# Copernicus, Better like math

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#### cbarnett97

• 2746
##### Copernicus, Better like math
« on: December 16, 2007, 12:35:14 PM »
Good Proof of RE theory.

From De Revolutionibus by Nicholas Copernicus
PROOF OF THE EARTH'S TRIPLE MOTION    Chapter 11

In so many and such important ways, then, do the planets bear witness to the earth's mobility. I shall now give a summary of this motion, insofar as the phenomena are explained by it as a principle. As a whole, it must be admitted to be a threefold motion.

The first motion, named nuchthemeron by the Greeks, as I said [I, 4], is the rotation which is the characteristic of a day plus a night. This turns around the earth's aids from west to east, just as the universe is deemed to be carried in the opposite direction. It describes the equator, which some people call the "circle of equal days", in imitation of the designation used by the Greeks, whose term for it is isemerinos.

The second is the yearly motion of the center, which traces the ecliptic around the sun. Its direction is likewise from west to east, that is, in the order of the zodiacal signs. It travels between Venus and Mars, as I mentioned [I, 10], together with its associates. Because of it, the sun seems to move through the zodiac in a similar motion. Thus, for example, when the earth's center is passing through the Goat, the sun appears to be traversing the Crab; with the earth in the Water Bearer, the sun seems to be in the Lion, and so on, as I remarked.

To this circle, which goes through the middle of the signs, and to its plane, the equator and the earth's axis must be understood to have a variable inclination. For if they stayed at a constant angle, and were affected exclusively by the motion of the center, no inequality of days and nights would be observed. On the contrary, it would always be either the longest or shortest day or the day of equal daylight and darkness, or summer or winter, or whatever the character of the season, it would remain identical and unchanged.

The third motion in inclination is consequently required. This also is a yearly revolution, but it occurs in the reverse order of the signs, that is, in the direction opposite to that of the motion of the center. These two motions are opposite in direction and nearly equal in period. The result is that the earth's axis and equator, the largest of the parallels of latitude on it, face almost the same portion of the heavens, just as if they remained motionless. Meanwhile the sun seems to move through the obliquity of the ecliptic with the motion of the earth's center, as though this were the center of the universe. Only remember that, in relation to the sphere of the fixed stars, the distance between the sun and the earth vanishes from our sight forthwith.

Since these are matters which crave to be set before our eyes rather than spoken of, let us describe a circle ABCD, which the annual revolution of the earth's center has traced in the plane of the ecliptic. Near its center let the sun be E. I shall divide this circle into four parts by drawing the diameters AEC and BED. Let A represent the first point of the Crab, B of the Balance, C of the Goat, and D of the Ram. Now let us assume that the earth's center is originally at A. About A I shall draw the terrestrial equator FGHI. This is not in the same plane [as the ecliptic], except that the diameter GAI is the intersection of the circles, I mean, of the equator and the ecliptic. Draw also the diameter FAH perpendicular to GAI, F being the limit of the [equator's] greatest inclination to the south, and H to the north. Under the conditions thus set forth, the earth's inhabitants will see the sun near the center E undergo the winter solstice in the Goat. This occurs because the greatest northward inclination, H, is turned toward the sun. For, the inclination of the equator to the line AE, through the agency of the daily rotation, traces the winter solstice parallel to the equator at an interval subtended by EAH, the angle of the obliquity.

Now let the earth's center start out in the order of the signs, and let F, the limit of maximum inclination, travel along an equal arc in the reverse order of the signs, until at B both have traversed a quadrant of their circles. In the interim the angle EAI always remain equal to AEB, on account of the equality of their revolutions; and the diameters always stay parallel to each other, FAH to FBH, and GAI to GBI, and the equator to the equator. In the immensity of the heavens, for the reason already frequently mentioned, the same phenomena appear. Terefore from B, the first point of the Balance, E will seem to be in the Ram. The intersection of the circles will coincide with the single line GBIE, from which [the plane of the axis] win not be permitted by the daily rotation to deviate. On the contrary, the [axis'] inclination will lie entirely in the lateral plane. Accordingly the sun will be seen in the spring equinox. Let the earth's center proceed under the assumed conditions, and when it has completed a semicircle at C, the sun will appear to enter the Crab. But F, the southernmost inclination of the equator, will be turned toward the sun. This will be made to appear in the north, undergoing the summer solstice as measured by the angle of the obliquity, ECR Again, when F turns away in the third quadrant of the circle, the intersection GI will once more fall on the line ED. From here the sun will be seen in the Balance undergoing the autumn equinox. Then as H by the same process gradually faces the sun, it will bring about a repetition of the initial situation, with which I began my survey

