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HARMONICES MUNDI #0606_2/ 2006
(  Satoshi Kinoshita )
| Series: | Paintings: Landscape 2 | | Medium: | Acrylic on stretched canvas | | Size (inches): | 11.7 x 8.3 | | Size (mm): | 297 x 210 | | Catalog #: | PA_0104 | | Description: | Signed, titled, date, copyright in magic ink on the reverse.
"The Science of the Harmony of the World" (1619) by Johannes Kepler.
Note: Continued from the preceding "page" as "PA_103" - Harmonices Mundi #0606_1/ 2006.
The Science and Harmony of the World:
Because the causes of harmonic proportions might be discovered by us from the divisions of a circle into the equal aliquot parts which are constructed geometrically and scientifically from the provable, regular, plane figures, I begin with what must be made known, I have brought forward at this time the conceptual differentiations of geometrical matters that, in as far as may be clear from what has been published, have not been known in the case of the solids. All the more so in that besides Euclid and his commentator Proclus, no one appeared among the ancients who indicated that he himself had knowledge of these specific differentiations of geometrical matters precisely. the distribution of problems into planes, solids and lines of Pappus of Alexandria, and of the ancients who he followed, was close enough to the quality of conception of one part of the geometrical subject arising to be explained. However, that treatment is both brief, and applied to practical questions. Pappus makes no mention of theory, but if we do not occupy our whole mind with the theory of this question, we will never be able to understand harmonic ratios. When Proclus Diadochus had published four books on Euclid's First, he wanted theoretical philosophy to be incorporated in the subject of mathematics by public profession. If he were to have left us his commentaries on the tenth book of Euclid, he would both have freed our geometers from stupid ignorance, and would have reduced my work in developing the differentiations of geometrical things in solid. For those distinctions of conceptual existences were known well enough by him, as is easily seen in the preface to his book, because he established that the principles of the whole essence of mathematics are the same as that principle which also pervades all existence, and that everything is caused by that, the finite and the infinite, the limited and the unlimited, the limit or circumscription in relation to a form, and the knowledge of the unlimited in relation to the matter of geometrical things.
Form and proportion are the characteristics of quantities, form of the particular, proportion of the combined. Form is completed by limits, a straight line by points, a plane surface by lines, a body is limited, circumscribed and formed by surfaces. Therefore, what has been made finite, circumscribed and formed, can also be comprehended by the mind. The infinite and the indeterminate cannot be constrained by any part of the knowledge which is given by definitions, and by no restraint of proofs. But, the figures have prior existence in the Archetype, then in the work. First they exist in the divine mind, then in created things, in the different modes of the subject, but nonetheless with the same form of its essence. Therefore, the formation with quantities, a certain mental or intellectual essence, creates the differentiations of their essence. That is much clearer when derived from proportions. When a form is completed by many limits, it is effected in such a way that the form would make use of proportions because of this plurality. But it cannot be possible to know what proportion would be at all without the action of the mind. And for that reason the person who gives limits to quantities in relation to the principle of essence, that person asserts that formed quantities have an intellectual essence. But there is no need for argument. Proclus' whole book should be read, it will be evident enough that he knew the intellectual differentiation of geometrical things in a provable way. And yet, when this had been confirmed, he did not go off on his own and assert it in isolation, but cried aloud so that the assertion could not be ignored, and so that he might even wake up sleepy minds. His language flows like a flooding river, layered thoughout with the most abundant and abstruse propositions of platonic philosophy, which is this, the argument of his whole book.
