A Treatise On the Differential And Integral Calculus And On the Calculus of Va
A Treatise On the Differential And Integral Calculus And On the Calculus of Va
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Prop. To determine the evolute of a given curve y = Fx.
If in the formulce for the co-ordinates of the centre of the oscu- latory circle, viz. : (Art. 127. ) ■P , l+;/2 (1) and h 1 -4- »'2 2J p we substitute the values of p' and jo", derived from the equation of the curve y = Fx (3), we shall have the three equations (1), (2), and (. T), involving the four variable quantities . R, y, «, and i; and by eliiiiiiiating x and y the result will be a general relation between G and 6, the co-ordinates ...of the required evolute. This equation being independent of x and y will apply to every point in the desired curve.
io8. In most cases the necessary elimina- tion is quite difficult; the following are com panuivoly simple examples.
]. '^llie evolute of the common parabola.
Here we have y^ _ o^;^: .... (1).
V p^ p' -'-, and p" = -^.
y yo EVOLUTES AND INVOLUTES.
177 y y^ p' P y1 . P2 y y — 2 - y y6 ■ (3).
From (2) and (3) we get x =. — ;-, — 5 and y"^ = p h ; and these values substituted in (1) give 3 7# l^ b 2/-^^' '■- = ^A'^-i>Y' the equation of the semi-cubieal parabohi, whose axis coincides with that of the given curve ; the distance Aa between the vertices being =z p the semi-parameter.
What to read after A Treatise On the Differential And Integral Calculus And On the Calculus of Va?
You can find similar books in the "Read Also" column, or choose other free books by Edward Henry Courtenay to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Prop. To determine the evolute of a given curve y = Fx.
If in the formulce for the co-ordinates of the centre of the oscu- latory circle, viz. : (Art. 127. ) ■P , l+;/2 (1) and h 1 -4- »'2 2J p we substitute the values of p' and jo", derived from the equation of the curve y = Fx (3), we shall have the three equations (1), (2), and (. T), involving the four variable quantities . R, y, «, and i; and by eliiiiiiiating x and y the result will be a general relation between G and 6, the co-ordinates ...of the required evolute. This equation being independent of x and y will apply to every point in the desired curve.
io8. In most cases the necessary elimina- tion is quite difficult; the following are com panuivoly simple examples.
]. '^llie evolute of the common parabola.
Here we have y^ _ o^;^: .... (1).
V p^ p' -'-, and p" = -^.
y yo EVOLUTES AND INVOLUTES.
177 y y^ p' P y1 . P2 y y — 2 - y y6 ■ (3).
From (2) and (3) we get x =. — ;-, — 5 and y"^ = p h ; and these values substituted in (1) give 3 7# l^ b 2/-^^' '■- = ^A'^-i>Y' the equation of the semi-cubieal parabohi, whose axis coincides with that of the given curve ; the distance Aa between the vertices being =z p the semi-parameter.
What to read after A Treatise On the Differential And Integral Calculus And On the Calculus of Va?
You can find similar books in the "Read Also" column, or choose other free books by Edward Henry Courtenay to read onlineMoreLess
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