Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 46
Сторінка 41
... co - ordinates in space . If we suppose V = 1 , ffdx dy dz is the expression for the volume of any solid referred to rectangular co - ordinates : and it becomes Jffr2 dr sine de do when referred to polar co - ordinates . ( 10 ) Having ...
... co - ordinates in space . If we suppose V = 1 , ffdx dy dz is the expression for the volume of any solid referred to rectangular co - ordinates : and it becomes Jffr2 dr sine de do when referred to polar co - ordinates . ( 10 ) Having ...
Сторінка 102
... co - ordinates of A and B be a , b , a1 , b1 . Then u = AP + BP = { b2 + ( x − a ) 3 } } + { b‚2 + ( a ̧ − x ) 2 } 3 = minimum . Whence 00 -α = 2 - a1 < -00 { b2 + ( x − a ) 2 } } = { b‚2 + ( a ̧ − x ) 2 } } ' or the angles APM ...
... co - ordinates of A and B be a , b , a1 , b1 . Then u = AP + BP = { b2 + ( x − a ) 3 } } + { b‚2 + ( a ̧ − x ) 2 } 3 = minimum . Whence 00 -α = 2 - a1 < -00 { b2 + ( x − a ) 2 } } = { b‚2 + ( a ̧ − x ) 2 } } ' or the angles APM ...
Сторінка 119
... co - ordinates of the ex- tremities of the least distance ( S ) , d2 = ( x − x ′ ) 2 + ( y − y ' ) 2 + ( ≈ − x ′ ) 2 is to be a minimum , the variables being subject to the con- ditions ( 1 ) and ( 2 ) . Differentiating , 0 = ( x ...
... co - ordinates of the ex- tremities of the least distance ( S ) , d2 = ( x − x ′ ) 2 + ( y − y ' ) 2 + ( ≈ − x ′ ) 2 is to be a minimum , the variables being subject to the con- ditions ( 1 ) and ( 2 ) . Differentiating , 0 = ( x ...
Сторінка 123
... co - ordinates of the centre of the curve . Let them be a , ß MAXIMA AND MINIMA . 123.
... co - ordinates of the centre of the curve . Let them be a , ß MAXIMA AND MINIMA . 123.
Сторінка 138
... ordinate QN ( fig . 20 ) of a semicircle be produced till it be equal to the arc CQ , its extremity will lie in a curve which is called the companion to the cycloid . The co - ordinates of a point in this curve are , putting_CO = a ...
... ordinate QN ( fig . 20 ) of a semicircle be produced till it be equal to the arc CQ , its extremity will lie in a curve which is called the companion to the cycloid . The co - ordinates of a point in this curve are , putting_CO = a ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³