Early Greek Planetary Theories

The Keskintos Inscription (found on Rhodes about 1890) and probably carved about 100 B.C. A circle compris 360 degrees or 9720 stigmai. A degree comprises 2 7 points. 15 to a thank-offering. These are period relations as before, but much longer The texts of ancient Indian astronomy give us a sort of wormhole through space-time back into an otherwise inaccessible era of Greco-Roman developments in astronomy. The orbits of the planets are concentric with the center of the earth. The single...

And a bit later

For Aristotle divides theoretical philosophy too, very fittingly, into three primary categories, physics, mathematics and theology For everything that tfcisls is composed of matter l rm and motion none of these three can he observed in its substratum by itself, without the others they can only be imagined. Now the first cause of the lirsl motion of the universe, if one considers it simply, can he thought of a.i an invisible and motionless deity the division of theoretical...

Keplers Three Laws of planetary motion

Orbits are ellipses, Sun at focus 2. equal area in equal time Instead of the Earth circling the Sun, we would have the Sun circling the Earth. For the inner planets, not only does the planet revolve on an epicycle, but the center of the epicycle is always lined up with the Sun. For the outer planets, the radius of the epicycle is always parallel to the direction of the Sun from the earth. All of the planets have, from time to time, a retrograde motion, i.e. the slow motion from west to east...

Expressing Numbers

Even today we measure angles in degrees, minutes, seconds, and we also measure time in hours, minutes, seconds. In both cases there are 60 minutes per degree or hour, and 60 seconds per minute. Apparently this began in Babylon, no later than early first millenium B.C. and probably a lot earlier, since we have many 1000's of surviving clay tablets covered with such numbers. Ptolemy also used this base-60 sexagesimal number format, at least for the fractional part of the number. Thus he expressed...