Steven H Propp
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Claudius Ptolemy (Latin: Claudius Ptolemaeus; c. AD 90 – c. AD 168) was a Greco-Egyptian writer of Alexandria, known as a mathematician, astronomer, geographer, and astrologer. This book is an indispensable source of information on ancient Greek astronomy.
He argues in favor of the Earth's sphericity: "it is possible to see that the sun and moon and the other stars do not rise and set at the same time for every observer on the earth, but always earlier for those living towards the orient and later for those living towards the occident. For we find that the phenomena of eclipses taking place at the same time... are not recorded at the same hours for everyone... we always find later hours recorded for observers toward the orient than for those toward the occident. And since the differences in the hours is found to be proportional to the distances between the places, one would reasonably suppose the surface of the earth spherical... if it were flat, the stars would rise and set for all people together and at the same time... the more we advance towards the north pole, the more the southern stars are hidden and the northern stars appear. So it is clear here that the curvature of the earth … proves its spherical form on every side. Again, whenever we sail towards mountains or any high places from whatever angle and in whatever direction, we see their bulk little by little increasing as if they were arising from the sea, whereas before they seemed submerged because of the curvature of the water’s surface.” (I, 4)
But he also argues that the earth does not move: “it can be shown that the earth can neither move …nor ever change at all from its place at the centre… it also seems to me superfluous to look for the causes of the motion of the centre when it is once for all clear … that the earth is in the middle of the world and all weights move towards it… For there is no ‘above’ or ‘below’ in the universe with respect to the earth, just as none could be conceived of in a sphere… Therefore the solid body of the earth is reasonably considered as being the largest relative to those moving against it and as remaining unmoved in any direction by the force of the very small weights, and as it were absorbing their fall. And if it had some one common movement… it would clearly leave them all behind because of its much greater magnitude. And the animals and other weights would be left hanging in the air, and the earth would very quickly fall out of the heavens. Merely to conceive such things makes them appear ridiculous.” (I, 7)
His egocentricity causes some acknowledged problems: “it is now necessary to take up the apparent irregularity of anomaly of the sun; because there is one only, and it is such that the time from the least movement to the mean is greater than the time from the mean to the greatest movement. For we find this agrees with the appearances….it would be more reasonable to stick to the hypothesis of eccentricity which is simpler and completely effected by one and not two movements.” (Pg. 93) Later, he adds, “our problem is to demonstrate, in the case of the five planets as in the case of the sun and moon, all their apparent irregularities as produced by means of regular and circular motions… In the case of research about the anomalies, the fact that there are two anomalies appearing for each of the planets, and that they are unequal in magnitude and in the time of their returns, works a good deal of confusion. For one of the anomalies is seen to have relation to the sun, and the other to the parts of the zodiac, but both are mixed together so it is very hard to determine what belongs to each…” (IX, 2)
But he reassures us, “Let on one, seeing the difficulty of our devices, find troublesome such hypotheses. For it is not proper to apply human things to divine things nor to get beliefs concerning such great things from such dissimilar examples. For what is more unlike than those which are always alike with respect to those which never are, and than those which are always alike with respect to those which are not even impeded by themselves? But it is proper to try and fit as far as possible the simpler hypotheses to the movements in the heavens; and if this does not succeed, then any hypotheses possible. Once all the appearances are saved by the consequences of the hypotheses, why should it seem strange that such complications can come about in the movements of heavenly things?” (XIII, 2)
Nicolaus Copernicus (1473- 1543) was a Renaissance mathematician and astronomer who formulated a heliocentric model of the universe. He speaks highly of Ptolemy, “who stands far in front of all the others no account of his wonderful care and industry, with the help of more than forty years of observations brought this art to such a high point that there seemed to be nothing left which he had not touched on.” (I, preface)
