Examples of the Processes of the Differential and Integral Calculus |
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Page 88
... relation , depending on the nature of the functions , between the new numerator and denominator which will enable us to trace the real value . A function u = P Q , which becomes - - when = a , can frequently be reduced to the form ; for ...
... relation , depending on the nature of the functions , between the new numerator and denominator which will enable us to trace the real value . A function u = P Q , which becomes - - when = a , can frequently be reduced to the form ; for ...
Page 110
... relation between them . This corresponds geometrically to a locus of maxima and minima , such as would be produced by the extremity of the major axis of an ellipse which revolves round an axis parallel to the major axis . In these cases ...
... relation between them . This corresponds geometrically to a locus of maxima and minima , such as would be produced by the extremity of the major axis of an ellipse which revolves round an axis parallel to the major axis . In these cases ...
Page 112
... relation between the quantities A , which is very useful in many problems . Let u be homogeneous of m dimensions , and let L1 = 0 , L = 0 , & c . be put under the form Ma + A = 0 , N1 + B = 0 , & c . b where Ma is homogeneous of a ...
... relation between the quantities A , which is very useful in many problems . Let u be homogeneous of m dimensions , and let L1 = 0 , L = 0 , & c . be put under the form Ma + A = 0 , N1 + B = 0 , & c . b where Ma is homogeneous of a ...
Page 158
... relation between » and O , then the tangent of the angle ( 4 ) between the radius vector and the tangent to the curve is r do dr The subtangent , which is the portion of a perpendicular to the radius vector at the origin intercepted by ...
... relation between » and O , then the tangent of the angle ( 4 ) between the radius vector and the tangent to the curve is r do dr The subtangent , which is the portion of a perpendicular to the radius vector at the origin intercepted by ...
Page 164
... the plane of reference in a point through which there passes a possible branch of the curve . Képas , a horn . † ' Paupos , a beak . For a fuller development of the relation between the various 164 SINGULAR POINTS OF CURVES .
... the plane of reference in a point through which there passes a possible branch of the curve . Képas , a horn . † ' Paupos , a beak . For a fuller development of the relation between the various 164 SINGULAR POINTS OF CURVES .
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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