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