Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy
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incorporeal and corporeal essence; the species of the incorporeal<br />
indeed, according to the superficies which is formed by<br />
squares; but of the corporeal according to the other dimension<br />
(depth) which is formed by cubes. But the credibility of what<br />
is said is most manifest in the above mentioned numbers. For<br />
the hebdomad 64 which is immediately increased from unity<br />
in a duple ratio, is a square produced by the multiplication of<br />
8 by 8; and it is also a cube, the side or root of which is 4. And<br />
again, the hebdomad which is increased in a triple ratio from<br />
the monad, viz. 729, is a square indeed, formed by the multiplication<br />
of 27 by itself, and is also a cube, the side of which<br />
is 9.+ By always making too a hebdomad the principle instead<br />
of the monad, and increasing according to the same analogy as<br />
far as to the hebdomad, you will always find that the increased<br />
numbers is both a square and a cube. The hebdomad therefore<br />
compounded in a duple ratio from 64, will be 4096,t which is<br />
both a square and a cube; a square indeed, having for its side<br />
64; but a cube, the side of which is 16.<br />
Let us now pass to the other species of the hebdomad which<br />
is comprehended in the decad, and which exhibits an admirable<br />
nature no less than the former hebdomad. This therefore<br />
is composed of one, two and four, which possess two most harmonic<br />
ratios, the duple and the quadruple; the former of<br />
which forms the symphony diapason, and the latter the symphony<br />
disdiapason. This hebdomad also comprehends other<br />
divisions, consisting after a manner of certain conjugations.<br />
For it is in the first place indeed, divided into the monad and<br />
hexad, afterwards into the duad and pentad, and lastly into<br />
the triad and tetrad. But this analogy or proportion of num-<br />
+ Thus lXZX2~2~2~2X2=64; and 1~3~3X3X3X3~3=729.<br />
f For 64 x 2 X 2 X 2 X 2 X 2 X 2 =4096. And thus also the hebdomad compounded<br />
in a triple ratio from 64 will be 46656, which is both a square and a cube; for<br />
the square root of it is 216, and the cube root is 36.
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