University of California, Irvine
Instructor: Dr. Barbara J. Becker
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Week 3. Humanism excerpts from
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1. PREFACE
Those who have been true philosophers ... seem to me to have very wisely separated the theoretical part of philosophy from the practical....
Aristotle quite properly divides ... the theoretical into three immediate genera: the physical, the mathematical, and the theological....
[The theological] can only be thought as high above somewhere near the loftiest things of the universe and is absolutely apart from sensible things.
[T]he kind of science which traces through the material and ever moving quality, and has to do with the white, the hot, the sweet, the soft, and such things, would be called physical; and ... is to be found in corruptible things and below the lunar sphere.
And the kind of science which shows up quality with respect to forms and local motions, seeking figure, number, and magnitude, and also place, time, and similar things, would be defined as mathematical. [I]t falls between the other two....
[T]he other two genera of the theoretical would be expounded in terms of conjecture rather than in terms of scientific understanding ... so that ... philosophers could never hope to agree on them.... [Because] only the mathematical, if approached enquiringly, would give its practitioners certain and trustworthy knowledge with demonstration both arithmetic and geometric resulting from indisputable procedures, we were led to cultivate most particularly as far as lay in our power this theoretical discipline....
[M]athematical theory ... alone could take aim at ... the properties having to do with translations and arrangements of movements, belonging to those heavenly beings which are sensible and both moving and moved, but eternal and impassible.... And indeed this same discipline would more than any other prepare understanding persons ... by means of the sameness, good order, due proportion, and simple directness contemplated in divine things, make its followers lovers of that divine beauty, and making habitual in them, and as it were natural, a like condition of the soul.
And so we ourselves try to increase continuously our love of the discipline of things which are always what they are, by learning what has already been discovered in such sciences by those really applying themselves to them, and also by making a small original contribution such as the period of time from them to us could well make possible.
And therefore we shall try and set forth as briefly as possible as many theorems as we recognize to have come to light up to the present, and in such a way that those who have already been initiated somewhat may follow, arranging in proper order for the completeness of the treatise all matters useful to the theory of heavenly things. And in order not to make the treatise too long we shall only report what was rigorously proved by the ancients, perfecting as far as we can what was not fully proved or not proved as well as possible.
2. ON THE ORDER OF THE THEOREMS
A view, therefore, of the general relation of the whole earth to the whole of the heavens will begin this composition of ours.
And next, of things in particular, there will first be an account of the ecliptic's position and of the places of that part of the earth inhabited by us, and again of the difference, in order, between each of them according to the inclinations of their horizons.... And, secondly, there will be an account of the solar and lunar movements....
The last part, in view of this plan, will be an account of the stars. Those things having to do with the sphere of what are called the fixed stars would reasonably come first, and then those having to do with what are called the five planets....
And so, in general, we have to state that the heavens are spherical and move spherically; that the earth, in figure, is sensibly spherical also when taken as a whole; in position, lies right in the middle of the heavens, like a geometrical center; in magnitude and distance, has the ratio of a point with respect to the sphere of the fixed stars, having itself no local motion at all. And we shall go through each of these points briefly to bring them to mind.
3. THAT THE HEAVENS MOVE SPHERICALLY
It is probable the first notions of these things came to the ancients from some such observation as this. For they kept seeing the sun and moon and other stars always moving from rising to setting in parallel circles, beginning to move upward from below as if out of the earth itself, rising little by little to the top, and then coming around again and going down in the same way until at last they would disappear as if falling into the earth. And then again they would see them, after remaining some time invisible, rising and setting as if from another beginning; and they saw that the times and also the places of rising and setting generally corresponded in an ordered and regular way.
But most of all the observed circular orbit of those stars which are always visible, and their revolution about one and the same center, led them to this spherical notion.... For absolutely all the appearances contradict the other opinions.
If, for example, one should assume the movement of the stars to be in a straight line to infinity, as some have opined, how could it be explained that each star will be observed daily moving from the same starting point? For how could the stars turn back while rushing on to infinity? Or how could they turn back without appearing to do so? Or how is it they do not disappear with their size gradually diminishing...?....
4. THAT ALSO THE EARTH, TAKEN AS A WHOLE, IS SENSIBLY SPHERICAL
Now, that also the earth taken as a whole is sensibly spherical, we could most likely think out in this way. For again 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 [east] and later for those living towards the occident [west]. For we find that the phenomena of eclipses taking place at the same time, especially those of the moon, are not recorded at the same hours for everyone--that is, relatively to equal intervals of time from noon; but 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, with the result that the general uniformity of curvature would assure every part's covering those following it proportionately. But this would not happen if the figure were any other, as can be seen from the following considerations.
For, if it were concave, the rising stars would appear first to people towards the occident; and if it were flat, the stars would rise and set for all people together and at the same time; and if it were a pyramid, a cube, or any other polygonal figure, they would again appear at the same time for all observers on the same straight line. But none of these things appears to happen....
[T]he more we advance towards the north pole, the more the southern stars are hidden and the northern stars appear....
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.
5. THAT THE EARTH IS IN THE MIDDLE OF THE HEAVENS....
6. THAT THE EARTH HAS THE RATIO OF A POINT TO THE HEAVENS....
7. THAT THE EARTH DOES NOT IN ANY WAY MOVE LOCALLY....
8. THAT THERE ARE TWO DIFFERENT PRIME MOVEMENTS IN THE HEAVENS....
... One is that by which everything moves from east to west, always in the same way and at the same speed with revolutions in circles parallel to each other and clearly described about the poles of the regularly revolving sphere....
The other movement is that according to which the spheres of the stars make certain local motions in the direction opposite to that of the movement just described and around other poles than those of that first revolution. And we assume that it is so because ... from subsequent and more continuous observation ... the sun and moon and planets make certain complex movements unequal to each other, but all contrary to the general movement, towards the east opposite to the movement of the fixed stars....
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