The Elements of the Differential Calculus Comprehending the General Theory of
The Elements of the Differential Calculus Comprehending the General Theory of
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To quickly assess the difficulty of the text, read a short excerpt:
) Normals to the curve are tangents to the evolute. Let the equations of the curve and of its evolute be y = Fx and /3 = fa, then differentiating the equation (2) p. 131, considering a, ^ as va- riables as well as x, y, we have but (130) ^ + p"(^-/3)+p'^-p'^=^0, Hence, by substitution, ax ax df3 da d^ 1 /5 — v, . -. -f-— ^or-f- = r=- ^fequa. 2, p. 131).
dx, dx da p a — a? "^ ' Now -J— expresses the trigonometrical tangent of the angle be- tween the axis of a; and a linear tangent through any po...int (a, (3) of the evolute, and expresses the trigonometrical tangent of the P angle between the axis of x and a normal at any point {x, y) of the involute ; but this normal necessarily passes through a point (a, fS) of the evolute, and, therefore, in consequence of the above equality, it must coincide with thq tangent at that point.
THEOREM.
(103. ) The difference of any two radii of curvature is equal to the arc of the evolute comprehended between them. Differentiating the equation % » 14^ THE DIFFERENTIAL CALCULUS.
What to read after The Elements of the Differential Calculus Comprehending the General Theory of?
You can find similar books in the "Read Also" column, or choose other free books by J R John Radford Young to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
) Normals to the curve are tangents to the evolute. Let the equations of the curve and of its evolute be y = Fx and /3 = fa, then differentiating the equation (2) p. 131, considering a, ^ as va- riables as well as x, y, we have but (130) ^ + p"(^-/3)+p'^-p'^=^0, Hence, by substitution, ax ax df3 da d^ 1 /5 — v, . -. -f-— ^or-f- = r=- ^fequa. 2, p. 131).
dx, dx da p a — a? "^ ' Now -J— expresses the trigonometrical tangent of the angle be- tween the axis of a; and a linear tangent through any po...int (a, (3) of the evolute, and expresses the trigonometrical tangent of the P angle between the axis of x and a normal at any point {x, y) of the involute ; but this normal necessarily passes through a point (a, fS) of the evolute, and, therefore, in consequence of the above equality, it must coincide with thq tangent at that point.
THEOREM.
(103. ) The difference of any two radii of curvature is equal to the arc of the evolute comprehended between them. Differentiating the equation % » 14^ THE DIFFERENTIAL CALCULUS.
What to read after The Elements of the Differential Calculus Comprehending the General Theory of?
You can find similar books in the "Read Also" column, or choose other free books by J R John Radford Young to read onlineMoreLess
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