Download Algebra: An Elementary Text-Book for the Higher Classes of by George Chrystal PDF

By George Chrystal

This Elibron Classics booklet is a facsimile reprint of a 1904 variation through Adam and Charles Black, London.

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Algebra: An Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges. Part 1

This Elibron Classics booklet is a facsimile reprint of a 1904 version by way of Adam and Charles Black, London.

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Extra info for Algebra: An Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges. Part 1

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I. Determination of the orbit of the comet which was observed in the month of March in the year 1742. 2. Theorems about the reduction of integral formulas to the quadrature of circles. 3. On the finding of integrals which, if the value determined is assigned after the integration of the variable quantity. 4. On the sum of series of reciprocals arising from the powers of natural numbers. 5. On the integration of differential equations of higher degrees. 6. On the properties which certain conic sections have in common with infinitely many other curved lines.

9 even though the actual sums (given they exist) will vary with the digit removed. Looked at in a different way, with the digit 0 the fraction of terms that we have removed is (lon - 1) - ~ (9 n - 1) 9 9n - I --------"----=1-IOn - 1 ~1-0=1 8 IOn - 1 n->oo and with the other digits it is (Ion - I) - (9 n - I) 9n - I -------=1~1-0=1. IOn - 1 IOn - I n->oo 32 SUB-HARMONIC SERIES That is, asymptotically, we have removed 'almost all' terms! Put another way, we have the initially startling fact that almost all integers contain every possible digit.

3 A TOUCH OF KEPLER One of the most immediate and significant uses to which logarithms were put was, unsurprisingly, in astronomy. In 1601, on the death of the fractious Brahe, Kepler was promoted to take his place. Not only did he inherit his master's prestigious position but also his voluminous and incredibly accurate data, which he used to help him conduct his 'war with Mars', a war that he eventually won and from which he extracted his first two laws of planetary motion. 1. Planets move in ellipses, with the Sun at one focus and the other empty.

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