XII PREFACE. The subject index contains a list of symbols; while [x] usually denotes the greatest integer £x, occasionally such square brackets are used to inclose an addition to a quotation. The symbol * before an author's name signifies that his paper was not available for report. The symbol | before a date signifies date of death. Initials are given only in the first of several immediately successive citations of an author. Although those volumes of Euler's Opera Omnia which contain his Com-mentationes Arithmetic® Collect® have been printed, they are not yet available; a table showing the pages of the Opera and the corresponding pages hi the present volume of this history will be given in the concluding volume. The author is under great obligations to the following experts in the theory of numbers for numerous improvements resulting from their reading the initial page proofs of this volume: R. D. Carmichael, L. Chanzy, A. Cunningham, E. B. Escott, A. G6rardin, A. J, Kempner, D. N. Lehmer, E. Maillet, L. S. Shively, and H. J. Woodall; also the benefit of D. E. Smith's accurate and extensive acquaintance with early books and writers was fortunately secured; and the author's special thanks are due to Carmichael and Kempner, who read the final page proofs with the same critical attention as the initial page proofs and pointed out various errors and obscurities. To these eleven men who gave so generously of their tune to perfect this volume, and especially to the last two, is due the gratitude of every devotee of number theory who may derive benefit or pleasure from this history. In return, such readers are requested to further increase the usefulness of this work by sending corrections, notices of omissions, and abstracts of papers marked not available for report, for insertion in the concluding volume. Finally, this laborious project would doubtless have been abandoned soon after its inception seven years ago had not President Woodward approved it so spontaneously, urged its completion with the greatest thoroughness, and given continued encouragement. L. E. DICKSON. November, 1918.