The Spirit of Mathematical Analysis: And Its Relation to a Logical SystemJ.W. Parker, 1843 - 103 páginas |
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Página viii
... hence this development n of ( 1+ ) would become the series for e if we could take n so that nr I n 1 - - n ( n − 1 ) ( n − 2 ) ( n − 3 ) . . . [ n – ( r − 1 ) ] ̧ that is , that is , 1 - · · n - • n.n.n n ... n - 3 n ... r- n should ...
... hence this development n of ( 1+ ) would become the series for e if we could take n so that nr I n 1 - - n ( n − 1 ) ( n − 2 ) ( n − 3 ) . . . [ n – ( r − 1 ) ] ̧ that is , that is , 1 - · · n - • n.n.n n ... n - 3 n ... r- n should ...
Página ix
... hence at the moment that the assertion that nrI - 1 n ' = 1 for n = ∞ ceases to be correct , the terms which are influenced by this incor- rect assertion , may be considered as equal to zero , and hence these two discrepancies correct ...
... hence at the moment that the assertion that nrI - 1 n ' = 1 for n = ∞ ceases to be correct , the terms which are influenced by this incor- rect assertion , may be considered as equal to zero , and hence these two discrepancies correct ...
Página 5
... hence we shall make no further reference in this place to the cause of paradoxes alluded to above , in ( e ) . We said on the other hand : ( a ) that zero is frequently con- ceived in too one - sided a manner . If we consider zero ...
... hence we shall make no further reference in this place to the cause of paradoxes alluded to above , in ( e ) . We said on the other hand : ( a ) that zero is frequently con- ceived in too one - sided a manner . If we consider zero ...
Página 7
... hence the results , before being employed , are as it were subjected to a One example may suffice for all . Whenever a magnitude is required in algebra , we can only reason thus : " If such a mag- nitude exists , and is therefore ...
... hence the results , before being employed , are as it were subjected to a One example may suffice for all . Whenever a magnitude is required in algebra , we can only reason thus : " If such a mag- nitude exists , and is therefore ...
Página 9
... hence we must take the quantities_repre- sented by the roots and multiply them together , " we would pro- pose another example , viz . to multiply 4 by √9 , where it is not very possible to recur to the quantities represented by the ...
... hence we must take the quantities_repre- sented by the roots and multiply them together , " we would pro- pose another example , viz . to multiply 4 by √9 , where it is not very possible to recur to the quantities represented by the ...
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