Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 148
... easily find , by taking the m whence mymo ( m - 1 ) xy ( m2x2 + y2 ) : ( 8 ) In the curve x = € logarithmic differential , Yo = y2 x To = xy Y x Το Subtangent = - y = xo X - y x Yo y • ( 9 ) The equation to the cycloid referred to its ...
... easily find , by taking the m whence mymo ( m - 1 ) xy ( m2x2 + y2 ) : ( 8 ) In the curve x = € logarithmic differential , Yo = y2 x To = xy Y x Το Subtangent = - y = xo X - y x Yo y • ( 9 ) The equation to the cycloid referred to its ...
Сторінка 157
... easily seen that when a = ∞ , y = c . On the other hand , if xa , y is impossible . Hence the line whose equa- tion is y = c is an asymptote to an impossible branch of the curve ; that is to say , a branch of the curve leaves the plane ...
... easily seen that when a = ∞ , y = c . On the other hand , if xa , y is impossible . Hence the line whose equa- tion is y = c is an asymptote to an impossible branch of the curve ; that is to say , a branch of the curve leaves the plane ...
Сторінка 165
... easily obtain analytical conditions for distinguishing be- tween the three classes of double points indicated by the condition dy 0 dx 0 - viz . true double points , points of oscula- tion , and conjugate points . The condition dy dx 0 ...
... easily obtain analytical conditions for distinguishing be- tween the three classes of double points indicated by the condition dy 0 dx 0 - viz . true double points , points of oscula- tion , and conjugate points . The condition dy dx 0 ...
Сторінка 166
... ellipse inscribed in the triangle formed by the asymptotes is easily shown . The equations to the three asymptotes are x = 0 , y = 0 , and ax + cy + 2b = 0 . From the last it appears that the interceps of the 166 SINGULAR POINTS OF CURVES .
... ellipse inscribed in the triangle formed by the asymptotes is easily shown . The equations to the three asymptotes are x = 0 , y = 0 , and ax + cy + 2b = 0 . From the last it appears that the interceps of the 166 SINGULAR POINTS OF CURVES .
Сторінка 184
... easily be seen by transferring the equation from polar to rectilinear co - ordinates , when it will be found that , according to the principles of interpretation used for the latter , the tracing of the curve from its rectilinear ...
... easily be seen by transferring the equation from polar to rectilinear co - ordinates , when it will be found that , according to the principles of interpretation used for the latter , the tracing of the curve from its rectilinear ...
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Загальні терміни та фрази
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