The Spirit of Mathematical Analysis: And Its Relation to a Logical SystemJ.W. Parker, 1843 - 103 páginas |
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Página 34
... potentiated by any positive whole number m , we shall then obtain another series which increases continuously from 0 to * . Consequently if a is any number of the latter series , there will always be a number of the first series , and ...
... potentiated by any positive whole number m , we shall then obtain another series which increases continuously from 0 to * . Consequently if a is any number of the latter series , there will always be a number of the first series , and ...
Página 35
... potentiated successively by all contiguous actual numbers ( from ∞ to 0 , and then from 0 to + ∞ ) , we shall obtain all contiguous positive numbers , viz . since bo = 1 , the first division all from the least , contiguous to zero ...
... potentiated successively by all contiguous actual numbers ( from ∞ to 0 , and then from 0 to + ∞ ) , we shall obtain all contiguous positive numbers , viz . since bo = 1 , the first division all from the least , contiguous to zero ...
Página 36
... potentiated by it , the result is the number a . b Let us now understand by an actual logarithm , a symbol of the form log a , in which a is any positive number , while b is any positive number > 1 , and which denotes such a positive or ...
... potentiated by it , the result is the number a . b Let us now understand by an actual logarithm , a symbol of the form log a , in which a is any positive number , while b is any positive number > 1 , and which denotes such a positive or ...
Página 42
... potentiated by 2 the result is -1 ) . ( C ) In general therefore we must write , agreeably to the formulæ 7.√ - 1-2√ - 1 = ( 72 ) . √1 , √ = 1.√√ - 1 = √√ + 1 = ± 1 . and SECTION 38 . The general solution of the general ...
... potentiated by 2 the result is -1 ) . ( C ) In general therefore we must write , agreeably to the formulæ 7.√ - 1-2√ - 1 = ( 72 ) . √1 , √ = 1.√√ - 1 = √√ + 1 = ± 1 . and SECTION 38 . The general solution of the general ...
Página 52
... potentiated by m , gives a new infinite series , whose terms coincide in infinitum with those of the series R. Now since " / R represents each of m expressions , which have the property of , when potentiated by m , giving the radicand R ...
... potentiated by m , gives a new infinite series , whose terms coincide in infinitum with those of the series R. Now since " / R represents each of m expressions , which have the property of , when potentiated by m , giving the radicand R ...
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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