Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 13
Сторінка 142
... Logarithmic Spiral . The definition of this spiral is , that the radius increases in a geometric while the angle increases in an arithmetic ratio . Hence its equation will be of the form r = cea , or , as it is usually written , r = ao ...
... Logarithmic Spiral . The definition of this spiral is , that the radius increases in a geometric while the angle increases in an arithmetic ratio . Hence its equation will be of the form r = cea , or , as it is usually written , r = ao ...
Сторінка 143
... spirals equal to the primary one ; and if another equal spiral be made to roll on the first , the pole of the rolling spiral will trace out another spiral equal to the original . This property of the logarithmic spiral of constantly ...
... spirals equal to the primary one ; and if another equal spiral be made to roll on the first , the pole of the rolling spiral will trace out another spiral equal to the original . This property of the logarithmic spiral of constantly ...
Сторінка 160
... logarithmic spiral is r = cε " . r = ce . Then tan1a , and is therefore constant ; = p = r sin ( tan1a ) The subtangent = ra . ra = ( 1 + a2 ) ° The locus of the extremity of the subtangent is the involute of the curve , the equation to ...
... logarithmic spiral is r = cε " . r = ce . Then tan1a , and is therefore constant ; = p = r sin ( tan1a ) The subtangent = ra . ra = ( 1 + a2 ) ° The locus of the extremity of the subtangent is the involute of the curve , the equation to ...
Сторінка 161
... logarithmic spiral , and many other curves for which r is zero when is infinite . ( 9 ) The curve whose equation is a 02 r = Ꮎ - 1 " offers examples of both rectilinear and circular asymptotes . For if 0 = ± 1 , r = ∞ , and as 2 = ± d ...
... logarithmic spiral , and many other curves for which r is zero when is infinite . ( 9 ) The curve whose equation is a 02 r = Ꮎ - 1 " offers examples of both rectilinear and circular asymptotes . For if 0 = ± 1 , r = ∞ , and as 2 = ± d ...
Сторінка 192
... logarithmic spiral when referred to p and r , 10 P p = mr , P = = .. m m2 ( 18 ) In the involute of the circle p2 = r2 - a2 , and p = p . ( 19 ) The equation to Cotes ' spirals is Р = P = r ( a2 + r2 ) § ( 20 ) In the epicycloid a2b c2 ...
... logarithmic spiral when referred to p and r , 10 P p = mr , P = = .. m m2 ( 18 ) In the involute of the circle p2 = r2 - a2 , and p = p . ( 19 ) The equation to Cotes ' spirals is Р = P = r ( a2 + r2 ) § ( 20 ) In the epicycloid a2b c2 ...
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Загальні терміни та фрази
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