Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка ix
... Curvature of Curved Lines .......... 188 XIII . Application of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces 224 XV . General Theorems in the Differential Calculus ...
... Curvature of Curved Lines .......... 188 XIII . Application of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces 224 XV . General Theorems in the Differential Calculus ...
Сторінка 162
... line ; for as y = ax + b is the equation to a straight dy dx2 = 0. The same result line , it follows that for such a line may be deduced from the consideration that when d2y = da2 that point the radius of curvature is infinite , or the line ...
... line ; for as y = ax + b is the equation to a straight dy dx2 = 0. The same result line , it follows that for such a line may be deduced from the consideration that when d2y = da2 that point the radius of curvature is infinite , or the line ...
Сторінка 178
... line of abscissæ . 3. Find whether the curve have asymptotes , and deter- mine them if they exist . 4. Find the value ... curvature of the different branches , and the points of contrary flexure if such exist . 6. Determine the existence ...
... line of abscissæ . 3. Find whether the curve have asymptotes , and deter- mine them if they exist . 4. Find the value ... curvature of the different branches , and the points of contrary flexure if such exist . 6. Determine the existence ...
Сторінка 187
... curve . From = to 0 0 π 2 5π = r is negative and diminishing , 4 and it traces out the portion KHACO : the prolongation AK of AL being an asymptote to this branch . When = 5 π 4 λ = 0 , and the ... CURVATURE OF CURVED TRACING OF CURVES . 187.
... curve . From = to 0 0 π 2 5π = r is negative and diminishing , 4 and it traces out the portion KHACO : the prolongation AK of AL being an asymptote to this branch . When = 5 π 4 λ = 0 , and the ... CURVATURE OF CURVED TRACING OF CURVES . 187.
Сторінка 188
Duncan Farquharson Gregory William Walton. if P CHAPTER XII . ON THE CURVATURE OF CURVED LINES . SECT . 1. Radius of Curvature . WHEN the curve is referred to rectangular co - ordinates , be the radius of curvature p2 ( +1 dy 2 dx2 213 a ...
Duncan Farquharson Gregory William Walton. if P CHAPTER XII . ON THE CURVATURE OF CURVED LINES . SECT . 1. Radius of Curvature . WHEN the curve is referred to rectangular co - ordinates , be the radius of curvature p2 ( +1 dy 2 dx2 213 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