Excerpt from Treatise on Arithmetic, Practical and Theoretical (1.) The early period of life at which we begin to acquire ideas of number, and the influence produced on our minds by becoming familiar with the language of numeration before any notions of the higher classes of number are formed, throw great difficulties in the way of any attempt to retrace the steps by which the art of counting arrived at its present high state of perfection. Under these circumstances we must naturally direct our enquiries to the state of arithmetic among people less advanced in civilisation than ourselves. But it is a remarkable fact, that while other sciences are almost unknown beyond the limits of civilisation, there is no example of a people without a system of numeration more or less extensive and perfect, with the exception of a few savage tribes, whose notions of number are singularly limited. It is, however, apparent, that before a people could make any progress in numeration beyond a few of the smaller combinations which may be signified by the fingers, two things were indispensably necessary to be accomplished. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

A virtuoso violinist, conductor, composer, and a professor of mathematics and botany, Francesco Galeazzi (1758–1819) firmly believed that musical education should be clear, demonstrable, and practical. In 1791 and 1796, he published the two volumes of his Elementi teorico-practici di musica, a treatise that demonstrated both his thorough grounding in the work of earlier theorists and his own approach to musical study. The first volume gave precise instructions on the violin and how to play it; the second demonstrated his command of other instruments and genres and provided comprehensive introductions to music theory, music history, and music aesthetics. The treatise also addresses the nature of compositional process and eighteenth-century concerns about natural and acquired talent and creativity. This volume offers an unprecedented English translation of the second volume of Elementi teorico-practici di musica, with annotations and commentary. The translation is introduced with a study of Galeazzi's life and milieu, the genesis and sources for the Elementi, and its reception through the present day.