=Bibliography.= Petersen, Methods and Theories for the Solution of Geometric Problems of Construction, Copenhagen, 1879, a curious piece of English and an extreme view of the subject, but well worth consulting; Alexandroff, Problemes de geometrie elementaire, Paris, 1899, with a German translation in 1903; Loomis, Original Investigation; or, How to attack an Exercise in Geometry, Boston, 1901; Sauvage, Les Lieux geometriques en geometrie elementaire, Paris, 1893; Hadamard, Lecons de geometrie, p. 261, Paris, 1898; Duhamel, Des Methodes dans les sciences de raisonnement, 3^e ed., Paris, 1885; Henrici and Treutlein, Lehrbuch der Elementar-Geometrie, Leipzig, 3. Aufl., 1897; Henrici, Congruent Figures, London, 1879. CHAPTER XIV BOOK I AND ITS PROPOSITIONS Having considered the nature of the geometry that we have inherited, and some of the opportunities for improving upon the methods of presenting it, the next question that arises is the all-important one of the subject matter, What shall geometry be in detail? Shall it be the text or the sequence of Euclid? Few teachers have any such idea at the present time. Shall it be a mere dabbling with forms that are seen in mechanics or architecture, with no serious logical sequence? This is an equally dangerous extreme. Shall it be an entirely new style of geometry based upon groups of motions? This may sometime be developed, but as yet it exists in the future if it exists at all, since the recent efforts in this respect are generally quite as ill suited to a young pupil as is Euclid's "Elements" itself. No one can deny the truth of M. Bourlet's recent assertion that "Industry, daughter of the science of the nineteenth century, reigns to-day the mistress of the world; she has transformed all ancient methods, and she has absorbed in herself almost all human activity."[57] Neither can one deny the justice of his comparison of Euclid with a noble piece of Gothic architecture and of his assertion that as modern life demands another type of building, so it demands another type of geometry. But what does this mean? That geometry is to exist merely as it touches industry, or that bad architecture is to replace the good? By no means. A building should to-day have steam heat and elevators and electric lights, but it should be constructed of just as enduring materials as the Parthenon, and it should have lines as pleasing as those of a Gothic facade. Architecture should still be artistic and construction should still be substantial, else a building can never endure. So geometry must still exemplify good logic and must still bring to the pupil a feeling of exaltation, or it will perish and become a mere relic in the museum of human culture.