Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 30
Сторінка 131
... intercepted between AB and BC at right angles to each other , is double of OB , the angle AOM is the third part of 40B . Now if we describe a conchoid with O as pole and the line AB as directrix , the constant parameter being equal to ...
... intercepted between AB and BC at right angles to each other , is double of OB , the angle AOM is the third part of 40B . Now if we describe a conchoid with O as pole and the line AB as directrix , the constant parameter being equal to ...
Сторінка 134
... intercepted between the curve and the axis of x is equal to the radius vector , but measured in the opposite direction ; and if we represent an ordinate corresponding to the ab- scissa a by f ( x ) , and the corresponding area by cF ( x ) ...
... intercepted between the curve and the axis of x is equal to the radius vector , but measured in the opposite direction ; and if we represent an ordinate corresponding to the ab- scissa a by f ( x ) , and the corresponding area by cF ( x ) ...
Сторінка 145
... intercepted between the point of contact and the perpendicular on it from the origin is du du y OC t = ada + ydy ( dx2 + dy2 ) } dy dx du 2 du + dx dy The portions of the axes cut off between the origin and the tangent , or the intercepts ...
... intercepted between the point of contact and the perpendicular on it from the origin is du du y OC t = ada + ydy ( dx2 + dy2 ) } dy dx du 2 du + dx dy The portions of the axes cut off between the origin and the tangent , or the intercepts ...
Сторінка 146
... intercepts of the tangent x。y = 4xy = 4m2 is constant ; and the triangle contained between the axes and the tangent ... intercepted between the axes = 2 ( x2 + y2 ) 3 = a ; or the hypocycloid is constantly touched by a straight line of ...
... intercepts of the tangent x。y = 4xy = 4m2 is constant ; and the triangle contained between the axes and the tangent ... intercepted between the axes = 2 ( x2 + y2 ) 3 = a ; or the hypocycloid is constantly touched by a straight line of ...
Сторінка 150
... intercepts of the tangent ≈。, Yo , dx dy xo = xy Yo = y - x ; dy dx x and y being the co - ordinates of the point of contact P. The area BEC = y sin E , therefore ac y dx dy ( ~ - x dy ) = ( 3 y - x dx dy dy2 dx dx is to be a maximum ...
... intercepts of the tangent ≈。, Yo , dx dy xo = xy Yo = y - x ; dy dx x and y being the co - ordinates of the point of contact P. The area BEC = y sin E , therefore ac y dx dy ( ~ - x dy ) = ( 3 y - x dx dy dy2 dx dx is to be a maximum ...
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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