THE LOVES OF THE TRIANGLES. A MATHEMATICAL AND PHILOSOPHICAL POEM. INSCRIBED TO DR. DARWIN. CANTO I. STAY TAY your rude steps, or e'er your feet invade 5 Ver. 1-4. Imitated from the introductory couplet to the ECONOMY OF VEGE TATION. "Stay your rude steps, whose throbbing breasts infold "The Legion Fiends of Glory and of Gold." This sentiment is here expanded into four lines. Ver. 6. Definition-A distinct notion explaining the Genesis of a thing—Wolfius. Ver. 7. Postulate-A self-evident proposition. Ver. 8. Axiom-An indemonstrable truth. For no TANGENTS touch, no ANGLES meet, 10 you, NO CIRCLES join in osculation sweet! For me, ye CisSOIDS, round my temples bend Your wandering Curves; ye CONCHOIDS extend; Let HYDROSTATICS, simpering as they go, 15 Lead the light Naiads on fantastic toe; Ver. 9. Tangents-So called from touching, because they touch Circles, and never cut them. Ver. 10. Circles-See Chambers's Dictionary, Article Circle. Ditto, 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. Ver. 11. Cissois-A Curve supposed to resemble the sprig of ivy, from which it has its name, and therefore peculiarly adapted to poetry. 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. 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. Let shrill ACOUSTICS tune the tiny lyre; I see the fair fantastic forms appear, 20 The flaunting drapery, and the languid leer; Fair Sylphish forms—who, tall, erect, and slim, Dart the keen glance, and stretch the length of limb; To viewless harpings weave the meanless dance, 25 Wave the gay wreath, and titter as they prance. Such rich confusion charms the ravish'd sight, When vernal Sabbaths to the Park invite. Ver. 17. Acoustics-The doctrine or theory of sound. 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. Ver. 19. Pulley-So called from our Saxon word to PULL, signifying to pull or draw. Ver. 23. Fair Sylphish forms-Vide modern prints of nymphs and shepherds dancing to nothing at all. 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. Mounts the thick dust, the coaches crowd along, 30 But chief, thou Nurse of the Didactic Muse, 35 40 As pendant spiders spin the filmy twine; Ver. 38. Angle-Gratus puellæ risus ab Angulo.-Hor. 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. Quare-Whether a practical application of this Theory would not enable us to account for the Genesis, or original formation of Space itself, in the same manner in which Dr. Darwin has traced the whole of the organized creation to his Six Filaments-Vide ZOONOMIA. We may conceive the whole of our present Universe How lengthen'd Lines, impetuous sweeping round, to have been originally concentered in a single Point-We may conceive this Primeval Point, or Punctum Saliens of the Universe, evolving itself by its own energies, to have moved forward in a right Line, ad infinitum, till it grew tired—After which, the right Line which it had generated would begin to put itself in motion in a lateral direction, describing an Area of infinite extent. This Area, as soon as it became conscious of its own existence, would begin to ascend or descend, according as its specific gravity might determine it, forming an immense solid space filled with Vacuum, and capable of containing the present existing Universe. Space being thus obtained, and presenting a suitable Nidus, or receptacle for the generation of Chaotic Matter, an immense deposit of it would gradually be accumulated:-After which, the Filament of Fire being produced in the Chaotic Mass, by an Idiosyncracy, or self-formed habit analogous to fermentation, Explosion would take place; Suns would be shot from the Central Chaos;-Planets from Suns; and Satellites from Planets. In this state of things, the Filament of Organization would begin to exert itself, in those independent masses which, in proportion to their bulk, exposed the greatest surface to the action of Light and Heat. This Filament, after an infinite series of ages, would begin to ramify, and its viviparous offspring would diversify their forms and habits, so as to accommodate themselves to the various incunabula which Nature had prepared for them.—Upon this view of things, it seems highly probable that the first effort of Nature terminated in the production of Vegetables, and that these being abandoned to their own energies, by degrees detached themselves from the surface of the earth, and supplied themselves with wings or feet, according as their different propensities determined them, in favour of aerial and terrestrial existence. Others by an inherent disposition to society and civilization, and by a stronger effort of volition, would become Men. These, in time, would restrict themselves to the use of their hind feet their tails would gradually rub off, by sitting in their caves or huts, as soon as they arrived at a domesticated state: they would invent language, and the use |