The Barddas of Iolo Morganwg, Vol. I., ed. by J. Williams Ab Ithel, , at sacred-texts.com
Why do arrangements require numbers?
To facilitate the memory, for where there is number, there is knowledge, but without number and weight and measure, there can be no knowledge of anything, therefore number is one of the three foundations of knowledge. That which is laid down in the system of numbers will be remembered, whatever number it may be; and every one of such numbers will be divided and re-arranged, for the regulation of the memory, because it is from order that the memorials of things and sciences are formed; wherefore it is said "there is no memory but order"--also "there is no order but system"--"there is no system but number, weight, and measure"--the same being known, fixed by nature, and confirmed by the judgment of wise men.
p. 104 p. 105
What number is the best for any system?
A natural number, where such is known, namely, that which will convey in itself the whole, in respect of kind and condition, of what is arranged by that number; and the best will be the least number, where it will admit of a division. There is no arrangement without number and its division, and this is called the primary number, having within it a division, from which comes an arrangement. But there are united numbers, such as is three, which has a beginning, a middle, and an end, and the least, greatest, and intermediate, also one thing, another thing opposite to it, and a third thing joining them together, as means, skill, and will, for if there be means, it may be there will be skill, and if there be means and skill together, they will be of no avail without what will join them, namely, desire or effectual will, that will bear upon the other two: the number mostly used for arrangements is three.
A number, natural in kind, is also four, which may be divided into two, that is, two halves, and four quarters; six also into three twos, and nine into three threes, are natural numbers used in arrangements. Ten is likewise altogether a systematic number, for it is in ten that the cycle of numbers terminates. Ten tens are a hundred, 1 ten hundreds a thousand, ten thousands in the myriad, ten myriads in the rhiallu, ten rhiallus in the buna, ten bunas in the cattorva, ten cattorvas in the annant, 2 ten annants in the trwn; 3 and these are called the ten cycles of number. Those also which may be divided equally are called distributive numbers, such as four, and eight, and sixteen, and twenty-four; and twenty-four admits of more divisions than any other quantity, for it has two twelves, three eights, four sixes, six fours, eight threes, and twelve twos.
p. 106 p. 107
Why is the number three used by the Bards of the Isle of Britain in their lessons of instruction?
Because it is easier to remember three, and because the three principal conditions form the division of three, that is, one, and another, and conjunctive; and the easiest to remember is the best of every learning; and the shortest distribution is three, and the easiest to remember is the shortest that can be arranged. On this account the Bards of the Isle of Britain arranged their learning and wisdom in triads, that those who were unacquainted with books might easily learn and remember them, for the number of the illiterate is greater than that of the literate, and it is to the majority that learning, and wisdom, and institutional and domestic sciences, in respect of precise meaning, ought to be imparted.
105:1 p. 104 Wallice, "cant," which literally means a circle. Ceugant again is the enclosing circle, which comprehends all.
105:2 The elementary principles of sound.
105:3 A throne, a circle.
And in the throne I know he dwells,
And there is no hope of his equal.
Huw ap Dafydd, 1480-1520.