Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

XII
INTRODUCTION
must her inherent number be supposed to be a multitude of
monads or units, nor must her idea of natures that are distended
with interval, be conceived to subsist corporeally; but all
the paradigms of apparent numbers and figures, ratios and
motions, must be admitted to exist in her, vitally and intellectually,
conformably to the Timaeus of Plato, who gives completion
to all the generation and fabrication of the soul, from
mathematical forms, and in her establishes the causes of all
things. For the seven boundaries* of all numbers, prexxist in
soul according to cause. And again, the principles of figures,
are established in her in a fabricative. manner. The first of
motions also, and which comprehends and moves all the rest,
are consubsistent with soul. For the circle, and a circular motion,
are the principle of every thing which is moved. The
mathematical productive principles therefore, which give completion
to the soul, are essential, and self-motive; and the reasoning
power exerting and evolving these, gives subsistence
to all the variety of the mathematical sciences. Nor will she
ever cease perpetually generating and discovering one science
after another, in consequnce of expanding the impartible
forms which she contains. For she antecedently received all
things causally; and she will call forth into energy all-various
theorems, according to her own infinite power, from the principles
which she previously received.+
* Viz. 1. 2. 4. 8. 3. 9. 27, concerning which see the Introduction to the Timaeus,
in the 2nd Vol. of my translation of Plato.
t The sagacious Kepler has not only inserted the above extract from the Commentaries
of Produs, in his trcatix On tAc Uarmomie Wovld, but also gives it the
fdbwing encomium: "At quod attinet quantitates continuas, omnino adsentior
Pdo; etsi oratio fluit ipsi torrentis instar, ripas inundans, et caeca dubitationum
vada gurgitesque occultans, durn mens plena majestatis antarum rerum, luctahlr
in angustiis linguae, et conclusio nunquam sibi ipsi verborurn copia satishciens,
@timum simplicitatem cxcedit." i.e. "With respect to what pertains to contimed
quantities, I entirely assent to Proclus, though his language flows like a
ticmeat inundating its banks, and hiding the dark fords and whirlpools of doubt,
ddk his mind, full of the majesty of things of such a magnitude, struggles in