Examples of the Processes of the Differential and Integral Calculus |
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Page v
... adapts itself to all cases in which it is required , while that which is proposed is not so accommodating , there ap- pears to me no doubt which is to be preferred . 1 The sources from which the Examples have been taken are PREFACE . V.
... adapts itself to all cases in which it is required , while that which is proposed is not so accommodating , there ap- pears to me no doubt which is to be preferred . 1 The sources from which the Examples have been taken are PREFACE . V.
Page vi
D. F. Gregory. The sources from which the Examples have been taken are indicated by the references which will be found in the body of the work . For although I have not thought it necessary to cite an authority for every example , I have ...
D. F. Gregory. The sources from which the Examples have been taken are indicated by the references which will be found in the body of the work . For although I have not thought it necessary to cite an authority for every example , I have ...
Page 81
... taken like that from Euler's Calc . Diff . p . 746 . ( 10 ) The sum of the series x + 2x2 + 3x3 + .... + nx ” , is W = ...... * − ( n + 1 ) + 1 + 2 + 2 - ( 1 - x ) 2 and we are required to find its value when a = 1 , or when the series ...
... taken like that from Euler's Calc . Diff . p . 746 . ( 10 ) The sum of the series x + 2x2 + 3x3 + .... + nx ” , is W = ...... * − ( n + 1 ) + 1 + 2 + 2 - ( 1 - x ) 2 and we are required to find its value when a = 1 , or when the series ...
Page 108
... in a negative result , the value of y is a maximum . dy give da2 The preceding examples are taken from Euler's Calc . Diff . Part . II . Cap . XI . SECT . 3 . Functions of Two or more Variables 108 MAXIMA AND MINIMA .
... in a negative result , the value of y is a maximum . dy give da2 The preceding examples are taken from Euler's Calc . Diff . Part . II . Cap . XI . SECT . 3 . Functions of Two or more Variables 108 MAXIMA AND MINIMA .
Page 130
... 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 .
... 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 .
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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