Gripla - 2021, Qupperneq 97

95
Each square number has two dimensions, that is breadth and length.
But a cubic number has three dimensions, that [16v] is breadth, length, and
thickness or height. And therefore the sages say every visible body is put
together with this number for it always76 has these three dimensions.
Since eternal wisdom, the one God wanted to create a visible and bodily
world, then he first made two of the outermost elements, fire and earth,
because nothing can be naturally visible without them, as fire makes light
and movement, but the earth is steadfast and unmoving. And since they
have three unequal and opposite qualities, it was then a natural necessity
to set something between them which reconciled their differences. And
since, as said before, fire and earth, and every such thing that is of a bodily
nature is composed out of a three-fold number, which we call cubic, then
we write for this two cubes. We write the earth this way: twice times two
twice, 2, 4, 8. But fire so: thrice three thrice, 3, 9, 27.
And since in this case no single mean77 can be between these numbers,
with only it being in equal proportion to both and of no other two cubes,
then we find two proportional numbers in this manner: We multiply the
root of the greater cube with the square of the smaller cube, that is twice
two thrice: 2, 4, 12. And the root of the smaller cube with the square of the
greater cube, that is thrice three twice: 3, 9, 18. These two numbers belong
equally to the outer two cubes since seven and 20 has in itself 18 and half of
18, and 18 has in itself 12 and half of 12. And so has 12 in itself 8 and half of
8. You shall in the same way always find proportions between two cubes.
Thus God arranged two elements between fire and earth: air and water.
And water has two qualities from earth and two numbers, but from fire
one quality and one number. And air has two qualities from fire and two
numbers, but one from earth and one number. And fire is as much lighter
than air as 27 is greater than 18. And air is as much lighter than water as
18 is greater than 12. Water is as much lighter than earth as 12 is greater
than 8.
This is to be more fully understood in that figure which is made here
later and is called the cubus perfectus.78
76 GKS 1812 has jamnan here, but Hauksbók has avallt.
77 miðskeið
78 This work is derived from my MA thesis in Medieval Icelandic Studies at the University
of Iceland. I would like to thank Gunnar Harðarson for his encouragement, suggestions,
and careful reading of the transcript and translation. His corrections have greatly improved
ALGORISMUS IN GKS 1812 4TO