Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 9
Сторінка 139
... Hypocycloid respectively . When a and b are commen- surable the curve will re - enter after a number of revolutions of the generating circle equal to the least common multiple of a and b in such cases the curve is expressible by an ...
... Hypocycloid respectively . When a and b are commen- surable the curve will re - enter after a number of revolutions of the generating circle equal to the least common multiple of a and b in such cases the curve is expressible by an ...
Сторінка 140
... hypocycloid occurs in the solution of many problems . If in the equations to the hypotrochoid we put b a = +4 ) h cos 0 , y = a = a - then " 2 - h ) hsin 0 . Whence 2 h x2 a 2 h y2 2 ( − ^ ) ' ~ ' + ( + ^ ) ' - ( - ) , = 4 which is the ...
... hypocycloid occurs in the solution of many problems . If in the equations to the hypotrochoid we put b a = +4 ) h cos 0 , y = a = a - then " 2 - h ) hsin 0 . Whence 2 h x2 a 2 h y2 2 ( − ^ ) ' ~ ' + ( + ^ ) ' - ( - ) , = 4 which is the ...
Сторінка 141
... hypocycloid it is ( 3a - 2b ) . α π b2 ( 3a + 2b ) a The evolute of the epicycloid is a similar figure , the radii of the fixed and generating circles being a2 and a + 26 ab a + 2b respectively . An analogous theorem holds for the hypo ...
... hypocycloid it is ( 3a - 2b ) . α π b2 ( 3a + 2b ) a The evolute of the epicycloid is a similar figure , the radii of the fixed and generating circles being a2 and a + 26 ab a + 2b respectively . An analogous theorem holds for the hypo ...
Сторінка 146
... portion of the tangent intercepted between the axes = ( x2 + y2 ) 3 = a ; or the hypocycloid is constantly touched by a straight line of given length which slides between two rectangular axes . The con- 146 TANGENTS TO CURVES .
... portion of the tangent intercepted between the axes = ( x2 + y2 ) 3 = a ; or the hypocycloid is constantly touched by a straight line of given length which slides between two rectangular axes . The con- 146 TANGENTS TO CURVES .
Сторінка 147
... hypocycloid , was first shewn by John Bernoulli . ( See his Works , Vol . 111. p . 447. ) For the perpendicular from the origin on the tangent we find p = ( axy ) 3 . ( 4 ) In the cissoid of Diocles , y2 = 2 a X3 - whence the subtangent ...
... hypocycloid , was first shewn by John Bernoulli . ( See his Works , Vol . 111. p . 447. ) For the perpendicular from the origin on the tangent we find p = ( axy ) 3 . ( 4 ) In the cissoid of Diocles , y2 = 2 a X3 - whence the subtangent ...
Зміст
1 | |
9 | |
28 | |
43 | |
52 | |
77 | |
79 | |
94 | |
224 | |
237 | |
249 | |
271 | |
282 | |
291 | |
340 | |
351 | |
129 | |
132 | |
144 | |
162 | |
175 | |
188 | |
200 | |
386 | |
400 | |
412 | |
440 | |
464 | |
506 | |
Інші видання - Показати все
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