A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 25
... Conic Sections , Dublin , 1855 , 3rd edit . Art . 64 . 12. ] Thus far we have spoken of single symbols , and of their properties ; it is of continuous variables that we shall treat , and we shall not introduce discontinuous ones without ...
... Conic Sections , Dublin , 1855 , 3rd edit . Art . 64 . 12. ] Thus far we have spoken of single symbols , and of their properties ; it is of continuous variables that we shall treat , and we shall not introduce discontinuous ones without ...
Page 30
... conics , the tan- gent to a conic is defined to be the straight line passing through two points on a curve infinitesimally near to each other , and its equation is derived from this definition . Similarly must all continuous curves be ...
... conics , the tan- gent to a conic is defined to be the straight line passing through two points on a curve infinitesimally near to each other , and its equation is derived from this definition . Similarly must all continuous curves be ...
Page 229
... y ) 2 hk + 3x2 ( a + y ) k2 + 3 ( a + y ) 2 h2 k + 6x ( a + y ) h k2 + x2 k3 + 3 ( a + y ) h2 k2 + 2 x hk3 + h2 k3 . Ex . 2. The equation to a conic is 2 141. ] 229 FUNCTIONS OF MANY VARIABLES . Examples of the preceding.
... y ) 2 hk + 3x2 ( a + y ) k2 + 3 ( a + y ) 2 h2 k + 6x ( a + y ) h k2 + x2 k3 + 3 ( a + y ) h2 k2 + 2 x hk3 + h2 k3 . Ex . 2. The equation to a conic is 2 141. ] 229 FUNCTIONS OF MANY VARIABLES . Examples of the preceding.
Page 230
... conic which are parallel to the axis of x , and is therefore a dia- meter conjugate to the diameter which is parallel to the axis of x . Similarly , if ( r ) = 0 , - ( 52 ) has no term involving the dk and therefore ( 17 ) = 0 , which ...
... conic which are parallel to the axis of x , and is therefore a dia- meter conjugate to the diameter which is parallel to the axis of x . Similarly , if ( r ) = 0 , - ( 52 ) has no term involving the dk and therefore ( 17 ) = 0 , which ...
Page 231
... conic F ( x , y ) = 0 , which bisect all chords parallel to the axes of x and y respect- ively . dr If and ( 1 ) simultaneously vanish , ( 52 ) contains no dh dk term involving the first powers of x and y ; and the conic is re- ferred ...
... conic F ( x , y ) = 0 , which bisect all chords parallel to the axes of x and y respect- ively . dr If and ( 1 ) simultaneously vanish , ( 52 ) contains no dh dk term involving the first powers of x and y ; and the conic is re- ferred ...
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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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