Such a study has been rendered possible only by the generous loan of rare books by Professor Herbert D. Foster of Dartmouth College, Professor Edwin E. Slosson of Columbia University, Doctor George A. Plimpton and Major George Haven Putnam, both of New York, and especially by the kindly generosity of Professor David Eugene Smith of Teachers College who placed his unique collection of rare mathematical books at the writer's disposal and gave her many valuable suggestions as to available material. Professors James T. Shotwell and Harold Jacoby of Columbia University have read parts of this study in manuscript. The writer gratefully acknowledges her indebtedness not only to these gentlemen, but to the many others, librarians and their assistants, fellow-students and friends, too numerous to mention individually, whose ready interest and whose suggestions have been of real service, and above all to Professor James Harvey Robinson at whose suggestion and under whose guidance the work was undertaken, and to the Reverend Doctor Henry A. Stimson whose advice and criticism have been an unfailing source of help and encouragement. PART ONE AN HISTORICAL SKETCH OF THE HELIOCENTRIC THEORY OF THE UNIVERSE. CHAPTER I. THE DEVELOPMENT OF ASTRONOMICAL THOUGHT TO 1400 A.D. _A Preliminary Sketch of Early Theories as a Background._ The appearances in the heavens have from earliest historic ages filled men with wonder and awe; then they gradually became a source of questioning, and thinkers sought for explanations of the daily and nightly phenomena of sun, moon and stars. Scientific astronomy, however, was an impossibility until an exact system of chronology was devised.[1] Meanwhile men puzzled over the shape of the earth, its position in the universe, what the stars were and why the positions of some shifted, and what those fiery comets were that now and again appeared and struck terror to their hearts. [Footnote 1: The earliest observation Ptolemy uses is an Egyptian one of an eclipse occurring March 21, 721 B.C. (Cumont: 7). [In these references, the Roman numerals refer to the volume, the Arabic to the page, except as stated otherwise. The full title is given in the bibliography at the back under the author's name.]]