But true and exact reason； vindicating the nature of true being；
maintains that while two things ＇i。e。 the image and space＇ are
different they cannot exist one of them in the other and so be one and
also two at the same time。
Thus have I concisely given the result of my thoughts； and my
verdict is that being and space and generation； these three； existed
in their three ways before the heaven； and that the nurse of
generation； moistened by water and inflamed by fire； and receiving the
forms of earth and air； and experiencing all the affections which
accompany these； presented a strange variety of appearances； and being
full of powers which were neither similar nor equally balanced； was
never in any part in a state of equipoise； but swaying unevenly hither
and thither； was shaken by them； and by its motion again shook them；
and the elements when moved were separated and carried continually；
some one way； some another； as； when rain is shaken and winnowed by
fans and other instruments used in the threshing of corn； the close
and heavy particles are borne away and settle in one direction； and
the loose and light particles in another。 In this manner； the four
kinds or elements were then shaken by the receiving vessel； which；
moving like a winnowing machine； scattered far away from one another
the elements most unlike； and forced the most similar elements into
dose contact。 Wherefore also the various elements had different places
before they were arranged so as to form the universe。 At first； they
were all without reason and measure。 But when the world began to get
into order； fire and water and earth and air had only certain faint
traces of themselves； and were altogether such as everything might
be expected to be in the absence of God； this； I say； was their nature
at that time； and God fashioned them by form and number。 Let it be
consistently maintained by us in all that we say that God made them as
far as possible the fairest and best； out of things which were not
fair and good。 And now I will endeavour to show you the disposition
and generation of them by an unaccustomed argument； which am compelled
to use； but I believe that you will be able to follow me； for your
education has made you familiar with the methods of science。
In the first place； then； as is evident to all； fire and earth and
water and air are bodies。 And every sort of body possesses solidity；
and every solid must necessarily be contained in planes； and every
plane rectilinear figure is composed of triangles； and all triangles
are originally of two kinds； both of which are made up of one right
and two acute angles； one of them has at either end of the base the
half of a divided right angle； having equal sides； while in the
other the right angle is divided into unequal parts； having unequal
sides。 These； then； proceeding by a combination of probability with
demonstration； we assume to be the original elements of fire and the
other bodies； but the principles which are prior to these God only
knows； and he of men who is the friend God。 And next we have to
determine what are the four most beautiful bodies which are unlike one
another； and of which some are capable of resolution into one another；
for having discovered thus much； we shall know the true origin of
earth and fire and of the proportionate and intermediate elements。 And
then we shall not be willing to allow that there are any distinct
kinds of visible bodies fairer than these。 Wherefore we must endeavour
to construct the four forms of bodies which excel in beauty； and
then we shall be able to say that we have sufficiently apprehended
their nature。 Now of the two triangles； the isosceles has one form
only； the scalene or unequal…sided has an infinite number。 Of the
infinite forms we must select the most beautiful； if we are to proceed
in due order； and any one who can point out a more beautiful form than
ours for the construction of these bodies； shall carry off the palm；
not as an enemy； but as a friend。 Now； the one which we maintain to be
the most beautiful of all the many triangles （and we need not speak of
the others） is that of which the double forms a third triangle which
is equilateral； the reason of this would be long to tell； he who
disproves what we are saying； and shows that we are mistaken； may
claim a friendly victory。 Then let us choose two triangles； out of
which fire and the other elements have been constructed； one
isosceles； the other having the square of the longer side equal to
three times the square of the lesser side。
Now is the time to explain what was before obscurely said： there was
an error in imagining that all the four elements might be generated by
and into one another； this； I say； was an erroneous supposition； for
there are generated from the triangles which we have selected four
kinds…three from the one which has the sides unequal； the fourth alone
is framed out of the isosceles triangle。 Hence they cannot all be
resolved into one another； a great number of small bodies being
