A Treatise on Infinitesimal Calculus ... |
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Page xi
... varying law : it is , I assert , on the notion of Infinitesimals only , that the pro- blems of varying velocity can be intelligibly treated by the Integral Calculus . The following is consequently the outline of the treatise . b 2 ...
... varying law : it is , I assert , on the notion of Infinitesimals only , that the pro- blems of varying velocity can be intelligibly treated by the Integral Calculus . The following is consequently the outline of the treatise . b 2 ...
Page 3
... varies continuously from OP 。。 up to OP , ; on OP , OP , OP , let squares be described , viz . OR , OR , OR , So that OR = let op be increased by an infinitesimal PQ dx , and on oq let a square be described ; then the increase of 2 ...
... varies continuously from OP 。。 up to OP , ; on OP , OP , OP , let squares be described , viz . OR , OR , OR , So that OR = let op be increased by an infinitesimal PQ dx , and on oq let a square be described ; then the increase of 2 ...
Page 4
... varies , as the function varies , the law of connexion depending on the process of Differentiation . The subject then on which Differentiation is performed is the function , and the result is the resolution of that function into its ...
... varies , as the function varies , the law of connexion depending on the process of Differentiation . The subject then on which Differentiation is performed is the function , and the result is the resolution of that function into its ...
Page 110
... varies , D dt 4 [ * S F ' ( a , x ) dx xo dxn dt = F ( a , x , ) -F ' ( a , x ) dxo xn + dt * d.r ' ( a , x ) da da dt dx . ( 91 ) The process by which this equation has been found is com- monly called differentiation under the sign of ...
... varies , D dt 4 [ * S F ' ( a , x ) dx xo dxn dt = F ( a , x , ) -F ' ( a , x ) dxo xn + dt * d.r ' ( a , x ) da da dt dx . ( 91 ) The process by which this equation has been found is com- monly called differentiation under the sign of ...
Page 113
... varies : the element - function being finite and continuous for all employed values of the para- meter as well as for those of its original subject - variable . Let u be the given definite integral ; then u = [ ** x ′ F ' ( a , x ) dx ...
... varies : the element - function being finite and continuous for all employed values of the para- meter as well as for those of its original subject - variable . Let u be the given definite integral ; then u = [ ** x ′ F ' ( a , x ) dx ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³