“Our second principle is, the ‘eternal and absolute perfectibility of man’. We contend, that if, as is demonstrable, we have risen from a level with the cabbages of the field to our present comparatively intelligent and dignified state of existence, by the mere exertion of our own energies; we should, if these energies were not repressed and subdued by the operation of prejudice, and folly, by King-Craft and Priest-Craft, and the other evils incident to what is called civilized society, continue to exert and expand ourselves in a proportion infinitely greater than anything of which we yet have any notion:—in a ratio hardly capable of being calculated by any science of which we are now masters: but which would in time raise man from his present biped state to a rank more worthy of his endowments and aspirations; to a rank in which he would be, as it were, all Mind; would enjoy unclouded perspicacity and perpetual vitality; feed on oxygene, and never die, but by his own consent.

“But though the poem of the Progress of Man alone would be sufficient to teach this system and enforce these doctrines, the whole practical effect of them cannot be expected to be produced, but by the gradual perfecting of each of the sublimer sciences;—at the husk and shell of which we are now nibbling and at the kernel whereof, in our present state, we cannot hope to arrive. These several sciences will be the subjects of the several auxiliary Didactic Poems which I have now in hand (one of which, entitled The Loves of the Triangles, I herewith transmit to you), and for the better arrangement and execution of which, I beseech you to direct your bookseller to furnish me with a handsome Chambers’s Dictionary; in order that I may be enabled to go through the several articles alphabetically, beginning with Abracadabra, under the first letter, and going down to Zodiac, which is to be found under the last.

“I am persuaded that there is no science, however abstruse, nay, no trade or manufacture, which may not be taught by a didactic poem. In that before you, an attempt is made (not unsuccessfully, I hope) to enlist the imagination under the banners of Geometry. Botany I found done to my hands. And though the more rigid and unbending stiffness of a mathematical subject does not admit of the same appeals to the warmer passions, which naturally arise out of the sexual (or, as I have heard several worthy gentlewomen of my acquaintance, who delight much in the poem to which I allude, term it, by a slight misnomer no way difficult to be accounted for—the sensual) system of Linnæus;—yet I trust that the range and variety of illustration with which I have endeavoured to ornament and enlighten the arid truths of Euclid and Algebra, will be found to have smoothed the road of Demonstration, to have softened the rugged features of Elementary Propositions, and, as it were, to have strewed the Asses’ Bridge with flowers.”

Such is the account which Mr. Higgins gives of his own undertaking, and of the motives which have led him to it. For our parts, though we have not the same sanguine persuasion of the absolute perfectibility of our species, and are in truth liable to the imputation of being more satisfied with things as they are, than Mr. Higgins and his associates;—yet, as we are, in at least the same proportion, less convinced of the practical influence of didactic poems, we apprehend little danger to our readers’ morals from laying before them Mr. Higgins’s doctrine in its most fascinating shape. The poem abounds, indeed, with beauties of the most striking kind,—various and vivid imagery, bold and unsparing impersonifications; and similitudes and illustrations brought from the most ordinary and the most extraordinary occurrences of nature—from history and fable—appealing equally to the heart and to the understanding, and calculated to make the subject of which the poem professes to treat rather amusing than intelligible. We shall be agreeably surprised to hear that it has assisted any young student at either University in his mathematical studies.

We need hardly add, that the plates illustrative of this poem (the engravings of which would have been too expensive for our publication) are to be found in Euclid’s Elements, and other books of a similar tendency.

LOVES OF THE TRIANGLES.[[196]]
ARGUMENT OF THE FIRST CANTO.

Warning to the profane not to approach—Nymphs and Deities of Mathematical Mythology—Cyclois of a pensive turn—Pendulums, on the contrary, playful—and why?—Sentimental Union of the Naiads and Hydrostatics—Marriage of Euclid and Algebra.—Pulley the emblem of Mechanics—Optics of a licentious disposition—distinguished by her telescope and green spectacles.—Hyde-Park Gate on a Sunday morning—Cockneys—Coaches.—Didactic Poetry—Nonsensia—Love delights in Angles or Corners—Theory of Fluxions explained—Trochais, the Nymph of the Wheel—Smoke-Jack described—Personification of elementary or culinary Fire.—Little Jack Horner—Story of Cinderella—Rectangle, a Magician, educated by Plato and Menecmus—in love with Three Curves at the same time—served by Gins, or Genii—transforms himself into a Cone—the Three Curves requite his passion—Description of them—Parabola, Hyperbola, and Ellipsis—Asymptotes—Conjugated Axes.—Illustrations—Rewbell, Barras, and Lepaux, the three virtuous Directors—Macbeth and the Three Witches—the Three Fates—the Three Graces—King Lear and his Three Daughters—Derby Diligence—Catherine Wheel.—Catastrophe of Mr. Gingham, with his Wife and Three Daughters overturned in a One-horse Chaise—Dislocation and Contusion two kindred Fiends—Mail Coaches—Exhortation to Drivers to be careful—Genius of the Post-Office—Invention of Letters—Digamma—Double Letters—Remarkable Direction of one—Hippona the Goddess of Hack-horses—Parameter and Abscissa unite to overpower the Ordinate, who retreats down the Axis-Major, and forms himself in a Square—Isosceles, a Giant—Dr. Rhomboides—Fifth Proposition, or Asses’ Bridge—Bridge of Lodi—Buonaparte—Raft and Windmills—Exhortation to the recovery of our Freedom—Conclusion.

THE LOVES OF THE TRIANGLES.
A Mathematical and Philosophical Poem,
INSCRIBED TO DR. DARWIN.

CANTO I.

Stay your rude steps, or e’er your feet invade[[197]]