED ONE THING, OR ONE. Also A SINGLE THING OF ANY KIND IS OFTEN CALLED A UNIT, OR UNITY. Thus, the anchor in the picture above is a unit. If there were another anchor in the picture, how many anchors would there be ? Ans. TWO. How many sheaves of wheat are there here? How many hands have you? How many thumbs? How many eyes? How many feet? When you see one thing, and one more together, what do you call them ? Hence, ONE UNIT AND ONE MORE ARE CALLED TWO; that is, ONE AND ONE ARE TWO. If there were one more sheaf in the last picture, how many sheaves would there be ? Ans. THREE. How many pairs of snuffers are there here? If you had another hand, how many hands would you have? If you had another eye, how many eyes would you have? When you see two things and one more together, what do you call them? Hence, TWO UNITS AND ONE MORE ARE CALLED THREE ; that is, TWO AND ONE ARE THREE. If there were another pair of snuffers in the last picture, how many would there be ? Ans. FOUR. How many hammers are there here? TTTT If you count your hands and feet together, how many have you? When you see three things and one more together, what do you call them? Hence, THREE UNITS AND ONE MORE ARE CALLED FOUR; that is, THREE AND ONE ARE FOUR. If there were another hammer in the last picture, how many would there be ? Ans. FIVE. |