If, for example, you will grant me, as an Axiom, that there is some finite minimum value for the sum of the angles of a Triangle, no matter how small you make it, all is easy at once: grant me, for instance, that no Triangle can possibly have the sum of its angles less than a millionth of a right angle, and I am happy! Finally, I am inclined to believe that, if ever Euc. I. 32 is proved without a new Axiom, it will be by some new and ampler definition of the Right Line—some definition which shall connote that peculiar and mysterious property, which it must somehow possess, which causes Euc. I. 32 to be true. Try that track, my gentle Reader! It is not much trodden as yet. And may success attend your search! THE END. [TURN OVER. WORKS BY C. L. DODGSON. PUBLISHED BY MACMILLAN & CO., LONDON. THE FORMULÆ OF PLANE TRIGONOMETRY, printed with symbols, instead of words, to express the goniometrical ratios. (First published in 1861.) Crown 4to, sewed. Price 1s. EUCLID AND HIS MODERN RIVALS. (First published in 1879.) Second Edition, 1885. Crown 8vo, cloth. Price 6s. SUPPLEMENT TO FIRST EDITION OF "EUCLID AND HIS MODERN RIVALS," containing a Notice of Henrici's Geometry, together with Selections from the Reviews. (First published in 1885.) Crown 8vo, sewed. Price 1s. EUCLID, BOOKS I, II, with Notes. (First published in 1882.) Sixth Edition, 1888. Crown 8vo, cloth. Price 2s. CURIOSA MATHEMATICA. Part I. A New Theory of Parallels. (First published in 1888.) Fourth Edition, 1895. Crown 8vo, cloth. Price 2s. Part II. Pillow-Problems, thought out during Wakeful Hours. (First published in 1893.) Fourth Edition, 1895. Crown 8vo, cloth. Price 2s. TRANSCRIBER’S NOTES Simple typographical errors have been silently corrected; unbalanced quotation marks were remedied when the change was obvious, and otherwise left unbalanced. Punctuation, hyphenation, and spelling were made consistent when a predominant preference was found in the original book; otherwise they were not changed.