The New Complete System of Arithmetick: Composed for the Use of the Citizens of the United States |
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Page 241
... extremes . And if any three quantities , 2 , 4 , 6 , be in Arithmet- ical Proportion , the double of the mean is equal to the fum of the extremes . THEOREM 2. - In any continued arithmetical propor- tion , 1 , 3 , 5 , 7 , 9 , 11 , the ...
... extremes . And if any three quantities , 2 , 4 , 6 , be in Arithmet- ical Proportion , the double of the mean is equal to the fum of the extremes . THEOREM 2. - In any continued arithmetical propor- tion , 1 , 3 , 5 , 7 , 9 , 11 , the ...
Page 242
... extremes , and the other terms the means Any three of the five following things being given , the other two may be easily be found . 1. The first term . 2. The laft term . 3. The number of terms . 4. The common difference . 5. The fum ...
... extremes , and the other terms the means Any three of the five following things being given , the other two may be easily be found . 1. The first term . 2. The laft term . 3. The number of terms . 4. The common difference . 5. The fum ...
Page 243
... extremes by the number of terms lefs i , and the quotient will be the com- mon difference fought . I. EXAMPLES . The extremes are 3 and 39 , and the number of terms is 19 ; What is the common difference ? 39 ) Ex- 3 tremes . 36 Divide ...
... extremes by the number of terms lefs i , and the quotient will be the com- mon difference fought . I. EXAMPLES . The extremes are 3 and 39 , and the number of terms is 19 ; What is the common difference ? 39 ) Ex- 3 tremes . 36 Divide ...
Page 244
... extremes of an arithmetical feries are 3 and 39 , and the number of terms 19 ; required the fam of the feries ? 39 +3 33 } } } Sum = 42 Number of terms = X 19 Extremes . Or , 39 + 3x19 = 399 2 378 42 2 ) 798 399 the Anfwer . 2. It is ...
... extremes of an arithmetical feries are 3 and 39 , and the number of terms 19 ; required the fam of the feries ? 39 +3 33 } } } Sum = 42 Number of terms = X 19 Extremes . Or , 39 + 3x19 = 399 2 378 42 2 ) 798 399 the Anfwer . 2. It is ...
Page 245
... extremes and the common dif- › ference , to find the number of terms . ** RULE . Divide the difference of the extremes by the common difference , and the quotient increased by I will be the number of terms required . EXAMPLES . Í . The ...
... extremes and the common dif- › ference , to find the number of terms . ** RULE . Divide the difference of the extremes by the common difference , and the quotient increased by I will be the number of terms required . EXAMPLES . Í . The ...
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A New and Complete System of Arithmetick: Composed for the Use of the ... Nicolas Pike No preview available - 2012 |
Common terms and phrases
affumed root amount of 11 anfwer annuity annum Anſ Avoirdupois bufhel Cafe compound intereft confequent coſt cube root currency cyphers decimal denominator diſcount divide the product dividend divifion divifor dollars equal EXAMPLES fame farthings fecond feet feries feven feveral fhall fhillings fhould fimple find the value firft firſt fquare root fraction fubtract fuch fugar gallons given fum given number given quantity greateſt grofs guineas improper fraction inches increaſed Integer laft laſt leaft lefs left hand Livres Livres Tournois lofs logarithm meaſure mixed number moidores months muft Mult multiplicand Multiply the giv muſt number of terms pence pounds prefent worth principal PROB Prod proportion purchaſe queſtion quotient rate per cent ratio Reduce 100l remainder RULE ſtock Subtrahend Suppofe TABLE tare third thofe tient TROY WEIGHT VULGAR FRACTIONS weight whofe whole numbers yards coft
Popular passages
Page 241 - Divide the difference of the extremes by the common difference, and the quotient increased by 1 is the number of terms.
Page 234 - Bring down the first figure of the next period to the remainder for a new dividend, to which find a new divisor as before, and in like manner proceed till the whole be finished.
Page 207 - Tare is an allowance made to the buyer for the weight of the box, barrel, or bag, &c. which contains the goods bought, and is either at so much per box, &c., at so much per cwt., or at so much in the gross weight.
Page 222 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 214 - Distinguish the given number into periods of two figures each, by putting a point over the place of units, another over the place of hundreds, and so on, which points show the number of figures the root will consist of. 2. Find the greatest square number in the first, or left hand period...
Page 222 - RULE. 1. Separate the given number into periods of three figures each, by putting a point over the unit figure and every third figure beyond the place of units. 2. Find the greatest cube in the left hand period, and put its root in the quotient. 3.
Page 222 - Find the greatest cube in the left hand period, and put its root in the quotient. 3. Subtract the cube thus found, from the said period, and to the remainder bring down the next period, and call this the dividend.
Page 214 - ... it therefrom, and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 93 - ... therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor.
Page 36 - ... setting down the remainder under the column added, and carry the quotient to the next superior denomination, continuing the same to the last, which add, as in simple addition.