A Treatise On the Differential And Integral Calculus

Cover A Treatise On the Differential And Integral Calculus
A Treatise On the Differential And Integral Calculus
Edward Henry Courtenay
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The Ellipse, aV + ^'^^^ = a*^^ 151 dx' . * . The equation of the tangent is •.^*=-— ^ and ^ = -^ dy^ h^x.
or, a*yyi + ^^^1 = ^*^^' 4 1 1^. . ^"^ tt^l « Also subtangent = — y, -r-^ = -r^ = a?,.
And subnormal *^__6^ y^^- ,2^- 3. The logarithmic curve, whose equation is y =zaF* ^ = loga.a'.
• * • subtan = log a . a't log a = — m.
where m is the modulus of the system of logarithms whose base is a.
Also subnorm = log a . a*tyi = — = • In this curve, the values of the abscissas are the logarithms of
...the values of the corresponding ordinates in the system whose base is u.
114. Prof, To determine expressions for the tangent, the normal, and the perpendicular from the origin to the tangent of a plane curve.
For the tangcLt PT, we have PT = -/FD^ + DT"^ NT" Digitized by VjOOQIC 152 DIFFERENTIAL CALCULUS.
For the normal PNy we have For the perpendicular 0§, we have Oq^OT,^mOTq-OT cosec iec4 ~ V 1 + cot»« r , f^"|l Ex. The general equation of all parabolas.
The general name of parabola is applied to all curves included in the equation y*" = a*"^ar, in which m may represent any positive number either whole or fractional.


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