The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 477
... logarithms are produced by addition . On the contrary , beginning with 1 , and proceeding towards the left hand , the terms in the geometrical progression are produced by divi- sion , but their corresponding logarithms are produced by ...
... logarithms are produced by addition . On the contrary , beginning with 1 , and proceeding towards the left hand , the terms in the geometrical progression are produced by divi- sion , but their corresponding logarithms are produced by ...
Page 478
... logarithm of 1 + a ) " or of its equal N , and for the same reason , m is the logarithm of M. Hence it follows that n + m the logarithm of N x M , for Nx M = 1 + a " x 1 + am = 1 + a + m by the nature of in- dices . If the logarithm of ...
... logarithm of 1 + a ) " or of its equal N , and for the same reason , m is the logarithm of M. Hence it follows that n + m the logarithm of N x M , for Nx M = 1 + a " x 1 + am = 1 + a + m by the nature of in- dices . If the logarithm of ...
Page 479
... logarithm of N ; and if the number M be equal to 1 + am , then ma is the hyperbolic logarithm of M. Hyperbolic logarithms are not those in com- mon use , but they can be calculated with less labour than any other kind , and common ...
... logarithm of N ; and if the number M be equal to 1 + am , then ma is the hyperbolic logarithm of M. Hyperbolic logarithms are not those in com- mon use , but they can be calculated with less labour than any other kind , and common ...
Page 480
... logarithm of N , by article 8. This series , however , if x be a whole number , does not con- verge . Let M be a whole number , and M 1 and then - x x is less than 1. For , multiplying ... logarithm of 2n + 2 2n + 112 $ 480 OF LOGARITHMS .
... logarithm of N , by article 8. This series , however , if x be a whole number , does not con- verge . Let M be a whole number , and M 1 and then - x x is less than 1. For , multiplying ... logarithm of 2n + 2 2n + 112 $ 480 OF LOGARITHMS .
Page 481
... logarithm of 2n + 2 2n + 112 . 2n + 1 For , as the 2 2n + 11 -1 addition of logarithms answers to the multiplica- tion of the numbers to which they belong , the log- arithm of the square of any number , is the log- arithm of the number ...
... logarithm of 2n + 2 2n + 112 . 2n + 1 For , as the 2 2n + 11 -1 addition of logarithms answers to the multiplica- tion of the numbers to which they belong , the log- arithm of the square of any number , is the log- arithm of the number ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore