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asymptotes
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The orbit has therefore two asymptotes, inclined at an angle lr/m.
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As regards the so-called hyperbolisms, observe that (besides the single asymptote) we have in the case of those of the hyperbola two parallel asymptotes; in the case of those of the ellipse the two parallel asymptotes become imaginary, that is, they disappear; and in the case of those of the parabol
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The two legs of a hyperbolic branch may belong to different asymptotes, and in this case we have the forms which Newton calls inscribed, circumscribed, ambigene, &c.; or they may belong to the same asymptote, and in this case we have the serpentine form, where the branch cuts the asymptote, so as to
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58) has two vertical asymptotes x = ~ 3/4irx; this shows that however the thickness of a cable be adjusted there is a limit irA to the horizontal span, where A depends on the tensile strength of the material.
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(See Infinitesimal Calculus.) He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes.
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