Examples of the Processes of the Differential and Integral Calculus |
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Page 29
... referred to , but the result is of such extreme complexity , that it happens for- tunately that we have seldom to employ these transformations for high orders of differentials ; and where this is necessary , that the nature of the case ...
... referred to , but the result is of such extreme complexity , that it happens for- tunately that we have seldom to employ these transformations for high orders of differentials ; and where this is necessary , that the nature of the case ...
Page 41
... referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
... referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
Page 75
... referred to Poinsot's Memoir on Angular Sec- tions , where the complete form of these expansions was first given . ( 9 ) To expand X in ascending powers of x . € 1 If we were to endeavour to effect this by means of Mac- laurin's Theorem ...
... referred to Poinsot's Memoir on Angular Sec- tions , where the complete form of these expansions was first given . ( 9 ) To expand X in ascending powers of x . € 1 If we were to endeavour to effect this by means of Mac- laurin's Theorem ...
Page 138
... referred to the treatises on the 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 ...
... referred to the treatises on the 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 ...
Page 145
... referred to its asymptotes is du du Then - = y , da dy xy = m3 . = x , and the equation to the tangent is - - y ( x ' − x ) + x ( y ' − y ) = 0 ; or yx ' + xy ' = 2xy = 2m2 . dy m2 dx Since the subtangent = y = dx 10 TANGENTS TO ...
... referred to its asymptotes is du du Then - = y , da dy xy = m3 . = x , and the equation to the tangent is - - y ( x ' − x ) + x ( y ' − y ) = 0 ; or yx ' + xy ' = 2xy = 2m2 . dy m2 dx Since the subtangent = y = dx 10 TANGENTS TO ...
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Common terms and phrases
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx 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 radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³