PREFACE.

Nearly ten years ago, while I was intending to study Latin authors and was a student of mathematics, I began to devote effort to Boethius. Not long after, Halmius a scholar and contemporary of the editor encouraged me to apply myself more strictly, especially to his mathematical works, thinking that a more accurate knowledge of the Latin language might also be gained from this. However, I first thought that I could contribute useful results regarding arithmetic, and I published what I had found in a short book edited on the geometry of Boethius 1). Gerbert, The Geometry of Boethius and the Indian Numerals. Erlangen, Bläsing 1861.. The very learned man Mauritius Cantor 2). Mathematical Contributions to the Cultural Life of Peoples, Halle, Schmidt 1863. attacked my opinions and urged me to attempt to refute, with the most certain arguments possible, the points he had established less correctly regarding Boethius's art of reasoning and calculating 3). Journal of Mathematics and Physics, IX, pp. 73–95, 145–171, 297–330. X, pp. 241–282.. I also brought forward a few things concerning the geometry of Boethius 4). New Yearbooks for Philology and Pedagogy. 1863. pp. 425–427., by which I proved that it did not originate from Boethius.