This heliocentric model of Plate [*Tabula<\/i>] 3 shows the six planetary orbs - of Mercury, Venus, Earth, Mars, Jupiter and Saturn - inscribing and circumscribing the five so-called Platonic solids - the regular octahedron, icosahedron, dodecahedron, tetrahedron and cube. The eccentricities of the planets' paths, and hence the thicknesses of their orbs, are indicated by the epicycles adjacent to the planetary signs within each orb. Kepler regarded the nested solids as a proof for the Copernican hypothesis, as he points out in the 'primary derivation' (summarised below). The model is dedicated to Friedrich, Duke of Wuerttemberg, who had commissioned a drink-dispenser based on it, with the planetary hemispheres serving appropriate beverages - a project that was, alas, abandoned.<\/p>"
},
{
"label": "Date of Creation",
"value": "1596"
},
{
"label": "Title",
"value": "The dimensions and distances of planetary orbs"
},
{
"label": "Material",
"value": "paper"
},
{
"label": "Classmark",
"value": "M.5.49"
},
{
"label": "Note(s)",
"value": "*

*An English translation and commentary may be found in Duncan (1981). Outlines of the primary derivation. Demonstrating Copernicus's hypothesis about a new Universe, but with new evidence. God created matter. Quantity is a form of matter, and God created it first so there was a means of comparing a curved with a straight line. A curved line is like God, and a straight line is like his creatures [Nicolaus Cusanus, Complementum theologicum (1453), ch. 3. On Kepler's use of Cusanus, see J. Huebner, Die Theologie Johannes Keplers zwischen Orthodoxie und Naturwissenschaft (Tuebingen, 1975), pp. 188-92]. It is a valuable service to compare a curve with a straight line, a circle with a square. To the appropriateness/correctness of quantities and the nobility of the curve is added a greater thing: the image of the Trinity in a spherical surface, that is, of the Father at the centre, the Son in the surface, and the Spirit in the regularity of the relationship between point and circumference. A spherical surface is the noblest and most perfect kind of curve. God produced the sphere because, as the perfect creator, it was necessary for him to produce a most beautiful work. The Creator conceived the idea of the Universe. The idea comprises of that which is best, so that the form of the future creation would be the best. He adopted the idea for establishing the Universe from his own essence, which is twofold: excellent and divine. He imprinted this pattern, or idea, on the Universe, so that it should be as good and fine as possible. In order that that the Universe might be capable of accepting this idea, he created quantity. He devised quantities so that they depended on two characteristics, straightness and curvedness, of which curvedness represents God. The whole Universe is enclosed by a spherical shape, as has been argued by Aristotle [De caelo, 286b10 - 287a5] and is demonstrated by Copernicus's outermost sphere of fixed stars, which preserves the same shape, without motion, and takes the Sun at its centre. There are three types of quantity: shape, number and extension of objects. We find the curve only in shape. The curved things are: the Sun at the centre of the Universe (the image of the Father), the sphere of the fixed stars or the Mosaic waters [Genesis 1:6-7] at its circumference (the Son), and the heavenly air which fills all parts (the Spirit). Other things in the cosmic structure (the fixed stars, planets, irregular sizes of the heavens) have causes in straightness. The solid bodies, as the quantities which are perfectly formed from the straight, are made up of three dimensions. 1) Straight lines and surfaces are infinite in kind, and do not admit of order, and solid bodies are infinitely infinite in kind. But classes of solid bodies can be determined on the basis of distinguishing features, which are further reducible, if we select those from which we can use the angles and centres of the plane faces of their bodies 2) to derive the myriad number, size and position of the fixed stars. If that is not humanly possible, then we should look instead to the planets (i.e. those stars that are near, few and moving). If we retain only those solid bodies with equilateral and equiangular faces, we will be left with the five regular solids which the Greeks called: cube, tetrahedron, dodecahedron, icosahedron, octahedron. There cannot be more than these five [Euclid, Book XIII]. Just as the number of the latter bodies is small, whilst the species of solid bodies are innumerable or infinite, so there are two types of stars: infinite and fixed (the fixed stars), limited and moving (the planets). This is not the place to discuss why planets move. However, if it is assumed that the planets required motion, it follows that 3) they had to receive round orbits in order to acquire it. The orbit is recognised by its motion and 4) the solid bodies by their number and sizes. Plato said 'God is always a geometer'. In the structure of planets he has inscribed solids within spheres, and spheres within solids, until there was no solid left that was not robed outside and inside with moving spheres [Euclid, Book XIII, Propositions 14-17]. If the five solids are fitted inside one another, with spheres between them and enclosing them, there is a total of six spheres. Proposition: In the Universe, there are six spheres moving round a fixed Sun. Copernicus has six such spheres, and each pair of spheres is in such proportion to each other that all of these five solids can be readily fitted in between them. We must concur with him, unless someone puts forward a hypothesis which gives a better solution. Pythagoras compared the Earth to a cube (because they are both stable), heaven to the icosahedron (because they both rotate), and fire to the pyramid (because that is the shape of a flame). The remaining bodies he divided between earth and water. But he did not have Copernicus's statement of the Universe. If he had, this proportion of the heavens would have been as well known now as the five solids themselves. The idea would have become accepted, just as since that time, the idea of the motion of the Sun and the immobility of the Earth has weakened. To test the proposition that the five solids are found in the spheres of Copernicus: The greatest difference of the distances in Copernicus is between Jupiter and Mars [Mysterium, tabella I]. A solid is required which makes the difference between the circumscribed and inscribed sphere a maximum: 6) this is the tetrahedron. Therefore, there is a pyramid between Jupiter and Mars. Jupiter and Saturn have the next greatest difference in distance. A similar difference is found inside and outside a cube. Therefore, Saturn goes round a cube, and a cube round Jupiter. The proportion between Venus and Mercury is almost equal, similar to that between the spheres of an octahedron. Venus goes round an octahedron, Mercury inside. The proportions between Venus and Earth, and between Earth and Mars are very small and almost equal. In the icosahedron and the dodecahedron, the radii of the two spheres are almost equal, and stand in the smallest proportion to one another compared to the rest of the regular solids. Mars goes round the Earth with one of these solids in between, whereas Earth is separated from Venus by the other. There are only six moving spheres as there are only five proportions: the same number as there are in mathematics. Six boundaries make up this number of proportions.<\/p>*

