Scalene is the way to go
He made the soul from the following constituents and in this manner. From Being that is
undivided and ever the same, and Being which, by contrast, comes into existence apportioned to
bodies, he formed a third intermediate form of Being from both of them. Next he mixed the nature
of Same and Other in like manner, making a third intermediate form between their undivided
form and their form as apportioned to bodies. He then took these three mixtures,6 and mixed them
all into one, and as the nature of Other was difficult to mix he blended it with Same by force.
Then having mixed 35B this with the help of Being and made one from the three, he apportioned
this whole once more into as many parts as was fitting, each part being a mixture of Same, Other
and Being.
He began to divide it as follows: first he separated one part from the entire; after this he separated
a part double the first, and next a third, which was one-and-a-half times the second and three
times the first; a fourth part, double the second; a fifth, three times the third; 35C a sixth, eight
times the first; and a seventh, twenty-seven times the first. After this he filled up 36A the double
and triple intervals, cutting off further sections of the mixture and placing these in between them
so that in each interval there were two means: one exceeding its extremes and being exceeded by
them by the same portion; the other exceeding one extreme and being exceeded by the other
extreme by an equal number.7 These connections gave rise to intervals of 3/2, 4/3 and 9/8
between the previous intervals.8 All the 4/3 intervals were filled up by the 9/8 intervals 36B leaving
a portion of each of them, and the interval associated with this remaining portion had the
numerical relation 256/243. What’s more, the mixture from which these were cut was at that
stage, entirely used up in the process.
So in accord with the correct and likely account, let the solid form that constitutes a pyramid be
the element30 and seed of fire, and we may say that the second in order of generation belongs to
air, and the third to water. Now we need to realise that these are all so small that an individual
particular 56C of each kind is invisible to us due to its extreme smallness, and yet, when a large
number are aggregated together, their bulks can be seen. As for the proportions associated with
their multiplicity, movements, and their other capacities, insofar as the nature of necessity
allowed under willing persuasion, we must realise that god fitted them together entirely in due
proportion, once he had precisely perfected them in this comprehensive manner.
Now from all that we have said earlier about the kinds, they would be most likely 56D to behave as
follows. Earth, on encountering fire and being broken apart by its sharpness, regardless of
whether it is in fire itself, when it gets broken up or in a mass of air or water, would travel along
until such time as it somehow meets up with its own parts which, once fitted together with
themselves, become earth again; for they could never have adopted any other form. Water, when
broken apart either by fire or air, is capable of combining to constitute one body of fire and two of
air, 56E while the components of air, when a single portion is broken up would become two bodies
of fire. And again, when a little fire is surrounded by a lot of air or water or even by some earth
and is in motion within them, does battle, gets defeated and is shattered, two bodies of fire
combine into a single figure of air. And if air is defeated and broken in pieces, one whole figure
of water will be compounded from two and a half of air.
, so it is especially necessary that this be the
sort that has the most stable bases; and of the two triangles we proposed at the outset, the one with
equal sides is naturally more stable than the one with unequal sides; and in the case of the equal
sided surfaces constructed from either triangle, the square is necessarily more resistant to motion
than the equilateral triangle, both as a whole and on the basis of its parts. Therefore we shall
preserve the likely account by assigning this form to earth, 56A and of those that remain, the
hardest to move is assigned to water, the easiest to move to fire, and the intermediate kind to air.
Again the smallest body is assigned to fire, the largest, for its part, to water, and the intermediate
to air; and the sharpest again to fire, the second sharpest to air, and the third sharpest to water.
Now in all these cases the one that has the fewest bases is necessarily, by nature, the most mobile
since it is the most incisive and the sharpest 56B of them all in every respect, and also the lightest
since it is composed of the fewest identical parts. The second lies in second place based on these
same factors while the third lies in third place.
Now that is enough said about their intergeneration; next we should explain what the form of each
of them is like and the number that come together to constitute it. Now we begin with the
construction of the first and smallest form; its element of composition is the triangle having its
hypotenuse double the shortest side in length. If a pair of such triangles is placed along a
diagonal, and this is done 54E three times, with the diagonals and the short sides fixed to the same
point as though it were a centre, then from these, six in number, a single equilateral triangle is
produced. And when four equilateral triangles are combined based on three flat angles coming
together, a single solid angle 55A is produced, the one that comes next after the most obtuse of flat
angles;27 and when four such solid angles have been completed, the first solid form that
apportions the entire surface of a sphere into equal and similar parts is constructed.28
The second is composed of the same triangles but arranged into eight equilateral triangles which
produce a single solid angle from four flat angles, and when six solid angles like this have been
generated the second solid form is, in turn, brought to completion. The third is composed of one
hundred and twenty of the elemental triangles combined together; 55B it has twelve solid angles
each bounded by five flat equilateral triangles and twenty faces consisting of equilateral triangles.
Now this elemental triangle was released from duty once it had produced these three forms, and
the isosceles triangle then produced the fourth kind when it was assembled in groups of four with
their right angles joining at the centre to form a single equilateral quadrangle;29 and six such
surfaces when brought together 55C produced eight solid angles each consisting of three flat right
angles, and the shape of the assembled body was the cube with its six flat equilateral quadrangular
27 This simply means that the three sixty degree angles that meet at the corner of a tetrahedron add up to 180o which is
not an obtuse angle but next after the most obtuse angle. 28 This refers to a tetrahedron inscribed within a sphere. 29 A square.
Copyright © 2021 by David Horan 22
faces. One construction still remained, the fifth, and god used this in order to embroider shapes
upon the universe.
Now suppose someone considering all this with due measure were to become perplexed over
whether we should say there are an unlimited number of worlds or that there is some limit. He
would regard the opinion that the number is unlimited 55D as belonging to someone who is
actually inexperienced on issues whereon he should be experienced but, on the other hand, the
question of whether it is, in truth, ever appropriate to say that there is naturally one world or five,
if he were to stop there, would provide more reasonable grounds for perplexity. Now our
approach, based upon the likely account, reveals that it is, by nature, a single god, but someone
else, in view of some other considerations may form different opinions.
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