extensive course, let him be transferred from that work to the place at which he has arrived in this, and thus be saved the loss of time and the perplexity which must ensue from studying two different treatises on the same subject, whether they be by the same, or by different authors. In this way the pupil's course will be constantly progressive. The author has esteemed it a matter of great importance to adapt his two Arithmetics, as well as his two Algebras, to this uninterrupted progression of studies.
A KEY containing all the Miscellaneous Exercises in this work, and the Miscellaneous Exercises in Mensuration in the elementary one, with their solutions, has been published, to save time to the Teacher, and to facilitate his necessary labors, whatever may be his competency as an Arithmetician.
In the first editions of his Arithmetics, the author adventured some rather violent changes in the common arrangement and nomenclature of this, science. So far as he has learned, these innovations have been approved by all who have used or examined his books. He is himself fully confirmed in his convictions of their propriety; and retains them in the revised editions, as improvements in the logic of the science, and as thereby facilitating its acquisition.