Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 22
Сторінка 106
... parabola is 4 b - - 3 a - EN . DN , or 3 x ( ax - x2 ) , which is to be a maximum . Whence ∞ = 3 a abs > and the area of the parabola = 4 4 ( 34 ) To determine the greatest ellipse which can be cut from a given cone . Let AC ( fig . 8 ) ...
... parabola is 4 b - - 3 a - EN . DN , or 3 x ( ax - x2 ) , which is to be a maximum . Whence ∞ = 3 a abs > and the area of the parabola = 4 4 ( 34 ) To determine the greatest ellipse which can be cut from a given cone . Let AC ( fig . 8 ) ...
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 included π 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 arc ...
... parabola ( whose latus rectum is included π 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 arc ...
Сторінка 146
... parabola referred to two tangents as axes is y + = 1 . Hence the equation to the tangent is x + y ( ax ) 11 ( by ) 1 = 1 . The intercepts are a 。= ( ax ) , Yo = Yo = ( by ) } ; therefore + - + - 1 ; a a or a , yo are the co - ordinates ...
... parabola referred to two tangents as axes is y + = 1 . Hence the equation to the tangent is x + y ( ax ) 11 ( by ) 1 = 1 . The intercepts are a 。= ( ax ) , Yo = Yo = ( by ) } ; therefore + - + - 1 ; a a or a , 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 a2y2 - 2b3y - x1 = 0 , has two parabolic asymptotes whose equations are b2 x02 x2 - a ( y - ~~ ) , = a and a ...
... 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 a2y2 - 2b3y - x1 = 0 , has two parabolic asymptotes whose equations are b2 x02 x2 - a ( y - ~~ ) , = a and a ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³