But again, of those which may be produced in infinitum, some comprehend no figure, as the right-line and the conic sections; but others, returning into themselves, and forming figure, may afterwards be infinitely produced. And of these some will not hereafter coincide, which resist coincidence, how far soever they may be produced; but others are coincident, which will some time or other coincide. But of non-coincident lines, some are mutually in one plane; and others not. And of non-coincidents subsisting in one plane, some are always mutually distant by an equal interval; but others always diminish the interval, as an hyperbola in its inclination to a right-line, and likewise the conchoid[186]. For these, though they always diminish the interval, never coincide. And they mutually converge, indeed, but never perfectly nod to each other; which is indeed a theorem in geometry especially admirable, exhibiting certain lines endued with a non-assenting nod. But the right-lines, which are always distant by an equal interval, and which never diminish the space placed between them in one plane, are parallel lines. And thus much we have extracted from the studies of the elegant Geminus, for the purpose of explaining the present definition. END OF THE FIRST VOLUME. FOOTNOTES: [1] The Grecian literature of this writer will now prove of real utility; and the graces and the sublimities of PLATO will soon be familiarised to the English reader, by a hand that I am persuaded will not appear inferior to his great original. Let me also be permitted to recommend his version of PLOTINUS on THE BEAUTIFUL. [2] i.e. Capable of parts. [3] i.e. Not capable of parts. [4] Dr. Young, in his Night Thoughts. [5] See book the second, of Aristotle’s Metaphysics. [6] Ennead vi. lib. vii. [7] In his commentary on the 2d, 12th, and 13th books of Aristotle’s Metaphysics, page 60. A Latin translation only of this invaluable work is extant; but I have fortunately a copy in my possession, with the version every where corrected by the learned Thomas Gale, and with large extracts from the Greek. [8] See Proclus on Plato’s Theology, p. 226. [9] Ennead vi. lib. 6.