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'b = a , Pob = 0 , AM = 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'b = a , Pob = 0 , AM = 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 46 ---- ( a - b ) . a The corresponding area of the epicycloid is π b2 and of the hypocycloid it is ... cycloid . ( 12 ) The Spiral of Archimedes . While the straight line OM ( fig . 25 ) revolves uniformly round O , let the ...
... cycloid is a 46 ---- ( a - b ) . a The corresponding area of the epicycloid is π b2 and of the hypocycloid it is ... cycloid . ( 12 ) The Spiral of Archimedes . While the straight line OM ( fig . 25 ) revolves uniformly round O , let the ...
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Загальні терміни та фрази
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