An Elementary Treatise On the Differential Calculus Containing the Theory of Pl
An Elementary Treatise On the Differential Calculus Containing the Theory of Pl
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To quickly assess the difficulty of the text, read a short excerpt:
If p be the radius of curvature at any point on a curve, prove that the radius of curvature at the corresponding point in the evolute is — ; where » dco is the angle the radius of curvature makes with a fixed line.
22. In a curve, prove that 1 m J* ( d ^\ p dx \ds/' Examples. 321 23. Find the equation of the evolute of an ellipse hy means of the eccentric angle.
24. Prove that the determination of the equation of the evolute of the curve y = kx n reduces to the elimination of x between the equa...tions a = x z 2n ' 1, and j8 = **» + n — 1 n - 1 kn(n- i)x n - % 25. In figure, Art. 239, if the tangent to the evolute at P meet the parabola in a point JET, prove that HN is perpendicular to the axis of the parabola.
26. If on the tangent at each point on a curve a constant length measured from the point of contact be taken, prove that the normal to the locus of the points so found passes through the centre of curvature of the proposed curve.
27. In general, if through each point of a curve a line of given length be drawn making a constant angle with the normal, the normal to the curve locus of the extremities of this line passes through the centre of curvature of the pro- posed.
What to read after An Elementary Treatise On the Differential Calculus Containing the Theory of Pl?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Williamson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If p be the radius of curvature at any point on a curve, prove that the radius of curvature at the corresponding point in the evolute is — ; where » dco is the angle the radius of curvature makes with a fixed line.
22. In a curve, prove that 1 m J* ( d ^\ p dx \ds/' Examples. 321 23. Find the equation of the evolute of an ellipse hy means of the eccentric angle.
24. Prove that the determination of the equation of the evolute of the curve y = kx n reduces to the elimination of x between the equa...tions a = x z 2n ' 1, and j8 = **» + n — 1 n - 1 kn(n- i)x n - % 25. In figure, Art. 239, if the tangent to the evolute at P meet the parabola in a point JET, prove that HN is perpendicular to the axis of the parabola.
26. If on the tangent at each point on a curve a constant length measured from the point of contact be taken, prove that the normal to the locus of the points so found passes through the centre of curvature of the proposed curve.
27. In general, if through each point of a curve a line of given length be drawn making a constant angle with the normal, the normal to the curve locus of the extremities of this line passes through the centre of curvature of the pro- posed.
What to read after An Elementary Treatise On the Differential Calculus Containing the Theory of Pl?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Williamson to read onlineMoreLess
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