Introduction Part 2

by Johannes Kepler

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 perused 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 Coernicus 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 refuted it

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, amd 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.

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*.

*Sueprphysics Note: Here only Kepler is mistaken. Euclid, Proclus, and the Pythagoreans were correct. The 5 shapes are the visualization of the 5 layers of Strong force, Weak force, Electromagnetism, Spacetime, and Aether. This is different from their current visualization which uses color as quantum chromodynamics.

Snel is a supporter of Ramus. In his preface to “The Problems of Ludolph van Ceulen”, he says, “That division of the inexpressibles into 13 kinds is useless for application.”

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

But why does he not follow Proclus, whom he mentions, and who recognizes that there is some greater good in geometry than those of the arts which are necessary for living?

In that case in fact the application of Book 10 in deciding the kinds of figures would have been evident. Snel men­ tions geometrical authors who are said to make no use of Book 10 of Euclid.

Of course, all of them deal with either linear or solid problems, and in connection with such figures or quantities as have no purpose within themselves, but obviously aim at other applications, and would not be investigated otherwise.

But the regular shapes are investigated on their own account as archetypes, have their own perfection within themselves, and are among the subjects of plane problems, notwithstanding the fact that a solid is also enclosed by plane faces. In the same way the material of the tenth Book also relates chiefly to plane surfaces. Why then should those of varying kinds be mentioned?

Or 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.

He considers that such subtleties should be kept out of a “primer,” and hidden away in a library. He plays completely the part of the faithful disciple of Ramus, and shows no mean judgement in placing his effort. Ramus removed the form from Euclid’s edifice, and tore down the coping stone, the five solids.

By their removal every joint was loosened, the walls stand split, the arches threatening to collapse. Snel therefore takes away the stonework as well, seeing that there is no application for it except for the stability of the house which was joined together under the five solids.

How fortunate is the disciple’s understanding, and how dexterously did he learn from Ramus to understand Euclid: that is, they think that the “Elements” is so called because there is found in Euclid a wealth of every kind of propositions and problems and theorems, for every kind of quantities and of the arts concerned with them, whereas the book is called “Elementary Primer” from its form, because the following proposition always depends on the preceding one right up to the last one of the last Book (and partly also that of the ninth Book), which cannot do without any of the previous ones. Instead of an architect they make him a builders’ merchant or a bailiff, thinking that Euclid wrote his book in order to accommodate everybody else, but was the only one who had no home of his own. But that is quite enough on the subject at this point: we must return to the main topic of discourse.

For I saw that the true and genuine distinguishing features of geometrical objects, from which I had to draw out the causes of the harmonic proportions, were totally unknown to the common herd; that Euclid, whose zeal had handed them on, is being hooted off by the scoffing of Ramus, and, as he is drowned by the din of frivolous people, is properly heard by no-one, or is reciting the secrets of philosophy to the deaf; and that Proclus, who could have opened the mind of Euclid, disclosed what was hidden, and made easy what was too difficult to grasp, was being mocked and had not continued his commentaries right up to Book 10.

I therefore realized that 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.

Many points which were demonstrated by Euclid in another way, had here, on account of the aim which I had in view, that is to say on account of my comparison of knowable and unknow­ able figures, to be repeated, or linked together if they were separated, or changed in order. I have embraced the series of definitions, propo­ sitions, and theorems in continuous numbering, as I did in the Dioptrice,’^ for convenience of reference.

Also in the actual lemmas I have not been precise, and have not troubled too much about names, as I have been more intent on the matters themselves, seeing that I am now playing the role not of a geometer in philosophy but of a philosopher in this part of geometry.

I wish I could have made my discussion still more popular, provided that it were also clearer and more accessible.

But I hope that fair-minded readers will receive my work kindly on both scores, both because I relate geometrical mat­ ters in a popular way, and because I could not by diligence overcome the obscurity of the material. I also give them this final piece of advice, that if they are completely unacquainted with mathematical matters, they should pass over my expositions and read only the propositions, from X X X to the end; and putting confidence in the propositions them­ selves, without proof, they should pass on to the remaining books, especially the last. They should not be frightened off by the difficulty of the geometrical arguments and deprive themselves of the very great enjoyment of harmonic studies.