Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
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Сторінка 135
... Cycloid . Rolling Curves . This curve is generated by a point P in the circumference of a circle b Pc ( fig . 19 ) , which rolls along a line AA ' . To find its equation put O'ba , Pob = 0 , AM = x , GENERATION OF CURVES . 135.
... Cycloid . Rolling Curves . This curve is generated by a point P in the circumference of a circle b Pc ( fig . 19 ) , which rolls along a line AA ' . To find its equation put O'ba , Pob = 0 , AM = x , GENERATION OF CURVES . 135.
Сторінка 136
... cycloid is not limited to the space between A and A ' , but that it consists of an infinite number of portions equal and similar to ACA ' and touching each other in cusps as in the figure . After the Conic Sections there is no curve in ...
... cycloid is not limited to the space between A and A ' , but that it consists of an infinite number of portions equal and similar to ACA ' and touching each other in cusps as in the figure . After the Conic Sections there is no curve in ...
Сторінка 137
... cycloid is an equal cycloid in an inverted position , and that the radius of curvature is double of the chord of the generating circle which is perpendicular to the tangent . He also discovered the important dynamical property of the ...
... cycloid is an equal cycloid in an inverted position , and that the radius of curvature is double of the chord of the generating circle which is perpendicular to the tangent . He also discovered the important dynamical property of the ...
Сторінка 138
... cycloid which have been written by various authors . Such are the Histoire de la Roulette of Pascal ; the History of the Cycloid of Carlo Dati ; the Treatise de Cycloide of Wallis ; the Historia Cycloidis of Groningius in his ...
... cycloid which have been written by various authors . Such are the Histoire de la Roulette of Pascal ; the History of the Cycloid of Carlo Dati ; the Treatise de Cycloide of Wallis ; the Historia Cycloidis of Groningius in his ...
Сторінка 141
... cycloid is ( a - b ) . a The corresponding area of the epicycloid is π b2 ( 3a + 2b ) a π b2 and of the hypocycloid ... cycloid . ( 12 ) The Spiral of Archimedes . While the straight line OM ( fig . 25 ) revolves uniformly round O , let ...
... cycloid is ( a - b ) . a The corresponding area of the epicycloid is π b2 ( 3a + 2b ) a π b2 and of the hypocycloid ... cycloid . ( 12 ) The Spiral of Archimedes . While the straight line OM ( fig . 25 ) revolves uniformly round O , let ...
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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