[137] I am altogether unable to compose worthy verses, for I am so confused by the caresses of the duchess.
[138] Oderic. Vit. B. vi. c. iv.
[139] Wis. vii. 17. 22-23.
[140] Richer’s history is printed at length in Pertz’s Monumenta Germaniæ Historica, Tom. iii.
[141] Gerbert taught his disciples the use of the monochord; a single string, which being struck at different intervals, gave out the different sounds of the gamut. These intervals were marked on the chord, and the words to be sung had written over them a cipher, showing to what interval on the monochord it corresponded. A person therefore could always set himself right by sounding the note he wanted, as we should use a pitch-key. A description of this instrument is given by the monk Odoramn, whose works have been discovered and published by Cardinal Mai, and whose musical treatises are said to be based on the scientific principles of Boëthius and Euclid.
[142] The Arabs received the knowledge of the Indian numerals in the ninth century. “But the profound and important historical investigations to which a distinguished mathematician, M. Chasles, was led by his correct interpretation of the so-called Pythagorean table in the geometry of Boëthius,” says M. Humboldt, “render it more than probable that the Christians in the West were acquainted even earlier than the Arabians with the Indian system of numeration; the use of the nine figures, having their value determined by position, being known by them under the name of the System of the Abacus.” (Cosmos, vol. ii. p. 226, also note 358. See also M. Chasles, Aperçu historique des méthodes en géométrie, 464-472, and his papers in the Comptes-rendus de l’Acad. des Sciences.)
[143] The story has of course been taken up by the usual chorus of modern writers, but its fallacy is well exposed by Gretser, who shows that the tenth century knew nothing of the rumour, which entirely originated in the fertile brain of Benno.
[144] Meibomius, Scrip. Rerum German. t. i. 706.
[145] In the year 1867 a controversy arose in Germany concerning the authenticity of the works attributed to Hroswitha. Professor Aschbach, of the Imperial Academy of Vienna, in a paper printed that year in the Acts of the Academy, endeavoured to prove them audacious forgeries; and supposed the author of the fraud to have been one Conrad Celtes, a Humanist of the fifteenth century. The question was taken up on both sides. Several distinguished writers and their arguments and investigations appear to have successfully vindicated the genuine character of the works, and to have established Hroswitha’s claim to be considered their real authoress. See B. Tenk, Neber Roswitha Carmen de Gestis Oddonis, Leipzig, 1876. R. Kœpke, Ottonische Studien zur deutschen geschichte im 10ten jahrhundert, II. Hroswith von Gandersheim (xv. s. 314.) Die Aelteste deutsche Dichterin (III. 127. S), Berlin, 1869. Hroswitha, die helltönende Stimme von Gandersheim. In Westermann’s Illustr. Monatsheften, 1871, &c.
[146] Rohrbacher, Hist. de l’Eglise, vol. xiii. 540.