Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 28
Сторінка 106
... parabola is EN . DN , or 4 b - - 3 a x ( ax - x2 ) , which is to be a maximum . Whence x = За , and the area of the parabola = 4 ab 3 ( 34 ) To determine the greatest ellipse which can be cut from a given cone . Let AC ( fig . 8 ) = a ...
... parabola is EN . DN , or 4 b - - 3 a x ( ax - x2 ) , which is to be a maximum . Whence x = За , and the area of the parabola = 4 ab 3 ( 34 ) To determine the greatest ellipse which can be cut from a given cone . Let AC ( fig . 8 ) = a ...
Сторінка 134
... parabola , see a paper by Professor Wallace in the Edinburgh Transactions , Vol . xiv . p . 625 . ( 7 ) The Quadratrix of Dinostratus . If the radius CQ of the circle ABD ( fig . 18 ) revolve uniformly round C from A to B , while the ...
... parabola , see a paper by Professor Wallace in the Edinburgh Transactions , Vol . xiv . p . 625 . ( 7 ) The Quadratrix of Dinostratus . If the radius CQ of the circle ABD ( fig . 18 ) revolve uniformly round C from A to B , while the ...
Сторінка 142
... parabola ( whose latus rectum is a - π included between the vertex and an ordinate = r . The length of the arc of the sector of the spiral is equal to that of the segment of the parabola . If a tangent be drawn at the extremity of the ...
... parabola ( whose latus rectum is a - π included between the vertex and an ordinate = r . The length of the arc of the sector of the spiral is equal to that of the segment of the parabola . If a tangent be drawn at the extremity of the ...
Сторінка 146
... parabola referred to two tangents as axes is x y + = 1 . Hence the equation to the tangent is y + ( ax ) ( by ) = 1 . The intercepts are x = ( ax ) , Yo = ( by ) 3 ; therefore + = xo Yo a b x + = 1 ; a or x , yo are the co - ordinates ...
... parabola referred to two tangents as axes is x y + = 1 . Hence the equation to the tangent is y + ( ax ) ( by ) = 1 . The intercepts are x = ( ax ) , Yo = ( by ) 3 ; therefore + = xo Yo a b x + = 1 ; a or x , yo are the co - ordinates ...
Сторінка 156
... parabola , the latus rectum of which is a , and the axis of which is parallel to that of y . ( 19 ) The curve whose equation is a2 y2 - 2b3y — x1 = 0 , - has two parabolic asymptotes whose equations are b2 and a2 = a a a a2 = a ( y - 1 ) ...
... parabola , the latus rectum of which is a , and the axis of which is parallel to that of y . ( 19 ) The curve whose equation is a2 y2 - 2b3y — x1 = 0 , - has two parabolic asymptotes whose equations are b2 and a2 = a a a a2 = a ( y - 1 ) ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³