 | Baden Powell - Calculus - 1829 - 210 pages
...curvature of the curve. EVOLUTES AND INVOLUTES. Since -^ expresses the trigonometrical tangent of the ax angle which the tangent at P makes with the axis of x, the equation of the normal to a point whose coordinates are « and /3, will be, _ dx. , and this equation... | |
 | Mathematics - 1868 - 276 pages
....„„. ... (17).. Equations involving the direction of the curve at the current point. Let i/r be the angle which the tangent at P makes with the axis of y. Then the angles of the triangle PP'H are ultimately i^, TT — o>, <o — i/r. Therefore by equations... | |
 | Mathematics - 1868 - 272 pages
...from (15), ... (17). Equations involving the direction of the curve at the current point. Let ijr be the angle which the tangent at P makes with the axis of y. Then the angles of the triangle PP'H are' ultimately i/r, TT — o>, co — i/r. Therefore by equations... | |
 | Edward Olney - Calculus - 1871 - 396 pages
...which are (x', y ). The equation of a tangent at the point P is y — y' = a(x — x'), in which a is the tangent of the angle which the tangent at P makes with the axis of x, that is tan STX ; and is to be determined from the equation of the curve as in the preceding part of... | |
 | W. J. C. Miller - Mathematics - 1874 - 172 pages
...the PROPOSER. If x, y be coordinates of a point P, referred to the tangent and normal at O, and в the angle which the tangent at P makes with the axis of x, then Л therefore da sin в сРy f da2 cos 9 p NST ,í = cos в + — — sin в, — - = — —... | |
 | 1874 - 120 pages
...by the PROPOSER. If x, y he coordinates of a point P, referred to the tangent and normal at O,and в the angle which the tangent at P makes with the axis of x, then da ds ^ = f> ,, „ d?x sin в d'y cosfl therefore __ = , —^ = , ds2 p ds2 pn *ж — = —... | |
 | Alexander Knox (B.A.) - 1884 - 210 pages
...directions of the arc, chord, and tangent are the same, and are identical with that of the tangent; and the tangent of the angle which the tangent at P makes with PN or OX is represented by the ratio of the very small inci-ease in PM to the very small increase in... | |
 | Simon Newcomb - Calculus - 1887 - 330 pages
...ratio of the change in the direction of the tangent (or normal) to the distance PP'. Let us put a = the angle which the tangent at P makes with the axis of X. a + da = the same angle for the tangent at P'. Fio. 41. ds = the infinitesimal distance PP'. Then,... | |
 | John Graham - Calculus - 1896 - 314 pages
...Denoting the arc PQ by ds, the angle P 0' Q by d в, and 0' P by V, then ds = rd в, or l ав Now, в is the angle which the tangent, at P, makes with the axis of X, and d в is equal to the angle between the tangents at P and Q. We have also hence &У 2udO -5-! =... | |
 | John Perry - Mechanical engineering - 1897 - 724 pages
...5# and Sy become smaller and smaller, so that $y/$z is to be written dyjdx, then dyjdx is evidently tangent of the angle which the tangent at p makes with the axis of x. We usually call this the slope of the curve at the point P. If y is any quantity that depends upon... | |
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... in the differential calculus, it will be well to point out its obvious geometrical meaning. This is simply that, if the curve APE (see Fig. 
