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 a . Similarly , if ( 7 ) = 0 , ( 52 ) has no term involving the x . dr dk dr of and therefore ( 17 ) ...
... 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 a . Similarly , if ( 7 ) = 0 , ( 52 ) has no term involving the x . dr dk dr of and therefore ( 17 ) ...
Page 231
... conic r ( x , y ) = 0 , which bisect all chords parallel to the axes of x and y respect- ively . If ( d ) and dh ( d ) simultaneously vanish , ( 52 ) contains no term involving the first powers of x and y ; and the conic is re- ferred ...
... conic r ( x , y ) = 0 , which bisect all chords parallel to the axes of x and y respect- ively . If ( d ) and dh ( d ) simultaneously vanish , ( 52 ) contains no term involving the first powers of x and y ; and the conic is re- ferred ...
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a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero