Ver. 9. _Tangents_—So called from touching, because they touch circles, and never cut them. Footnote 202: Ver. 10. _Circles_—See Chambers’s Dictionary, article “Circle”. Footnote 203: Ver. 10. _Osculation_—For the _osculation_, or kissing of circles and other curves, see Huygens, who has veiled this delicate and inflammatory subject in the decent obscurity of a learned language. Footnote 204: Ver. 11. _Cissois_—A curve supposed to resemble the sprig of ivy, from which it has its name, and therefore peculiarly adapted to poetry. Footnote 205: Ver. 12. _Conchois_, or _Conchylis_—A most beautiful and picturesque curve; it bears a fanciful resemblance to a _conch_ shell. The conchois is capable of infinite extension, and presents a striking analogy between the animal and mathematical creation—every individual of this species containing within itself a series of _young_ conchoids for several generations, in the same manner as the Aphides and other insect tribes are observed to do. Footnote 206: Ver. 15. _Hydrostatics_—Water has been supposed, by several of our philosophers, to be capable of the passion of love. Some later experiments appear to favour this idea. Water, when pressed by a moderate degree of heat, has been observed to simper, or simmer, as it is more usually called. The same does not hold true of any other element. Footnote 207: Ver. 17. _Acoustics_—The doctrine or theory of sound. Footnote 208: Ver. 18. _Euclid and Algebra_—The loves and nuptials of these two interesting personages, forming a considerable episode in the third canto, are purposely omitted here. Footnote 209: Ver. 19. _Pulley_—So called from our Saxon word to PULL, signifying to pull or draw. Footnote 210: Ver. 23. _Fair sylphish forms_—_Vide_ modern prints of nymphs and shepherds dancing to nothing at all. Footnote 211: Ver. 27. _Such rich confusion_—Imitated from the following genteel and sprightly lines in the first canto of the “Loves of the Plants”: “So bright its folding canopy withdrawn, Glides the gilt landau o’er the velvet lawn, Of beaux and belles displays the glittering throng, And soft airs fan them as they glide along”. Footnote 212: Ver. 38. _Angle_—Gratus puellæ risus ab Angulo.—_Hor._ Footnote 213: Ver. 39. _How slow progressive Points_—The Author has reserved the picturesque imagery which the _theory of fluxions_ naturally suggested for his “Algebraic Garden,” where the _fluents_ are described as rolling with an even current between a margin of _curves_ of the higher order over a pebbly channel, inlaid with _differential calculi_. In the following six lines he has confined himself to a strict explanation of the theory, according to which lines are supposed to be generated by the motion of points, planes by the lateral motion of lines, and solids from planes, by a similar process.