The Spirit of Mathematical Analysis: And Its Relation to a Logical SystemJ.W. Parker, 1843 - 103 páginas |
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Página 46
... infinitum because the coefficients of all the terms after the r + 1th receive the factor zero , and are therefore themselves equal to zero . Now if we consider this series as really continued in inf . and at the same time the co ...
... infinitum because the coefficients of all the terms after the r + 1th receive the factor zero , and are therefore themselves equal to zero . Now if we consider this series as really continued in inf . and at the same time the co ...
Página 48
... infinitum . Now since the infinite series proceeding according to whole powers of x is given simultaneously with the whole function of x of an indeterminate degree , we not only may but we must " cal- culate " with these forms , whose ...
... infinitum . Now since the infinite series proceeding according to whole powers of x is given simultaneously with the whole function of x of an indeterminate degree , we not only may but we must " cal- culate " with these forms , whose ...
Página 50
... infinitum ; and we obtain new equations in infinitum between the coefficients , so that from each consecutive equation a consecutive coefficient is con- tinually found from among the coefficients A. , A1 , A2 , A. , & c . which were all ...
... infinitum ; and we obtain new equations in infinitum between the coefficients , so that from each consecutive equation a consecutive coefficient is con- tinually found from among the coefficients A. , A1 , A2 , A. , & c . which were all ...
Página 51
... infinitum . In this case we have transformed a broken rational function of x , as 1 1 + x " and generally 1 1 - 9 1 - x Ꮖ 1 + x2 , b2 + b1 x + b2 x2 + 2 Co + C1 x + C2 x2 + . ... + bmxm + cx " continually in infinitum , and at the same ...
... infinitum . In this case we have transformed a broken rational function of x , as 1 1 + x " and generally 1 1 - 9 1 - x Ꮖ 1 + x2 , b2 + b1 x + b2 x2 + 2 Co + C1 x + C2 x2 + . ... + bmxm + cx " continually in infinitum , and at the same ...
Página 52
... infinitum will determine a con- secutive one of the coefficients A , A1 , A2 , A3 , & c . & c . which were at first unknown . Therefore there exists an infinite series , A + A1a + A2 + ... which when potentiated by m , gives a new ...
... infinitum will determine a con- secutive one of the coefficients A , A1 , A2 , A3 , & c . & c . which were at first unknown . Therefore there exists an infinite series , A + A1a + A2 + ... which when potentiated by m , gives a new ...
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