Chapters 1-2
Chapters 3-8
Impure Consonance
Galilei's Convenient Division
Modes

©2006 LaRouche Youth L.L.P.
The Harmony of the World
BOOK III

ON THE ORIGIN OF THE HARMONIC PROPORTIONS, AND ON THE NATURE AND DIFFERENCES OF THOSE THINGS WHICH ARE CONCERNED WITH MELODY.

 

Proclus Diadochus, Commentary on Book I of the Elements of Euclid, Book I:

Mental endeavor is the preparation for theology. For those features which to the uninitiated in the truth of divine matters seem difficult to grasp and lofty are by mathematical reasoning shown to be trustworthy, manifest and uncontroversial, by means of certain images. For they show proof of the supernatural properties in numbers; and they make clear the powers of the remarkable things about the nature of the gods through the appearance of mathematical things; and the Pythagorean philosophy disguises its teaching on divine matters with these, so to speak, veils. For of this kind is the whole of that sacred writing, both Philolaus on the Bacche, and the whole Pythagorean system of teaching about God.



Chapters 1-2