He begins by arguing for the sphericity of the earth: “the world is globe-shaped… this form belongs to the heavenly bodies… But it is not perceived straightway to be a perfect sphere, on account of the great height of its mountains and the lowness of its valleys, though they modify its universal roundness to only a very small extent. That is made clear in this way. For when people journey northward from anywhere, the northern vertex of the axis of daily revolution gradually moves overhead, and the other moves downward to the same extent; and many starts situated to the north are not to set, and many to the south are seen not to rise any more. So Italy does not see Canopus, which is visible to Egypt. And Italy sees the last star of Fluvius, which is not visible to this region situated in a more frigid zone… Moreover, the inclinations of the poles have everywhere the same ration with places at equal distances from the poles of the Earth and that happens in no other figure except the spherical. Whence it is manifest that the earth itself is contained between the vertices and is therefore a globe. Add to this the fact that the inhabitants of the east do not perceive the evening eclipses of the sun and moon; nor the inhabitants of the West, the morning eclipses… Furthermore, voyagers perceive … when land is not visible from the deck of a ship, it may be seen from the top of the mast…” (I, 2)
He argues, “I think we must see whether or not a movement follows upon its form and what the place of the Earth is in the universe. For without doing that it will not be possible to find a sure reason for the movements appearing in the heavens…Now it is from the Earth that the celestial circuit is beheld and presented to our sight. Therefore, if some movement should belong to the earth, it will appear, in the parts of the universe which are outside, as the same movement but in the opposite direction… And thedaily revolution is especial in such a movement. For the daily revolution appears to carry the whole universe along, with the exception of the Earth and the things around it. And if you admit that the heavens possess none of this movement but that the Earth turns from west to east, you will find… that as regards the apparent rising and setting of the sun, moon, and stars the case is so. And since it is the heavens which contain and embrace all things as the place common to the universe, it will not be clear at once why movement should not be assigned to the contained rather to the container… For the fact that the wandering stars are seen to be sometimes nearer the Earth and at other times farther away necessarily argues that the centre of the Earth is not the centre of their circles.” (I, 5)
He adds, “For the apparent irregular movement of the planets and their variable distances from the Earth---which cannot be understood as occurring in circles homocentric with the earth---make it clear that the earth is not the centre of their circular movements. Therefore, since there are many centres, it is not foolhardy to doubt whether the centre of gravity of the Earth rather than some other is the centre of the world. I myself think that gravity or heaviness is nothing except a certain natural appetency implanted in the parts by the divine providence of the universal Artisan, in order that they should unite with one another in their oneness and wholeness and come together in the form of a globe.” (I, 9) He concludes, “Therefore we are not ashamed to maintain that this totality---which the moon embraces---and the centre of the Earth too traverse that great orbital circle among the other wandering stars in an annual revolution around the sun; and that the centre of the world is around the sun. I also say that the sun remains forever immobile and that whatever apparent movement belongs to it can be verified of the mobility of the earth…” (I, 10)
Johannes Kepler (1571–1630) was a German mathematician, astronomer, and astrologer, best known for his laws of planetary motion. He points out, “if anyone should doubt whether the faculties of a lodestone… are present in the heavens, or whether the Earth, a heavy body, could be transported from place to place by an immaterial form from the sun; let him regard the moon, which is so much akin to the Earth; he sees it revolve without any solid sphere underlying it. But that bodily forms which pass one another back and forth are strong enough to cause movement is shown by this same moon, which moves the seas on the Earth by the form given out.” (IV, 3)
He rejects Ptolemy: “the laws were made as we described them. For the halves of the circuit are equal to one another---the one in which the planet is attracted and the other in which it is repelled. Equal times are taken by both halves. Moreover, the virtue of the sun is the same and everlasting---both as attractive and as repulsing. And it has the same ration to planetary inertia, which is always the same, because in an everlasting body. Accordingly it does as much by attraction in one half, as it does by repulsion in the other. Why then should we be doubtful concerning the restitution of the planetary body to the original distance within one period of time?” (IV, 3) He also argues that the motions constant ellipses, rather than perfect circles. (V, 4)
And of course (and somewhat weirdly), he speaks of the “celestial harmonies”: “In the Celestial Harmonies which planet sings soprano, which alto, which tenor, and which bass? Although these words are applied to human voices, while voices and sounds do not exist in the heavens, on account of the very great tranquility of movements, and not even the subjects in which we find the consonances are comprehended under the true genus of movement, since we were considering the movements solely as apparent from the sun, and finally, although there is no such cause in the heavens, as in human singing, for requiring a definite number of voices in order to make consonance… I do not know why but nevertheless this wonderful congruence with human song ahs such a strong effect upon me that I am compelled to pursue this part of the comparison, also, even without any solid natural cause.” (“Harmonies of the World,” 8)
This book will be of great interest and value to anyone studying the history of astronomical science.