Introduction Part 2

Following Ramus, Lazarus Schoner in his Geometry confessed that he could see absolutely no use for the 5 regular solids in the world.

This was until he read my little book ‘The Secret of the Universe’ in which I prove that the number and distances of the planets were taken from the 5 regular solids.

See what damage Ramus the master did to Schoner the disciple.

Aristotle had refuted the Pythagorean philosophy on the properties of the elements as deduced from the 5 solids.

• Ramus thoroughly read Aristotle.
• He at once conceived a contempt for all of the Pythagorean philosophy.
• He knew that Proclus was a member of the Pythagorean sect.

Ramus did not believe Proclus when he asserted truly that the ultimate aim of Euclid’s work, was the 5 regular solids.

• Hence, a very confident conviction arose in Ramus that the 5 solids must be removed from the aim of the books of the Elements of Euclid.

With the aim of the work removed, as if the form were removed from a building, there was left a formless heap of propositions in Euclid.

• Ramus attacked these as if it were a fiend in all the 28 books of his Schools.

Schoner followed Ramus’ convictions.

• Yet from Proclus he could learn the application of the 5 solids both:
  • in the Elements of Euclid and
  • in the structure of the world.

In fact, Schoner was more fortunate than his master Ramus, because he gratefully received my revelation of the application of the solids in the structure of the world.

If the Pythagoreans attributed these shapes to the elements and not to the orbits of the world as I did, then Ramus would have striven to undo this error as I have done.

• He would not have demolished this whole philosophy with one tyrannical word.

If the Pythagoreans put forward the same teaching as mine and hid their doctrine by wrapping it up in words then Ramus would not say what he said.

• In this way, the Copernican ‘world’ would be found in Aristotle himself
• Ramus would then be wrong to falsely refute Copernicus under other names, as they called the Sun, Fire, and the Moon the Counter Earth

Suppose that:

• the disposition of the orbits of the Pythagoreans and Copernicus were the same
• the 5 solids were known
• the necessity for their fivefold number were also known

Suppose that the Pythagoreans and Copernicus all consistently taught that the 5 solids were the archetypes of the parts of the world.

It would then be so easy for us to believe that their doctrine was in the form of a riddle was.

• The Pythagoreans assigned the cube to the Earth, but I think they really meant Saturn – its orbit was separated from Jupiter by the interposition of the cube.
• This riddle was read by Aristotle who refuted it correctly

The common herd ascribe rest to the Earth. But data shows that Saturn has a very slow motion which is very close to rest.

• This is why the Hebrews gave it a name from the word “rest”*

The Pythagoreans assigned the octahedron to air. But I think they meant Mercury – its orbit was enclosed by the octahedron.

• Mercury is as swift as our nimble air is

Mars was the interpreted to the word “fire, and so the tetrahedron was given to Mars perhaps because its orbit is enclosed by that shape.

The icosahedron was assigned to water, which I assign to the star of Venus (as the one of which the course is contained within the icosahedron).

• This is because liquids are subject to Venus, and she herself is said to have risen from the sea foam, whence the name “Aphrodite”.

Lastly, the word “world” could signify the Earth.

The dodecahedron is assigned to the world. I think this is because the Earth’s course is contained within that shape, and marked off into 12 sections of its length, as a dodecahedron is contained within 12 faces around.

The 5 Shapes are the 5 Planets, not the 5 Elements

Therefore, the Pythagoreans were assigning the the 5 shapes not among the elements, as Aristotle believed, but among the planets themselves.

• This is very strongly confirmed by Proclus telling us that the aim of geometry is to tell how the heaven has received appropriate shapes for definite parts of itself*.

Snel is a supporter of Ramus. He says:

But this is the same as saying that the study of nature is not applicable to everyday life.

He mentions Proclus, but does not follow him.

• Proclus recognizes that there is some greater good in geometry than those of the arts which are necessary for living.

In that case, the application of Book 10 in deciding the kinds of shapes would have been evident. Snel mentions geometrical authors who make no use of Book 10 of Euclid.

All of them deal with either linear or solid problems, with shapes or quantities that have no purpose within themselves.

They use those shapes at other applications, and would not be investigated otherwise.

But the regular shapes are:

• investigated on their own account as archetypes
• perfect within themselves
• among the subjects of plane problems, even if a solid is also enclosed by plane faces.

Book 10 also relates chiefly to plane surfaces.

Why then should those of varying kinds be mentioned? Why should the goods which Codrus did not buy to feed his belly with them, but which Cleopatra bought to ornament her ears, be reckoned cheap?

Is it only a cross fastened to our talents?

I say, to those who molest the inexpressibles with numbers, that is by expressing them.

But I deal with those kinds not with numbers, not by algebra, but by mental processes of reasoning, because of course I do not need them in order to draw up accounts of merchandise, but to explain the causes of things.

Snel considers that such subtleties should be kept out of a “primer” and hidden away in a library.

• He keeps as the faithful disciple of Ramus

Ramus removed the form from Euclid’s edifice, and tore down the coping stone, the 5 solids.

• This threatened a collapse.

Snel takes away the stonework as well because he saw no use for it other than the stability of the house which was joined together under the 5 solids.

They think that:

• the “Elements” is so called because Euclid knew every kind of propositions, problems, and theorems, for every kind of quantities.

• the “Elementary Primer” is the first in the chain of propositions

Instead of an architect, they make him a builders’ merchant or a bailiff.

They think that Euclid wrote his book to accommodate everybody else, but was the only one who had no home of his own.

I saw that the true distinguishing features of geometrical objects. From them I drew out the causes of the harmonic proportions which were totally unknown to the common herd.

Euclid had the zeal to hand them down.

I therefore realized that I had to:

• transcribe from Book 10 of Euclid what chiefly related to my present undertaking
• bring to light the train of thought of that Book, inserting mention of certain definite divisions
• indicate why some branches of the divisions were omitted by Euclid.

Then, finally, I had to deal with the shapes themselves.

There, in cases where Euclid’s demonstrations were perfectly clear I have been content with a simple reference to the propositions.