Along a **parabola** life like a rocket flies,Mainly in darkness, now and then on a rainbow.

— "Parabolic Ballad"; translated by W. H. Auden, p. 113.

A **parabola** is bound by one law which fixes its relations with two straight lines at every point; yet it has no end short of infinity, and it continually changes its direction. The Initiate who is aware Who he is can always check is conduct by reference to the determinants of his curve, and calculate his past, his future, his bearings, and his proper course at any assigned moment; he can even comprehend himself as a simple idea.

— Appendix VI : A few principal rituals –

By the word 'conoid,' in his book on Conoids and Spheroids, is meant the solid produced by the revolution of a **parabola** or a hyperbola about its axis. Spheroids are produced by the revolution of an ellipse, and are long or flat, according as the ellipse revolves around the major or minor axis. The book leads up to the cubature of these solids.

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It is worthy of notice that Apollonius nowhere introduces the notion of directrix for a conic, and that, though he incidentally discovered the focus of an ellipse and hyperbola, he did not discover the focus of a **parabola**. Conspicuous in his geometry is also the absence of technical terms and symbols, which renders the proofs long and cumbrous.

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