I shall here take the liberty to repeat the proofs I advanced in a former work as the ground of this belief, and to which the author, from whose essay I have quoted, undoubtedly refers. It is well known that, in the time of Pythagoras, the treasures of science were veiled in mystery to all but the properly initiated, and the results of its various branches only given to the world in the works of those who had acquired this knowledge. So strictly was this secresy maintained amongst the disciples and pupils of Pythagoras, that any one divulging the sacred doctrines to the profane, was expelled the community, and none of his former associates allowed to hold further intercourse with him; it is even said, that one of his pupils incurred the displeasure of the philosopher for having published the solution of a problem in geometry.[28] The difficulty, therefore, which is expressed by writers, shortly after the period in which Pythagoras lived, regarding a precise knowledge of his theories, is not to be wondered at, more especially when it is considered that he never committed them to writing. It would appear, however, that he proceeded upon the principle, that the order and beauty so apparent throughout the whole universe, must compel men to believe in, and refer them to, an intelligible cause. Pythagoras and his disciples sought for properties in the science of numbers, by the knowledge of which they might attain to that of nature; and they conceived those properties to be indicated in the phenomena of sonorous bodies. Observing that Nature herself had thus irrevocably fixed the numerical value of the intervals of musical tones, they justly concluded that, as she is always uniform in her works, the same laws must regulate the general system of the universe.[29] Pythagoras, therefore, considered numerical proportion as the great principle inherent in all things, and traced the various forms and phenomena of the world to numbers as their basis and essence.