Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 25
Сторінка 141
... locus of the point P is the spiral of Archimedes . To find its equa- tion let AOP = 0 , OP = r , and when = 2 let r = a . a a Then = Ꮎ or r = Ꮎ , 2π 2π which is the equation to the curve . * Principia , I. Prop . 49 . The following ...
... locus of the point P is the spiral of Archimedes . To find its equa- tion let AOP = 0 , OP = r , and when = 2 let r = a . a a Then = Ꮎ or r = Ꮎ , 2π 2π which is the equation to the curve . * Principia , I. Prop . 49 . The following ...
Сторінка 147
... locus of the ultimate intersections of a line of given length sliding between rect- angular axes is this hypocycloid , was first shewn by John Bernoulli . ( See his Works , Vol . 111. p . 447. ) For the perpendicular from the origin on ...
... locus of the ultimate intersections of a line of given length sliding between rect- angular axes is this hypocycloid , was first shewn by John Bernoulli . ( See his Works , Vol . 111. p . 447. ) For the perpendicular from the origin on ...
Сторінка 149
... locus of the extremity of p . Let x , y , be the co - ordinates of the first curve , a , ß , of the second ; then p being the perpendicular on the tangent , its equation is ax + By = p2 = a2 + ß3 , ( 1 ) since a , ß , are the co ...
... locus of the extremity of p . Let x , y , be the co - ordinates of the first curve , a , ß , of the second ; then p being the perpendicular on the tangent , its equation is ax + By = p2 = a2 + ß3 , ( 1 ) since a , ß , are the co ...
Сторінка 158
... r . Ex . 1. The equation to the spiral of Archimedes is λ = αθ . The angle between the radius and tangent is d Ꮎ = tan 2 ° -1 = tan - 10 . dr The subtangent = 2.2 a The equation to the locus of the extremity of the 158 TANGENTS TO CURVES .
... r . Ex . 1. The equation to the spiral of Archimedes is λ = αθ . The angle between the radius and tangent is d Ꮎ = tan 2 ° -1 = tan - 10 . dr The subtangent = 2.2 a The equation to the locus of the extremity of the 158 TANGENTS TO CURVES .
Сторінка 159
... locus of the extremity of the subtangent of the curve ra0 , and so on in succession , we shall have a series of spirals , the equations to which are " " = a 03 1.2 ' a 01 " " = 1.2.3 a Ꮎ g + ( 10 ) = 1.2 ... ( n - 1 ) ' the angle in ...
... locus of the extremity of the subtangent of the curve ra0 , and so on in succession , we shall have a series of spirals , the equations to which are " " = a 03 1.2 ' a 01 " " = 1.2.3 a Ꮎ g + ( 10 ) = 1.2 ... ( n - 1 ) ' the angle in ...
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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