Alternatively, let AEC be in the same way a diameter of the plane under discussion [the ecliptic] as well as the intersection of that plane with a circle perpendicular thereto. On AEC, around A and C, that is, in the Crab and the Goat, draw a circle of the earth in each case through the poles. Let this [meridian] be DGFI, the earth's axis DF, the north pole D, the south pole F, and GI the diameter of the equator. Now when F is turned toward the sun, which is near E, the equator's northward inclination being measured by the angle IAE, then the axial rotation will describe, parallel to the equator and to the south of it, at a distance LI and with diameter KL, the tropic of Capricorn as seen in the sun. Or, to speak more accurately, the axial rotation, as viewed from AE, generates a conic surface, having its vertex in the center of the earth, and its base in a circle parallel to the equator. Also at the opposite point, C, everything works out in like manner, but is reversed. It is clear therefore how the two motions, I mean, the motion of the center and the motion in inclination, by their combined effect make the earth's axis remain in the same direction and in very much the same position, and make all these phenomena appear as though they were motions of the sun.

I said, however, that the annual revolutions of the center and of inclination are nearly equal. For if they were exactly equal, the equinoctial and solstitial points as well as the entire obliquity of the ecliptic would have to show no shift at all with reference to the sphere of the fixed stars. But since there is a slight variation, it was discovered only as it grew larger with the passage of time. From Ptolemy to us the precession of the equinoxes amounts to almost 21°. For this reason some people believed that the sphere of the fixed stars also moves, and accordingly they adopted a surmounting ninth sphere. This having proved inadequate, more recent writers now add on a tenth sphere. Yet they do not in the least attain their goal, which I hope to reach by the earth's motion. This I shall use as a principle and hypothesis in the demonstration of the other [motions].

To see the full text http://webexhibits.org/calendars/year-text-Copernicus.html
« Last Edit: December 16, 2007, 12:39:43 PM by cbarnett97 »
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

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#### Bushido

##### Re: Copernicus, Better like math
« Reply #1 on: December 16, 2007, 01:02:37 PM »
tl;dr

Copernicus assumed a Round Earth, just like the Ptolemaic geocentric system.

#### Max Fagin

• 695
##### Re: Copernicus, Better like math
« Reply #2 on: December 16, 2007, 04:21:07 PM »
tl;dr

Copernicus assumed a Round Earth, just like the Ptolemaic geocentric system.

Exactly, and Copernicus' system predicted planetary positions better that Ptolemy's.  What does that say about the validity of Ptolemy's assumptions?
"The earth looks flat; therefore it is flat."
-Flat Earthers

"Triangle ABC looks isosceles; therefore . . ."

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#### Bushido

##### Re: Copernicus, Better like math
« Reply #3 on: December 16, 2007, 05:06:38 PM »
tl;dr

Copernicus assumed a Round Earth, just like the Ptolemaic geocentric system.

Exactly, and Copernicus' system predicted planetary positions better that Ptolemy's.  What does that say about the validity of Ptolemy's assumptions?

More importantly, how are the two systems related to the Flat Earth model?

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#### cbarnett97

• 2746
##### Re: Copernicus, Better like math
« Reply #4 on: December 16, 2007, 05:49:24 PM »
tl;dr

Copernicus assumed a Round Earth, just like the Ptolemaic geocentric system.

Exactly, and Copernicus' system predicted planetary positions better that Ptolemy's.  What does that say about the validity of Ptolemy's assumptions?

More importantly, how are the two systems related to the Flat Earth model?
they help to demonstrate that the FE model is not valid
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

?

#### Bushido

##### Re: Copernicus, Better like math
« Reply #5 on: December 16, 2007, 05:52:16 PM »
tl;dr

Copernicus assumed a Round Earth, just like the Ptolemaic geocentric system.

Exactly, and Copernicus' system predicted planetary positions better that Ptolemy's.  What does that say about the validity of Ptolemy's assumptions?

More importantly, how are the two systems related to the Flat Earth model?
they help to demonstrate that the FE model is not valid
how?

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#### cbarnett97

• 2746
##### Re: Copernicus, Better like math
« Reply #6 on: December 16, 2007, 05:54:09 PM »
The title of the chapter should about sum it up. 3 things that the FE model does not allow to happen
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

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#### Bushido

##### Re: Copernicus, Better like math
« Reply #7 on: December 16, 2007, 05:55:31 PM »
The title of the chapter should about sum it up. 3 things that the FE model does not allow to happen
If you look carefully, you will see that there is a circular argument.