ferent they cannot inhere in one another, so as to be one and two at
the same time.

To sum up: Being and generation and space, these three, existed before
the heavens, and the nurse or vessel of generation, moistened by water
and inflamed by fire, and taking the forms of air and earth, assumed
various shapes. By the motion of the vessel, the elements were divided,
and like grain winnowed by fans, the close and heavy particles settled
in one place, the light and airy ones in another. At first they were
without reason and measure, and had only certain faint traces of
themselves, until God fashioned them by figure and number. In this, as
in every other part of creation, I suppose God to have made things, as
far as was possible, fair and good, out of things not fair and good.

And now I will explain to you the generation of the world by a method
with which your scientific training will have made you familiar. Fire,
air, earth, and water are bodies and therefore solids, and solids
are contained in planes, and plane rectilinear figures are made up of
triangles. Of triangles there are two kinds; one having the opposite
sides equal (isosceles), the other with unequal sides (scalene). These
we may fairly assume to be the original elements of fire and the other
bodies; what principles are prior to these God only knows, and he of men
whom God loves. Next, we must determine what are the four most beautiful
figures which are unlike one another and yet sometimes capable of
resolution into one another...Of the two kinds of triangles the
equal-sided has but one form, the unequal-sided has an infinite variety
of forms; and there is none more beautiful than that which forms the
half of an equilateral triangle. Let us then choose two triangles; one,
the isosceles, the other, that form of scalene which has the square of
the longer side three times as great as the square of the lesser side;
and affirm that, out of these, fire and the other elements have been
constructed.

I was wrong in imagining that all the four elements could be generated
into and out of one another. For as they are formed, three of them from
the triangle which has the sides unequal, the fourth from the triangle
which has equal sides, three can be resolved into one another, but the
fourth cannot be resolved into them nor they into it. So much for their
passage into one another: I must now speak of their construction. From
the triangle of which the hypotenuse is twice