Truth has not freed our century from penetrating to such hidden matters. Proclus' book has been read by Pierre Ramee, but, in what concerns the heart of philosophy, it has been scorned and thrown aside, along with Euclid's tenth book. And, anyone who has written a commentary on Euclid, if such were to have been written in his defense, has been ridiculed and ordered to remain silent. The aroused wrath of the embittered censor has been turned on Euclid as on a criminal. The tenth book of Euclid, which, when read and understood may be able to unfold the mysteries of philosophy, has been doomed by savage sentence to not be read. Nothing more shameful was ever written by Ramee, I ask you to read his words from "The Study of Mathematics," Book 21:
"Stuff, he says, has been handed down in that tenth book, in such a way that I would never have found the same obscurity in human letters and arts. I say obscurity not to be understood, Euclid anticipates that (that could be clear to the illiterate and uneducated who only look at what is right in front of their eyes) but in order to investigate and search out what the purpose, and proposed use of the work might be, what the classes, types and differences of the subjects might be. I have never read anything more confused and involuted. Might not the Pythagorean superstition seem to have been drawn into this book as if into a pit, etc."
By God, Ramee, if you would not have believed that this book may be read with too much ease, you would never have slandered so much obscurity. You need more work. You need quiet. You need forethought. And, above all, you need attentiveness of mind. Then, you may understand the intent of the writer. With that, the good sort of mind will be lifted up to the point where, resolving to live at last in the light of truth, inspired, exulting with incredible pleasure, it perceives the whole world and all its different parts most exactly, as if from a very high place. But to you, you who act in this place as the advocate of ignorance, and of the common man seeking advantage from everything whether divine or human, I say to you, that these matters may be "unnatural sophistries," to you "Euclid will have been quickly and immoderately taken advantage of," to you, "this subtlety has no place in geometry." Let it be your lot to slander what you do not understand. For me, who hunts for the causes of things, no other path will lead to them apart from that which is in the tenth book of Euclid.
Lazarus Schoener followed Ramee in his geometry, he confessed that he was not able to see any use in the world for the five regular solids. Then he would have read the book I wrote, "The Secret of the Universe," in which I prove that the numbers and distances of the planets hae been chosen from the five regular solids. Now look what injuries professor Ramee inflicted on his student Schoener. First, once Ramee had read Aristotle, who refuted pythagorean philosophy on the properties of the elements derived from the five solids, he at once conceived in his soul contempt for the whole of the pythagorean philosophy, then, when he knows that Proclus was part of the pythagorean sect, he used to affirm to his student that he did not believe, what was most true, that the ultimate purpose of Euclid's book, towards which all the propositions of all the books together are brought back, is the five regular solids. This is the origin of Ramee's most confident conviction that the five solids ought to be removed from the end of the books of Euclid's Elements.
After the end of the book has been chopped off, like the shell of a levelled building, Euclid was left, a formless heap of propositions, against which, as if against some ghost, Ramee inveighs in all the 28 books of his "Study of Mathematics," speaking with a great harshness and a great rashness, most unbecoming to such a great man. Schoener followed this conviction of Ramee, and he himself believed that there is no use for the regular solids at all. But not completely, he neglected, or refused to follow Ramee's judgment on Proclus. He was able to learn the use of the five solids, both in Euclid's Elements, and in the making of the world, from Proclus. And the student was much happier than the professor because he accepted the use of the solids opened up by me in the making of the world which Ramee refused to impress upon him from Proclus. For what does it matter if the pythagoreans did attribute these figures to the elements, but not to the spheres of the world, as I do? Ramee would not have offered up one tyrannical word against this whole philosophy, he would have exerted himself to have removed this error of theirs in regard to the real subject of the figures, as I did.
What if the Pythagoreans did teach the same thing that I do, weaving their meaning into a cover of words? May not the Copernican form of the world have existed in Aristotle, may it not have been incorrectly refuted by him in other words when he would call the sun, fire, and the moon Antichthone? For if the same ordering of the orbits which was known to Copernicus was known to the Pythagoreans, if the five solids and the necessity for their five-fold number was known, if they continuously taught that the five solids are the Archetypes of the parts of the world, how little more would it be for us to believe that the thinking of the pythagoreans has been collected together secretly by Aristotle, but had alredy been refuted by the meaning of the words?
Note: Continued on the following "page" as "PA_0105" - Harmonices Mundi #0606_3/ 2006.
-www.schillerinstitute.org/transl/trans_kepler.html
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