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HARMONICES MUNDI #0606_3/ 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_0105 | | Description: | Signed, titled, date, copyright in magic ink on the reverse.
"The Science of the Harmony of the World" (1619) by Johannes Kepler.
The Science and Harmony of the World:
Note: Continued from the preceding "page" as "PA_104" - Harmonices Mundi #0606_2/ 2006.
When Aristotle reads "earth," they were giving him "cube," because they may perhaps have understood Saturn whose orbit is distanced from Jupiter by an interposed cube. And the common sort attribute rest to earth, but Saturn moving the slowest of all has been marked out as the closest to rest, for which reason the planet was given the name "rest" by the Hebrews. In the same way Aristotle reads octahedron as given to "air," when they may, perhaps, understand Mercury, whose orbit is contained by an octahedron, and Mercury is no less fast (certainly the fastest of all the planets) than the air is mobile. Mars was perhaps worked in with the word "fire," the name for this planet is "pyrois," which is derived from fire, and a tetrahedron was given to it perhaps because the orbit of this planet has been enclosed by this figure. And "water" could have concealed the star of Venus to which the icosahedron was allotted (because the orbit is contained by an icosahedron) because fluids are subject to Venus, and she herself was said to have been born from the ocean spray, whence the name Aphrodite.
And lastly, the sound of the word "world" could mean "earth" and the dodecahedron be allotted to the world, because its orbit is contained by this figure, separated into twelve longitudinal parts so that this figure is contained by twelve planes for the whole orbit. Agreement has therefore been reached that in the mysteries of the Pythagoreans the five figures have not been distributed among the elements, as Aristotle believed, but rther, among the planets. This is a great confirmation of what Proclus handed down, among other things, as th purpose of geometry, and what he would tech, namely, how heaven would have accepted harmonious forms for its particular parts.
Although not this purpose, but injury is what Ramee inflicts on us, so Snell, the most skillful of today's geometers giving open support to Ramus, says first that "the very division of the unnameables (1) into thirteen different types is of no profitable use" in the preface to "The Problems of Ludolph of Coellen." I concede that, if he should know no use, if not in every day life, and if there would be no use for life in the investigations of physics.
But why does he not follow Proclus, who said he did not know any greater good of geometry than the arts which are necessary to life? But then the use of the tenth book would be clear from the evaluated types of the figures. Snell says that all those authors of geometrical works who do not use the tenth book of Euclid, deal with either the problems of lines, or solids, and with figures or such quantities which do not have their purpose within themselves but tend toward other uses, and that they may not be investigated separately from those other purposes.
But the regular figures are investigated for intrinsic reasons, they have their own perfection in themselves, and are included among the problems of planes, not withstanding the fact that a solid is enclosed by plane surfaces, and that the most important subject matter of the tenth book concerns planes. Why would anything different be mentioned? Or why are the goods, which Codrus does not buy to stuff his belly, but Cleopatra does to decorate her ears, thought so worthless in value? Has so much torment been fashioned by minds? The unnameables are offensive to those for whom this question must be defined by numbers. But I deal with these types by the reasoning of the mind, not by numbers, and not by algebra.
Because there is no work for me in reckoning up the balance sheets of merchants, but there is in developing the causes of things. It is a common opinion that these subtleties must be separated out from the Elements of geometry, and must be stuffed away in the archives. Ramee's altogether faithful student discusses that, and he does not perform an academic undertaking. Ramee took away the form from Euclid's construction, and overthrew the crown of the work, the five solids. The whole structure wa destroyed after these had been removed, the cracked walls remain standing, the jutting arches left in ruins, then Snell took away the cement as well, so there has been no use for the solidity of Euclid's house cemented together under the five figures.
What a happy comprehension by the student, how correctly he affirmed that he understood Euclid by reading Ramus. So they think of what was called the Elements, because an abundant variety of propositions, problems and theorems is discovered in Euclid for all the different kinds and quantities of the arts bound up with them, although the book "The Elements" might have been named from its form, because a subsequent proposition is always supported by a preceding one, right through to the last proposition of the last book (usually Book 9), what lack could there be of anything prior? They make a forest-ranger, or timber merchant out of the architect by thinking that Euclid obviously wrote his book so that it might supply all others, only he would have no dwelling of his own. This is more than enough of these matters for this point, now we must return to the main line of discussion.
Because I would understand the true and real differentiations of the geometrical matters by which the causes of harmonic proportions must be derived by me, I declare the following to be widely unknown: that Euclid who handed on these proportions carefully has been driven away overwhelmed by the mockery of Ramus, and confused by the babbling of the lewd, is heard by nobody, or else tells the mysteries of philosophy to the deaf. That Proclus who lays bare the mind of Euclid, digs up the hidden things, and may have been able to make easy again what is difficult to comprehend, was made an object of derision, and did not continue his commentary up to the tenth book. I saw that all this was to be done to me by me.
As I begin I would transcribe those things from Euclid's tenth book which may contribute in an especial way to my present undertaking. I would bring into the light the series of matters in that book, separated by certain definite divisions. I would show the reasons why some members of the divisions were omitted by Euclid, then, lastly the figures themselves must be discussed. I have been content to simply reference the propositions in those cases which were proven clearly by Euclid. There are many questions which have been proven by Euclid in a different way, now these must be reworked, or were separated, joined together again, or the order must be changed on account of the purpose that has been given me, namely the comparison of the figures which can be known and those which cannot. I have combined the series of definitions, propositions and theorems in numerical order, as I did in the "Dioptics," because of the ease of reference.
I have not been accurate in regard to the lemmasd, nor over anxious in regard to names, being more concerned with the constructions themselves. Certainly this is not yet geometry in philosophical terms, but in this part I do discuss the philosophy of geometry. Would that I were able to treat still more popularly of geometrical questions, provided the treatment were clearer and more palpable. But, I hope that readers equal to both will think about my work for the good, both because I teach geometry popularly, and because I was not able to overcome by my effort the obscurity of the subject matter. Finally I give this advice to any people who might be completely unfamiliar wityh mathematical questions, carried along by my exposition they should red only the propositions from number 30 to the end, and faithfully employing those propositions without proof, they should proceed to the other books, especially to the last. If such readers were to be terrified by the difficulty of the geometrical argument, they might deprive themselves of the most joyful fruit of contemplating the harmonies. Now, let us go to work with God.
-www.schillerinstitute.org/transl/trans_kepler.html
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