The Spirit of Mathematical Analysis: And Its Relation to a Logical SystemJ.W. Parker, 1843 - 103 páginas |
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Página viii
... holds perfectly generally , i . e . that the equation ( 1 ) ( 1 + x ) " = 1 + n.2 + n21 2 ! - 1 82+ n31 3 ! 1 1 z3 + n41 4 ! 1 - s + in inf . * holds with perfect generality for every z and for every n , so that n and z may be ...
... holds perfectly generally , i . e . that the equation ( 1 ) ( 1 + x ) " = 1 + n.2 + n21 2 ! - 1 82+ n31 3 ! 1 1 z3 + n41 4 ! 1 - s + in inf . * holds with perfect generality for every z and for every n , so that n and z may be ...
Página ix
... holds with perfect gene- rality , when is considered as perfectly insignificant , being a mere supporter of the operations , and when therefore we cannot speak of the convergence or divergence of the series , we perceive * Hence if we ...
... holds with perfect gene- rality , when is considered as perfectly insignificant , being a mere supporter of the operations , and when therefore we cannot speak of the convergence or divergence of the series , we perceive * Hence if we ...
Página x
... hold generally but only upon the particular hypothesis that they are numeric equations , the theory of such numeric equations must be esta- blished for itself in a second Essay , and the " Theory of Definite Integrals " ( in which ...
... hold generally but only upon the particular hypothesis that they are numeric equations , the theory of such numeric equations must be esta- blished for itself in a second Essay , and the " Theory of Definite Integrals " ( in which ...
Página 2
... holds for the multiplication and division of infinite series . I have begun to examine the most important rules which are ( at present ) esteemed to hold good in this re- spect , and to shew in what cases they are correct , and in what ...
... holds for the multiplication and division of infinite series . I have begun to examine the most important rules which are ( at present ) esteemed to hold good in this re- spect , and to shew in what cases they are correct , and in what ...
Página 4
... hold for broken factorials , as may be easily proved . This is exactly the same error as would be committed if we were to pronounce that the equation ( -1 ) " = = COS Nπ , which is correct for any whole number n , would also hold for ...
... hold for broken factorials , as may be easily proved . This is exactly the same error as would be committed if we were to pronounce that the equation ( -1 ) " = = COS Nπ , which is correct for any whole number n , would also hold for ...
Outras edições - Ver tudo
The Spirit of Mathematical Analysis: And Its Relation to a Logical System Martin Ohm Visualização integral - 1843 |
The Spirit of Mathematical Analysis: And Its Relation to a Logical System Martin Ohm Visualização integral - 1843 |
The Spirit of Mathematical Analysis: And Its Relation to a Logical System Martin Ohm Visualização integral - 1843 |
Palavras e frases frequentes
according to powers according to whole actual numbers actual or imaginary actual values algebraical sum applied binomial series binomial theorem broken number coefficients conceived considered contradiction convergent convergent series correct equation denominate numbers denote determinate value differences of whole divergent series divisor enunciated equa equal expressions equal to zero formulæ Hence idea imaginary number imaginary value inadmissible in calculation indenominate infinite number infinite series infinitely multiple-meaning infinitum Instruction-Book laws of operation letters m+n-p magnitudes MARTIN OHM mathematical analysis multiplied natural logarithm negative number negative whole number numerical series obtain Octavo p+qi particular positive number positive or negative positive whole number quotient represents result root SECTION sense of sect series proceeding according shew signification simplest value single-meaning summand symbol transformed unknown expression value in cyphers values of log whole functions whole or broken whole powers