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HARMONICES MUNDI #0707/ 2007
(  Satoshi Kinoshita )
| Series: | Paintings: Landscape 2 | | Medium: | Acrylic, sand mortar and extra coarse pumice gel on stretched canvas | | Size (inches): | 38.5 x 28.5 | | Size (mm): | 978 x 724 | | Catalog #: | PA_0121 | | Description: | Signed, titled, date, copyright in magic ink on the reverse.
On May 15, 1618 Johannes Kepler discovered The Third Law:
The squares of the periodic times are to each other as the cubes of the mean distances.
This law he published in 1619 in his Harmonices Mundi . It was this law, not an apple, that lead Newton to his law of gravitation. Kepler can truly be called the founder of celestial mechanics.
-kepler.nasa.gov/johannes/
Johannes Kepler (1571 - 1630)
Johannes Kepler was a German mathematician and astronomer who discovered that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. He also did important work in optics and geometry.
-www-history.mcs.st-andrews.ac.uk/Mathematicians/
Kepler.html
Quotations by Johannes Kepler
Translations are by J. V. Field unless otherwise attributed. Latin text has been given only when an English translation of the complete work is not available in print.
Abbreviation: KGW: Johannes Kepler gesammelte Werke, ed. M Caspar et al., Munich, 1937.
On belief in astrology:
Some of what these pamphlets [of astrological forecasts] say will turn out to be true, but most of it time and experience will expose as empty and worthless. The latter part will be forgotten [literally: written on the winds] while the former will be carefully entered in people's memories, as is usual with the crowd.
On giving astrology sounder foundations: De fundamentis astrologiae certioribus (Prague, 1602) Thesis 2, KGW 4 12
trans. J V Field, Archive for History of Exact Sciences, 31 (1984) 229 - 72.
On the origin of the New Star of 1604:
Priusquam autem ad creationem, hoc est ad finem omnis disputationis, veniamus: tentanda omnia existimo.
However, before we come to [special] creation, which puts an end to all discussion: I think we should try everything else.
On the New Star: De stella nova (Prague, 1606) Chapter 22, KGW 1 257, lines 23 -24.
I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
New Astronomy: Astronomia nova (Heidelberg, 1609) Introduction, second paragraph.
On using observed values:
And from this such small difference of eight minutes [of arc] it is clear why Ptolemy , since he was working with bisection [of the linear eccentricity], accepted a fixed equant point. ... For Ptolemy set out that he actually did not get below ten minutes [of arc], that is a sixth of a degree, in making observations.
To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy's in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. So let us work upon it so as to at last track down the real form of celestial motions (these arguments giving support to our belief that the assumptions are incorrect). This is the path I shall, in my own way, strike out in what follows. For if I thought the eight minutes in [ecliptic] longitude were unimportant, I could make a sufficient correction (by bisecting the [linear] eccentricity) to the hypothesis found in Chapter 16. Now, because they could not be disregarded, these eight minutes alone will lead us along a path to the reform of the whole of Astronomy, and they are the matter for a great part of this work.
New Astronomy: Astronomia nova (Heidelberg, 1609) Chapter 19, 113 - 14, KGW 3 177 -78.
Finding the ellipse:
My argument was as in Chapters 49, 50 and 56: The Circle of Chapter 43 is wrong because it is too large, and the ellipse of Chapter 45 is too small. And the amounts by which they respectively exceed and fall short are the same. Now between the circle and the ellipse there is no other intermediary except a different ellipse. Therefore the path of the planet is an Ellipse; and the lunula cut off from the semicircle has half the previous width, that is 429.
New Astronomy: Astronomia nova (Heidelberg, 1609) Chapter 58, 284 - 85, KGW 3 366.
Geometria una et aeterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.
Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God.
Conversation with the Sidereal Messenger [an open letter to Galileo Galilei]: Dissertatio cum Nuncio Sidereo (Prague, 1610) KGW 4 308, lines 9 - 10.
On one of Galileo's opponents:
...repudiato mundo sensibili, quem nec ipse vidit, nec expertis credit, ratiunculis puerilibus spaciatur Peripateticus in mundo chartaceo, negatque Solem lucere, quia ipse coecus est.
... repudiating the sensible world, which he neither sees himself nor believes from those who have, the Peripatetic [follower of Aristotle] joins combat by childish quibbling in a world on paper, and denies the Sun shines because he himself is blind.
Kepler to Galileo Galilei, 28 March 1611, Letter 611, ll. 17 - 20, KGW 16 372.
Note: Galileo later used the phrase a world on paper and it is sometimes ascribed to him.
Temporis filia veritas; cui me obstetricari non pudet.
Truth is the daughter of time, and I feel no shame in being her midwife.
Account of personal observations of the four moving satellites of Jupiter...: Narratio de observatis a se quatuor Jovis satellitibus erronibus ... (Frankfurt, 1611) first words of text, KGW 4 317.
