Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 127
... geometry of the figure we have the equations v2 + vw + w2 = a2 , u2 + uw + w3 = b2 , u2 + u v + v2 = 4m2 and u v + uw + v w = 33 Adding the sum of the m2 being the area of the triangle . first three equations to three times the last , 2 ...
... geometry of the figure we have the equations v2 + vw + w2 = a2 , u2 + uw + w3 = b2 , u2 + u v + v2 = 4m2 and u v + uw + v w = 33 Adding the sum of the m2 being the area of the triangle . first three equations to three times the last , 2 ...
Сторінка 136
... geometry which has more exercised the ingenuity of mathematicians than the cycloid , and their labours have been rewarded by the discovery of a multitude of interesting properties , im- portant both in geometry and in dynamics . * The ...
... geometry which has more exercised the ingenuity of mathematicians than the cycloid , and their labours have been rewarded by the discovery of a multitude of interesting properties , im- portant both in geometry and in dynamics . * The ...
Сторінка 142
... geometric while the angle increases in an arithmetic ratio . 0 Hence its equation will be of the form r = cea , rcea , = a . or , as it is usually written , r = = - This curve was imagined by Descartes , who also noticed two of its ...
... geometric while the angle increases in an arithmetic ratio . 0 Hence its equation will be of the form r = cea , rcea , = a . or , as it is usually written , r = = - This curve was imagined by Descartes , who also noticed two of its ...
Сторінка 157
... geometry . The impossibility of one of the variables , when certain values are assigned to the other , may be in- terpreted as signifying that the curve for these values leaves the plane to which it is referred . Now when by assigning ...
... geometry . The impossibility of one of the variables , when certain values are assigned to the other , may be in- terpreted as signifying that the curve for these values leaves the plane to which it is referred . Now when by assigning ...
Сторінка 175
... geometry , as a know- ledge of these is requisite for the understanding of the views which I have adopted both in the preceding and in the fol- lowing pages . By the principles of the Geometry of Descartes , the position of a point in a ...
... geometry , as a know- ledge of these is requisite for the understanding of the views which I have adopted both in the preceding and in the fol- lowing pages . By the principles of the Geometry of Descartes , the position of a point in a ...
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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