Free Pythagoras: His Life and Teaching, a Compendium of Classical Sources by James Wasserman, Thomas Stanley, Henry L. Drake, J Daniel Gunther Page A

griev'd;
    What wish'd which had been better not desir'd;
    Why profit before honesty requir'd?
    If any by some speech or look offended,
    Why nature more than discipline attended?
    All words & deeds thus searched from morn to night,
    He sorrows for the ill, rewards the right.

Part Three
    The Doctrine of Pythagoras
    Section I. Mathematics
Section II. Philosophy
Section III. Symbols

    Among the earliest coins of the Greek colonists in Southern Italy, this silver stater of Croton dates to the late 6th century B.C. It shows on its obverse the tripod of Apollo and the abbreviated name of the city, and on its reverse the incuse impression of that same design, less the inscription.
Photo courtesy of Numismatica Ars Classica

CHAPTER 4
    S YMBOLIC N UMBERS
    T he Pythagoreans, using the mathematical sciences as degrees of preparations to the contemplations of the things that are, were studiously addicted to the business of numbers for this reason. (So says Moderatus of Gades, who learnedly comprised their opinions in eleven books. 353 )
    Seeing they could not clearly explain the first forms and principles in discourse (those being the most difficult to understand and express), they had recourse to numbers for the better explication of their doctrine, imitating geometricians and such as teach to read. For as these, going about to explain letters and their powers, recur to marks—saying that these are, as it were, the first elements of learning—nevertheless, afterwards they tell us that they are not the elements, but that the true elements are known by them. And as the geometricians, not being able to express incorporeal forms in words, have recourse to the description of figures saying, “This is a triangle”; yet not meaning that this which falls under the sight is a triangle, but that which has the same figure and which is by the help thereof, and represents the knowledge of a triangle to the mind.
    The same did the Pythagoreans in the first reasons and forms. For seeing they could not in words express incorporeal forms and first principles, they had recourse to demonstration by numbers. And thus they called the reason of unity and identity, and equality, and the cause of amicable conspiration, and of sympathy, and of the conservation of the universe which continues according to the same, and in the same manner, ONE. For the One which is in particulars, is united to the parts and conspiring by participation of the first cause.
    But the two-fold reason of diversity and inequality, and of every thing that is divisible and in mutation, and exists sometimes one way, sometimes another, they called DUAD. For the nature of the Duad in particular things is such.

    These reasons are not only according to the Pythagoreans, and not acknowledged by others; but we see that other philosophers also have left certain unitive powers, which comprise all things in the Universe. And amongst them there are certain reasons for equality, dissimilitude, and diversity. Now these reasons—that the way of teaching might be more perspicuous—he called by the names of Monad and Duad. But it is all one amongst them if it be called biform, or aequaliform, or diversiform.
    The same reason is in other numbers, for everyone is ranked according to some powers. In the nature of things exists something which has beginning, middle and end. To such a form and nature they attributed the number Three, saying that whatsoever has a middle is triform; so they called every perfect thing. And if anything be perfect, they affirm it makes use of this principle and is adorned according to it; which, since they could not name otherwise, they made use of the term TRIAD to express it. And when they endeavor to bring us to the knowledge thereof, they lead us to it by the form of this triad. The same in other numbers.
    These, therefore, are the reasons according to which the aforesaid numbers were placed. But these that follow are comprehended under one form and power, which they