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nydus/On Growth and FormPublic
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Table of Contents

CHAPTER XI THE LOGARITHMIC SPIRAL

referred to a plane, is apôÙproxôÙiôÙmateôÙly bounded by two elliptic curves, similar and similarly situated, whose areas are to one another in a definite ratio, namely as

and a similar ratio exists in Ammonites and all other close-whorled spirals, in which however we cannot always make the simple assumption of elliptical form. In a median section of Nautilus, we see each septum forming a tangent to the inner and to the outer wall, just as it did in a section of the straight Orthoceras; but the curvatures in the neighbourhood of these two points of contact are not identical, for they now vary inversely as the radii, drawn from the pole of the spiral shell. The contour of the septum in this median plane is a spiral curve identical with the original logarithmic spiral. Of this it is the 〜invert,〝 and the fact that the original curve and its invert are both identical is one of the

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