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 the Ancients. I have chosen, however, to speak of it in this Place, for these following Reasons.

1. That whereas all Modern Mathematicians have paid a mighty Deference to the Ancients; and have not only used the Names of Archimedes, Apollonius and Diophantus, and the other Ancient Mathematicians, with great Respect; but have also acknowledged, that what further Advancements have since been made, are, in a manner, wholly owing to the first Rudiments, formerly taught: Modern Musicians have rarely made use of the Writings of Aristoxenus, Ptolemee, and the rest of the Ancient Musicians; and, of those that have studied them, very few, unless their Editors, have confessed that they could understand them; and others have laid them so far aside, as useless for their Purpose; that it is very probable, that many excellent Composers have scarce ever heard of their Names.

II. Musick has still, and always will have very lasting Charms. Wherefore, since the Moderns have used their utmost Diligence to improve whatever was improvable in the Writings of all sorts of Ancient Authors, upon other equally difficult, and very often not so delightful Subjects, one can hardly imagine but