PREFACE While much has been written on the history of mathematics, comparatively little attention has been given to the history of its teaching. Günther's "Geschichte des mathematischen Unterrichts im Deutschen Mittelalter bis zum Jahre 1525" and Suter's "Die Mathematik auf den Universitäten des Mittelalters" are the only prominent works that emphasize the teaching side. Among the works that treat the general history of mathematics, those of Cantor, Hankel, Gow, and Allman have been of great assistance. Much information has also been gained from miscellaneous articles, standard works on the history of education, and early texts, the latter constituting, for the most part, the original sources for this study. The material that has been utilized in the first three chapters is to be found chiefly in the standard histories of mathematics, but wherever possible the original sources have been consulted. Originality is claimed only for the selection and arrangement of this portion of the subject-matter and for the conclusions drawn. The material for the next three chapters has been gleaned very largely from the original sources. The author is under great obligation to Professor David Eugene Smith of Teachers College, Columbia University, under whose direction this dissertation has been prepared, for helpful counsel and criticism, and for rendering much of this work possible through his valuable collection of early printed books. Alva Walker Stamper. New York, June, 1906. CONTENTS THE TEACHING OF GEOMETRY BEFORE EUCLID THE BEGINNING OF GEOMETRY AMONG PRIMITIVE PEOPLE Logical stage Application with logic as a basis Practical use Influences that helped to develop their geometry The pyramids. Rope Stretchers. Astronomy Utilitarian influence. The overflow of the Nile 1-4 2-3 4-10 4-7 7-9 The first propositions given to geometry. The Pythagoras and his school 10-11 11-13 Development of the geometry of areas. contributions. Nothing known of methods of proof. Geometry becomes an abstract science The development of geometry at Athens Interest in geometry. The Sophists. The schools of Plato and Aristotle. The Three Problems of Antiquity and their relation to the development of the subject-matter of geometry Books written on geometry. Euclid not the first. Lack of harmony between the historic sequence The Socratic method. The old Greek education. Plato's disposition of geometry in the curriculum 17-18 Euclid's sequence of subject-matter. Points of de- Some adverse criticisms of Euclid tions of the integral calculus. Geometric and me- Applications of geometry to astronomy and surveying. |
