Sunday, March 25, 2018

Triangle, Square, and Hexagon │ Basic Figures Filling the Space

The Equiangular Period Spiral includes periods, distances and velocities. It is delimited by three basic equiangular figures – the triangle, the square (more correctly the rectangle) and the hexagon. Nicolas d'Oresme wrote in his major work Le Livre du Ciel et du Monde (The Book of the Heaven and the Earth, 1377):

» Notwithstanding that He is everywhere, still is He absolutely indivisible and the same time infinite with respect to the three qualities that are divisible in living creatures, which we call duration, position, and power or perfection; for temporal duration of creatures is divisible in succession; their position, especially of material bodies, is divisible in extension; and their power is divisible in any degree or intensity […] Besides the varieties of trinity noted there, there is another which is pertinent to our present discussion, because, in accord with what we said […], there are three regular plane figures – the triangle, the square, and the hexagon – each of which we can imagine to be capable of filling so completely a flat area or surface that it is absolutely impossible that there could be more space to be filled; likewise there are three divine persons, each of whom fills all space. Isaiah the Prophet spoke of them thus: Holy, Holy, Holy, Lord God, etc. all the earth is full of thy glory. And there is one God, who spoke through His Prophet Jeremiah: I will fill the heaven and earth; and of whom Virgil said: All things are replete with Jove. « (Book IV, Chapter 10).

A page from d'Oresme's Livre du Ciel et du Monde, showing the celestial spheres:
Although the order of the spheres is conventional, with the Moon and Mercury
closest the Earth and Saturn and the stars farthest, the spheres are convex upward
centered on God rather than convex downward centered on the Earth.
[Paris, Bibliothèque Nationale de France, Manuscrits, Fr. 565, fo 69].