TABLE OF PROPOSITIONS

of the nineteen Books of Universal Harmony.

AFTER having read the first general Preface, in which there are twelve or thirteen very significant matters: that of the six books of Consonances Consonances: the study of intervals and chords that sound pleasing together, where one sees seven things to note; that of the book of the Voice, which contains four or five excellent things for the establishment of the most perfect Idiom referring to the search for a perfect or universal language: that of the Instruments, where one has all the different characters and their names, which are used in Printing houses: and that of the Organ in which many things belonging to the book of the Organ are supplemented: and after having corrected all the faults errata which are marked at the end of the said Prefaces, or at the end of the third book of Movements, of the seventh book of Percussion Instruments, by which I desire that one begins, for the reason that those of the first four books of Consonances are marked there, which are very notable because of the musical notes and the practice, and those which are at the end of the book on the Utility of Harmony, which one can have bound first: after, I say, having done all this, one may read the following Propositions, in order to see all at once what is contained in all the books of this work; although the explanation or the proof of several Propositions often contains much more than they promise upon reading: so that they can compensate for those which give less than what one expects. Be that as it may, the charity and benevolence of the Readers will excuse the defects which will be encountered in whatever place it may be in this work: it is only necessary to note that I sometimes change some words in these Propositions, in order to make them more conformable to my meaning; added to which the numbering which is sometimes missing from the Propositions in the books is here restored in its entirety. Now this table of Propositions will supplement what one might desire in the Table of Contents, and will show the relationship that some Propositions maintain with one another, when one sees the citation afterward; as appears in the 21st Proposition of the first book which follows, after which there is, See the 9th Proposition of Utility, etc. because they both speak of the same thing.

34 Propositions of the first book of the Nature of Sounds.

See first the general Preface, and the particular one.
Besides the Propositions there are several Corollaries Corollary: a proposition that follows naturally from one already proved which contain many remarks.
I. To determine if Sound is made before it is received by the hearing, and if it is different from the movement of the air. Page one.
II. To determine how movement and Sound are made; and why several movements, although very fast, make no Sound that we can hear, as do those of several wheels both in water and in air: and never-