Library of Useful Knowledge: Mathematics I., Volumen1Baldwin and Cradock, 1836 - 323 páginas |
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... Logarithms , 57-59 Mathematics , evidence of compared with that of history , 1 , 76 - , why preferred as an exercise of reasoning , 3 , 76 Measure , greatest common , 9 , 25 , 28 Measurement , numerical , general theory of , 87-93 ...
... Logarithms , 57-59 Mathematics , evidence of compared with that of history , 1 , 76 - , why preferred as an exercise of reasoning , 3 , 76 Measure , greatest common , 9 , 25 , 28 Measurement , numerical , general theory of , 87-93 ...
Página 70
... Logarithms to this base are therefore the most frequently used , and are called common logarithms ; they are always expressed by decimals . When we write log . 5 0.69897 , we mean that the common logarithm of 5 is 0.69897 ; that is ...
... Logarithms to this base are therefore the most frequently used , and are called common logarithms ; they are always expressed by decimals . When we write log . 5 0.69897 , we mean that the common logarithm of 5 is 0.69897 ; that is ...
Página 71
... common pur- poses . [ art . 233. ] 237. That part of any logarithm which stands to the left of the decimal point ... logarithms are either 0000105 or. explanation of the way in which the ogarithm of any number to any base may be found . We ...
... common pur- poses . [ art . 233. ] 237. That part of any logarithm which stands to the left of the decimal point ... logarithms are either 0000105 or. explanation of the way in which the ogarithm of any number to any base may be found . We ...
Página 72
... common difference of the progression which these means form will be .0000105 or . 00000105 , , 10 since.0000105 is the difference of the first and last terms . Accordingly , if we add this quantity to log . 413370 , we ob- tain log ...
... common difference of the progression which these means form will be .0000105 or . 00000105 , , 10 since.0000105 is the difference of the first and last terms . Accordingly , if we add this quantity to log . 413370 , we ob- tain log ...
Página 74
... common logarithms , 1 2 or.5 is the logarithm of the positive square root of 10 , or of 3.162278 , it is therefore the logarithm of - 3.162278 . But as the subject of the logarithms of negative numbers is of no practical importance , we ...
... common logarithms , 1 2 or.5 is the logarithm of the positive square root of 10 , or of 3.162278 , it is therefore the logarithm of - 3.162278 . But as the subject of the logarithms of negative numbers is of no practical importance , we ...
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added algebra angles answer arithmetical arithmetical progression becomes binomial binomial theorem called ciphers coefficient common logarithms common multiple contained continued fraction cube root decimal fraction decimal places decimal point digits divide dividend division divisor equa equal equation example exponent expression figure geometry given gives greater greatest common measure inches instance last article least common multiple less loga means metical multiply negative nth root observe permutations positive preceding prime number proceed proportion quan question quotient reduced remainder result rithm rule shillings solution square root student substituted subtract suppose theorem things taken third tion tity units unity unknown quantities vulgar fraction whole number write yards zeros دو
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Página 49 - Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions, which are placed in separate consecutive paragraphs, which paragraphs are numbered in the first column on the left ; in the second column on the left we state the reasons for each paragraph, either by referring to the preceding paragraphs from which they follow, or the preceding propositions in which they have been...
Página 4 - D' contains £T of G. Here then appears a connexion between the multiplication of whole numbers, and the formation of a fraction whose numerator is the product of two numerators, and its denominator the product of the corresponding denominators. These operations will always come together, that is whenever a question occurs in which, when whole numbers are given, those numbers are to be multiplied together ; when fractional numbers are given, it will be necessary, in the same case, to multiply the...
Página 33 - ... with one another. This cannot be attained by a mere reading of the book, however great the attention which may be given. It is impossible, in a mathematical work, to fill up every process in the manner in which it must be filled up in the mind of the student before he can be said to have completely mastered it. Many results must be given, of which the details are suppressed, such are the additions, multiplications, extractions of the square root, etc., with which the investigations abound.
Página 50 - Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ?
Página 3 - ... faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty. The properties of mind...
Página 64 - When it is said that the angle = arc , it is only meant that, is equal to the radius, the number of these units in any other angle is found by dividing the number of linear units in its arc by the number of linear units in the radius. It only remains to give a formula for finding the number of degrees, minutes, and seconds in an angle, whose theoretical measure is given. It is proved in geometry that the ratio of the circumference of a circle to its diameter, or that of half the circumference to...
Página 5 - This process is then, by extension, called division : y is called the quotient of £ divided by J., and is found by multiplying the numerator of the first by the denominator of the second for the numerator of the result, and the denominator of the first by the numerator of the second for the denominator of the result. That this process does give the same result as ordinary division in all cases where ordinary division is applicable, we can easily shew from any two whole numbers, for example, 12 and...
Página 60 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Página 3 - ... thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties : it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds : 1. Every term is distinctly...
Página 54 - ... number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work.