Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 27
Page 9
... branch of the Calculus has acquired considerable importance , and it appears to be the quarter from which we may look for great additions to our knowledge of analysis . I shall however in this chapter confine myself to examples of ...
... branch of the Calculus has acquired considerable importance , and it appears to be the quarter from which we may look for great additions to our knowledge of analysis . I shall however in this chapter confine myself to examples of ...
Page 129
... branch on the other side of AB ; the two branches meet in a cusp at the point A , and have the line HK as a common asymptote . included between the curve and the asymptote is three times the area of the generating circle . The ...
... branch on the other side of AB ; the two branches meet in a cusp at the point A , and have the line HK as a common asymptote . included between the curve and the asymptote is three times the area of the generating circle . The ...
Page 131
... branch of the curve which is called the inferior conchoid . To determine the equation , let AN , PN = y , PM ( which ... branches . When a > b there is a loop in the inferior conchoid at O as in the figure ; when ab the loop degenerates ...
... branch of the curve which is called the inferior conchoid . To determine the equation , let AN , PN = y , PM ( which ... branches . When a > b there is a loop in the inferior conchoid at O as in the figure ; when ab the loop degenerates ...
Page 133
... branch as introducing discontinuity , must choose between its discontinuity and that of an abrupt termination . " It appears to me that if we interpret our analytical symbols with proper generality so as to introduce those branches of ...
... branch as introducing discontinuity , must choose between its discontinuity and that of an abrupt termination . " It appears to me that if we interpret our analytical symbols with proper generality so as to introduce those branches of ...
Page 135
... branches extending below the axis of a , and bounded by asymptotes parallel to the axis of y at distances - a and 3a from the origin . In addition to this , the curve has an infinite number of infinite branches , which are bounded by ...
... branches extending below the axis of a , and bounded by asymptotes parallel to the axis of y at distances - a and 3a from the origin . In addition to this , the curve has an infinite number of infinite branches , which are bounded by ...
Other editions - View all
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