*Links to other items:<\/p>*

*Representations of world systems: CUL M.7.36 (Riccioli explains Galileo's Copernican argument from the motion of sunspots)<\/a><\/p>*

*Representations of world systems: CUL Hanson.bb.80 (Idea of the Universe, detail)<\/a><\/p>*

*Representations of world systems: CUL Hanson.bb.80 (Idea of the Universe)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Tychonic world system)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (First motion of the Earth according to Copernicus)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (The order and proportion of celestial orbs according to Copernicus)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (The order and proportion of celestial orbs according to the Ancients)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Second motion of the Earth according to Copernicus)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Copernican world system)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Ptolemaic world system)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Purported third motion of the Earth according to Copernicus)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Cartesian world system)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 ('Place and motion of the Earth' in the purported Cartesian world system)<\/a><\/p>*

*Representations of world systems: CUL F169.d.1.14 (Motions of the Earth according to Copernicus)<\/a><\/p>*

*Representations of world systems: CUL F154.b.1.1 (Copernican world system, first edition)<\/a><\/p>*

*Representations of world systems: CUL M.9.46 (The Tychonic world system)<\/a><\/p>*

*Representations of world systems: CUL P*.16.21(F) (Representation of the aggregation of solar systems to fill up space)<\/a><\/p>*

*Representations of world systems: CUL T*.4.18(D) (The Copernican system)<\/a><\/p>*

*Representations of world systems: CUL T*.4.18(D) (Cannon shots are not proof of the Earth's rest)<\/a><\/p>*

*Representations of world systems: CUL M.9.49(1) (Elemental and celestial regions)<\/a><\/p>*

*Representations of world systems: CUL M.7.36 (Motion experiments (Tower of Asinella))<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The motion of the Earth around the Sun explained according to the theory of magnetism)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The Brunian hypothesis)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Theory of the Sun, or rather of the great orb of the Earth)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Position of the centres of the eccentric spheres of the Universe)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The Earth compared to a magnetic whirl)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Theory of the sphere of Venus)<\/a><\/p>*

*Representations of world systems: CUL M.9.37 (System of the World according to Ptolemy)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (The true thickness of the celestial orbs and spaces)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Theory of the motion of the superior planets)<\/a><\/p>*

*Representations of world systems: CUL P*.3.55(D) (System of the World according to Ptolemy)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The vapours near the Sun)<\/a><\/p>*

*Representations of world systems: CUL P*.3.55(D) (System of the World according to Copernicus)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Size of the lunar sphere)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (Primary and secondary planets: the Earth and the Moon, and Jupiter and its satellites)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The Earth has its centre of gravity, although it is not the centre of the World)<\/a><\/p>*

*Representations of world systems: CUL P*.3.55(D) (System of the World according to Tycho Brahe)<\/a><\/p>*

*Representations of world systems: CUL M.9.37 (System of the World according to Tycho Brahe)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Theory of the motion of the Moon)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The Sun, the orb of the Earth and the sphere of the fixed stars)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Arrangement of the spheres of the World according to Copernicus)<\/a><\/p>*

*Representations of world systems: CUL M.9.37 (System of the World according to Copernicus and Galileo)<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.12.40 (The motion of planets 'pushed' by the Sun's immaterial species )<\/a><\/p>*

*Representations of world systems - in defence of Copernicus: CUL M.5.49 (Theory of the sphere of Mercury)<\/a><\/p>"
},
{
"label": "Decoration",
"value": "Relief"
},
{
"label": "Associated Name(s)",
"value": "Georg Gruppenbach"
},
{
"label": "Format",
"value": "Book"
},
{
"label": "Language(s)",
"value": "Latin"
},
{
"label": "Author(s)",
"value": "Johannes Kepler"
},
{
"label": "Bibliography",
"value": "*