A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page x
... line joining two con- secutive points in a circle to be straight , and represent it by a symbol which denotes a straight line ; whereas from the geometrical definition of a circle we know that the curvature of a circle is continuous ...
... line joining two con- secutive points in a circle to be straight , and represent it by a symbol which denotes a straight line ; whereas from the geometrical definition of a circle we know that the curvature of a circle is continuous ...
Page xxvi
... straight line and to a plane .... 332. The equation to a tangent plane to a curved surface .. 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the ...
... straight line and to a plane .... 332. The equation to a tangent plane to a curved surface .. 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the ...
Page 25
... straight line at an infinite distance from the origin . Now we have here the reason for this seeming impossibility : if c = 0 , it is implied that c is one term of an equation , the other terms of which are infinite ; and that in ...
... straight line at an infinite distance from the origin . Now we have here the reason for this seeming impossibility : if c = 0 , it is implied that c is one term of an equation , the other terms of which are infinite ; and that in ...
Page 28
... line of the form in fig . 1 , so that BA should be a continuous curve drawn after some determinate law , but at A the law suddenly should change , and the curve , from being , say , a circle , become a straight line , then the second of ...
... line of the form in fig . 1 , so that BA should be a continuous curve drawn after some determinate law , but at A the law suddenly should change , and the curve , from being , say , a circle , become a straight line , then the second of ...
Page 30
... line joining them must be considered straight ; and thus must the circle be conceived to be made up of an infinity of infinitesimal straight lines , and the tangent at any point is the line which coincides with the straight line joining ...
... line joining them must be considered straight ; and thus must the circle be conceived to be made up of an infinity of infinitesimal straight lines , and the tangent at any point is the line which coincides with the straight line joining ...
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Common terms and phrases
a₁ algebraical ascending powers b₁ becomes calculated change of sign changes sign coefficients constant curve d²u d²x d²y d2y dx2 d³u d³y denominator determine differential equation dr dr dr dx dx dr dx dx dx dy dx dz dx² dx2 dy2 dy d2u dy dx dy dy dy dz dy² dy³ dz dx dz dz equal equicrescent Evaluate explicit function expression F(xo F(xo+h factor finite quantity fraction given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity logarithm loge maxima and minima minimum value negative partial derived-functions particular values positive primitive equation proper fraction replaced result roots Similarly sin x singular value substituting suppose symbols Taylor's Series tion total differentials vanish variation whence x+▲x zero
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