Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 110
... 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 we have d'u d'u u de dy- ( dady ) " dx 2 = 0 , an equation ...
... 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 we have d'u d'u u de dy- ( dady ) " dx 2 = 0 , an equation ...
Сторінка 129
... locus of the point P where the line AQ cuts the ordinate RN is the cissoid of Diocles . To find its equation , put AN , PN - y , AC - a : then as PN QM y AN = AM x = ( 2 ax - x2 ) 2 а -x or y ( 2ax ) = x3 , which is the equation to the ...
... locus of the point P where the line AQ cuts the ordinate RN is the cissoid of Diocles . To find its equation , put AN , PN - y , AC - a : then as PN QM y AN = AM x = ( 2 ax - x2 ) 2 а -x or y ( 2ax ) = x3 , which is the equation to the ...
Сторінка 130
... in M ; take the point P , such that PM shall be always of a constant length : the locus of the point P is the conchoid . The point P may be taken Append . ad Arith . Univ . between 0 and M , in which case it will 130 GENERATION OF CURVES .
... in M ; take the point P , such that PM shall be always of a constant length : the locus of the point P is the conchoid . The point P may be taken Append . ad Arith . Univ . between 0 and M , in which case it will 130 GENERATION OF CURVES .
Сторінка 132
... locus of the point P is the curve called the Witch . Putting AC = a , AN x , PN = y , equation to the curve = x y2 = 4a2 ( 2 a − x ) . we find as the This curve is given by Donna Maria Agnesi in her In- stituzioni Analitiche , Art ...
... locus of the point P is the curve called the Witch . Putting AC = a , AN x , PN = y , equation to the curve = x y2 = 4a2 ( 2 a − x ) . we find as the This curve is given by Donna Maria Agnesi in her In- stituzioni Analitiche , Art ...
Сторінка 134
... locus of their intersection will be the quadratrix of Dinos- tratus . To find its equation , let AM = x , PM = y , AC = a . Then from the uniformity of the motion of CQ and MN , we have AM : AC ; ACQ ACB = π I whence ACQ = 3 But PM CM ...
... locus of their intersection will be the quadratrix of Dinos- tratus . To find its equation , let AM = x , PM = y , AC = a . Then from the uniformity of the motion of CQ and MN , we have AM : AC ; ACQ ACB = π I whence ACQ = 3 But PM CM ...
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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