On what he and some companions saw through one of the telescopes made by Galileo:
Nam et nobis Jupiter, ut et Mars, et mane Mercurius, et Sirius apparuerunt quadranguli. Alter enim diametrorum angulosorum caeruleus erat, alter puniceus, in medio corpus flavum fulgore admirabili.
And to us Jupiter, like Mars, and in the morning Mercury and Sirius, appeared four-cornered. And one of the diameters running between the corners was blue, the other red, in the middle the body was yellow, and amazingly bright.
Account of personal observations...: Narratio... (Frankfurt, 1611) KGW 4 320, lines 6 - 8.
Of The Harmony of the World:
...I am stealing the golden vessels of the Egyptians to build a tabernacle to my God from them, far far away from the boundaries of Egypt. If you forgive me, I shall rejoice.; if you are enraged with me, I shall bear it. See, I cast the die, and I write the book. Whether it is to be read by the people of the present or of the future makes no difference: let it await its reader for a hundred years, if God himself has stood ready for six thousand years for one to study him.
Harmonices mundi libri 5 (Linz, 1619) end of Introduction to Book 5, trans. Aiton, Duncan and Field, p. 391.
On how he discovered his Third law:
...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred an eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labor of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ...
Harmonice mundi (Linz, 1619) Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411.
On how the motion of a planet defines its sphere:
... and thus it comes about gradually by the linking and accumulation of a great many revolutions that a kind of concave sphere is displayed, having the same center as the Sun, just as by a great many circles of silken thread, linked with each other and wound together, the dwelling of a silkworm is made.
Harmonice mundi (Linz, 1619) Book 5, Chapter 9, 4. Axiom, trans. Aiton, Duncan and Field, p. 453.
Epitaph (by Kepler, for himself)
Mensus eram coelos, nunc Terrae metior umbras.
Mens coelestis erat, corporis umbra jacet.
I used to measure the Heavens, now I measure the shadows of Earth. The mind belonged to Heaven, the body's shadow lies here.
KGW 19 393.
I wanted to be a theologian; for a long time I was unhappy. Now, behold, God is praised by my work even in astronomy.
Letter to Michael Maestlin, 3 October 1595. KGW 13, 40.
My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honour due to its maker) and that in it almost all the varety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight.
Letter to J. G. Herwart von Hohenburg, 16 February 1605, KGW 15, 146.
Geometry, which before the origin of things was coeternal with the divine mind and is God himself (for what could there be in God which would not be God himself?), supplied God with patterns for the creation of the world, and passed over to Man along with the image of God.
The Harmony of the World (Linz,1619), Book IV, Ch. 1. Trans. E. J. Aiton, A. M. Duncan, and J. V. Field (1997), 304.
Now, eighteen months after the first light, three months after the true day, but a very few days after the pure Sun of that most wonderful study began to shine, nothing restrains me; it is my pleasure to yield to the inspired frenzy, it is my pleasure to taunt mortal men with the candid acknowledgement that I am stealing the golden vessels of the Egyptians to build a tabernacle to my God from them, far, far away from the boundaries of Egypt. If you forgive me, I shall rejoice; if you are enraged with me, I shall bear it. See, I cast the die, and I write the book. Whether it is to be read by the people of the present or of the future makes no difference: let it await its reader for a hundred years, if God Himself has stood ready for six thousand years for one to study Him.
The Harmony of the World (1619), Book V, Introduction. Trans. E. J. Aiton, A. M. Duncan, and J. V. Field (1997), 391.
I also ask you, my friends, not to condemn me entirely to the mill of mathematical calculations, and to allow me time for philosophical speculations, my only pleasures.
Letter to Vincenzo Bianchi, 17 February 1619. KGW 17, 327.
The cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plants and of numerical constants; and since in them nothing occurs without supreme reason -- not, to be sure, such as discursive reasoning discovers, but such as existed from the first in the Creator's design and is presented from the origin to the day in the wonderful nature of animal faculties, I do not believe that even in a snowflake this ordered pattern exists at random.
The Six-Cornered Snowflake, (Prague, 1611), edited and translated by Colin Hardie (1966), 33.
So the uncertainty of the observation or (as they say) its spread, is greater than this error in Ptolemy's calculation [of the longitude].
Since divine goodness has bestowed on us Tycho Brahe the most diligent observer, from whose observations this error of 8 minutes in Ptolemy's calculation for Mars has been deduced; it is right that with grateful minds we acknowledge and profit by God's good gift. ...
For if I had thought that those 8 minutes of longitude were to be despised I should (that is by bisecting the eccentricity) already have applied a sufficient correction to the model I devised in Chapter 16.
Now, because they could not be despised, these eight minutes, all alone, have opened up the road to reforming the whole of Astronomy, and they have become the material for a large part of this work.
Astronomia nova (Heidelberg, 1609), 113 - 114; KGW 3, 177 - 178.
Compiled by: J. V. Field, London, March 1999, November 2003
-www-history.mcs.st-andrews.ac.uk/Quotations/Kepler.html
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