combined into a few large ones； or the converse。 But three of them can
be thus resolved and compounded； for they all spring from one； and
when the greater bodies are broken up； many small bodies will spring
up out of them and take their own proper figures； or； again； when many
small bodies are dissolved into their triangles； if they become one；
they will form one large mass of another kind。 So much for their
passage into one another。 I have now to speak of their several
kinds； and show out of what combinations of numbers each of them was
formed。 The first will be the simplest and smallest construction；
and its element is that triangle which has its hypotenuse twice the
lesser side。 When two such triangles are joined at the diagonal； and
this is repeated three times； and the triangles rest their diagonals
and shorter sides on the same point as a centre； a single
equilateral triangle is formed out of six triangles； and four
equilateral triangles； if put together； make out of every three
plane angles one solid angle； being that which is nearest to the
most obtuse of plane angles； and out of the combination of these
four angles arises the first solid form which distributes into equal
and similar parts the whole circle in which it is inscribed。 The
second species of solid is formed out of the same triangles； which
unite as eight equilateral triangles and form one solid angle out of
four plane angles； and out of six such angles the second body is
completed。 And the third body is made up of 120 triangular elements；
forming twelve solid angles； each of them included in five plane
equilateral triangles； having altogether twenty bases； each of which
is an equilateral triangle。 The one element ＇that is； the triangle
which has its hypotenuse twice the lesser side＇ having generated these
figures； generated no more； but the isosceles triangle produced the
fourth elementary figure； which is compounded of four such
triangles； joining their right angles in a centre； and forming one
equilateral quadrangle。 Six of these united form eight solid angles；
each of which is made by the combination of three plane right
angles； the figure of the body thus composed is a cube； having six
plane quadrangular equilateral bases。 There was yet a fifth
combination which God used in the delineation of the universe。
Now； he who； duly reflecting on all this； enquires whether the
worlds are to be regarded as indefinite or definite in number； will be
of opinion that the notion of their indefiniteness is characteristic
of a sadly indefinite and ignorant mind。 He； however； who raises the
question whether they are to be truly regarded as one or five； takes
up a more reasonable position。 Arguing from probabilities； I am of
opinion that they are one； another； regarding the question from
another point of view； will be of another mind。 But； leaving this
enquiry； let us proceed to distribute the elementary forms； which have
now been created in idea； among the four elements。
To earth； then； let us assign the cubical form； for earth is the
most immoveable of the four and the most plastic of all bodies； and
that which has the most stable bases must of necessity be of such a
nature。 Now； of the triangles which we assumed at first； that which
has two equal sides is by nature more firmly based than that which has
unequal sides； and of the compound figures which are formed out of
either； the plane equilateral quadrangle has necessarily； a more
stable basis than the equilateral triangle； both in the whole and in
the parts。 Wherefore； in assigning this figure to earth； we adhere
to probability； and to water we assign that one of the remaining forms
which is the least moveable； and the most moveable of them to fire；
and to air that which is intermediate。 Also we assign the smallest
body to fire； and the greatest to water； and the intermediate in
size to air； and； again； the acutest body to fire； and the next in
acuteness to； air； and the third to water。 Of all these elements； that
which has the fewest bases must necessarily be the most moveable；
for it must be the acutest and most penetrating in every way； and also
the lightest as being composed of the smallest number of similar
particles： and the second body has similar properties in a second
degree； and the third body in the third degree。 Let it be agreed；
then； both according to strict reason and according to probability；
that the pyramid is the solid which is the original element and seed
of fire； and let us assign the element which was next in the order
of generation to air； and the third to water。 We must imagine all
these to be so small that no single particle of any of the four
kinds is seen by us on account of their smallness： but when many of
them are collected together their aggregates are seen。 And the
ratios of their numbers； motions； and other properties； everywhere
God； as far as necessity allowed or gave consent； has exactly
perfected； and harmonised in due proportion。
From all that we have just been sayi