## The young dual arithmetician; or, Dual arithmetic |

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according added addition amount applied arrangement ascending bases becomes beginning calculation changed CHAPTER ciphers coefficients common number consecutive contracted corresponding decimals descending branch determined developments Diff difference direct divided Dual Arithmetic dual digits Dual log dual logarithm dual number easily eight places employed equal established EXAMPLES expressed feet Find the dual Find the value follows fourth function give given number greater half Hence illustrate indicated involved known length less loga method Multiply natural number nearly negative nine places number answering obtained occupied operations ordinary number periods places of decimals places of figures position PRELIMINARY PROBLEM readily Reduce remainder represented rithm root RULE similar simple subtract supposing tables tabulated Take taken theorem third twenty twice units whole number written

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Page 84 - Take out the logarithm of the given number from the table, and divide it by 2 for the square root, 3 for the cube root, &c. and the natural number answering to the result will be the root required. But if it be a compound root, or one that consists both of a root and a power, multiply the logarithm of the given number by the numerator of the index, and divide the product by the denominator, for the logarithm of the root sought. Observing, in either case, when the index of the logarithm...

Page 84 - But if it be a compound root, or one that consists both of a root and a power, multiply the logarithm of the given number by the numerator of the index, and divide the product by the denominator, for the logarithm of the root sought. Observing, in either case, when the index of the logarithm is negative, and cannot be divided without a remainder, to increase it by such a number as will render it exactly divisible ; and then carry the units borrowed, as so many tens, to the first figure of the decimal...

Page 22 - It is here also to be observed, that powers and roots of the same quantity, are divided by subtracting the index of the, divisor from that of the dividend. Thus, a 3 -r- a 2 , or -5 = 0; a 2 -r

Page 87 - In what time will a sum of money double itself at 5 %, (a) at simple interest, (6) at compound interest, reckoned yearly i (72) If when wheat is 60s.

Page 11 - For 14 3 example: — , — , and — are all proper fractions and therefore less than 1. 25 n If the numerator is larger than the denominator, the fraction is called improper and is greater than 1 . For example: — , — , and — are all improper fractions and therefore greater than 1. An improper fraction can be converted into a mixed fraction by dividing its denominator into its numerator. For example, since 2 divides into 7 three times with a remainder of 1 , we get To convert a mixed...

Page 81 - Ans. 413739 11. Divide .067859 by 1234.59, by logarithms. Ans. .0000549648 THE RULE OF THREE, OR PROPORTION, BY LOGARITHMS. For any single proportion, add the logarithms of the second and third terms together, and subtract the logarithm of the first from their sum, according to the foregoing rules ; then the natural number answering to the result will be the fourth term required. But if the proportion be compound, add together the logarithms of all the terms that are to be...

Page 13 - France, which = 1076-42996 square feet English. The Stere is a cubic metre = 35-316582 cubic feet English. The Litre for liquid measure is a cubic decimetre = 1-76077 imperial pints English, at the temperature of melting ice ; a litre of distilled water weighs 15434 grains troy. The unit of weight is the gramme : it is the weight of a cubic centimetre of distilled water, or of a millilitre, and therefore equal to 15-434 grains troy. The kilogramme is the weight of a cubic decimetre of distilled water,...

Page 29 - I)3 = {1 + (-I)8}114478742, where it is now reduced to a " Dual number ' ' in which the first 7 digits are ciphers. This type of number is a Dual Number of the Ascending Branch. Similarly, a number expressed as a product of powers of -9, -99, ... is a Dual Number of the Descending Branch. The transformation of a dual number of eight digits into another whose first seven digits are ciphers is termed "reducing a dual number to the eighth position," and a dual number reduced to the eighth position is...

Page 79 - ... find, by means of the simple rules, before laid down for multiplication, division and the raising of powers, as many other logarithms as we please, or may speedily examine any logarithm in the table. MULTIPLICATION BY LOGARITHMS. Take out the logarithms of the factors from the table, and add them together ; then the natural number answering to the sum will be the product required. Observing, in the addition, that what is to be carried from the decimal part of the logarithms is always affirmative,...

Page 103 - HCK, therefore by Cor. 1, Art. 2, Q will be the point at which the body will come to a state of rest. 4. PROP. To find the locus of the planes of equal velocities. Let the vertical AK represent the height from which a body must fall to acquire the given velocity ; draw KCC, making, with the horizontal line CH, Fig. 4. plane in C, and making the angle AKC equal to the complement of the angle of the angle KCH equal to the angle of friction; then KCC,, &c., will be the locus of the extremities of the...