Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

evenlyeven numbers, and for not distinguishing one of these
from evenlyeven numbers. And certainly, as Bullialdus observes,
Euclid ought to have distinguished odd numbers from
the unevenly-even, and these again from the evenly-even,
which are confounded by him.
P. 68. Chap6 A square number, &c.-In this and the two
following chapters, the generation of squares, pentagons, hexagons,
kc. is delivered. And in the first place it is necessary to
observe, that another generation of squares is delivered by ancient
authors, and is called by them %rao~o~, or, a circuitous
course from the same to the same. For in this method, says
Jamblichus on Nicomachus, "the monad becomes both the
barrier and the goal in each composition. For from it the progression
begins in the generation of every square, from the
barriers as it were, as far as to the goal, which is the side of the
square." Thus for instance in order to produce a square whose
side is 4, let numbers be disposed from unity, as from the barriers
of a Circus, as far as to 4, and from 4 again in a retrograde
order as far as to unity, as below:
For the sum of all these is 16, a square number, the side of
which is 4. Thus too, in order to produce a square whose side
is 5, numbers must be disposed from unity in a similar manner
as follows:
For the sum of these is 25, and consequently the side is 5. And
so in all other instances.
But numbers will be thus disposed, if a number is distributed
into units, and in this distributed form multiplied into itself,
as may be seen below: