First Book

Fifth Conclusion.

Proving that the Earth does not have local motion.

Decorative drop cap 'Q' containing a miniature illustration of a figure in a garden or courtyard setting.

From what has been stated above, it is certain that the Earth does not undergo linear motion original: "motum rectum," meaning motion in a straight line up, down, or sideways.. For in such a case, it would be forced to leave the center of the world, which we have previously forbidden. Finally, the Earth would have to move most rapidly, driven by its own mass. Thus, other less heavy bodies adjacent to the Earth would be left behind in the air, if all heavy things strove toward a single limit; this is nowhere seen to happen. ¶ Finally, the Earth does not have circular motion. For if it were moved around the axis of the world from west to east, everything moving in the air would always seem to move toward the west. For they could not keep up with the motion of the Earth. We frequently experience the opposite of this in moving clouds and birds. The same would also happen if you supposed the air moved together with the Earth in this manner This argument was a standard Aristotelian objection to a rotating Earth before the understanding of inertia and atmospheric drag.. ¶ Lastly, the Earth does not move around any other axis. For thus the height of the pole would be variable for us resting on the Earth. Since this appears to no one, it is certain that the Earth cannot move according to this law.

Sixth Conclusion.

That celestial motions are found in two different types.

Decorative drop cap 'M' containing a miniature illustration of a landscape with buildings and a figure.

That celestial motions are found in two different types. For there is a certain motion common to all celestial bodies, from east to west, which we showed in the first [conclusion] of this book to be most regular, occurring around the two poles of the world. Those bodies follow this motion so that all points marked outside its axis describe circles equidistant from each other and perpendicular to the axis itself. The greatest of these circles is described by a point equally distant from the poles of the world, which they call the equinoctial equinoctial: the celestial equator, because when the sun occupies it, the day is equal to the night. ¶ There is another motion contrary to the aforementioned: namely, from west to east, not around the poles of the world, but around others. According to this motion, circles are not described equidistant to the equinoctial, which would surely happen if both motions shared the same poles. How that second motion became known, you shall understand thus. The first observers of celestial bodies and their motions had observed the sun rise and gradually rise until it reached the meridian; then, leaving that meridian, tend toward the setting, and then dwell beneath the Earth, and rise again as before. And when they had noted the locations of rising and setting on Earth, they saw after many days that the sun did not rise and set in the same places, but had approached either the south or the north. Likewise, that the sun, positioned in the meridian circle, sometimes inclines toward the zenith zenith: the point directly overhead; original: "vertices capitum" and sometimes moves further away from them. From this they conjectured it moved in some other sphere, not indeed around the poles of the world, since in its motion it did not maintain equal distances from those very poles. Furthermore, the same appeared in many other observations concerning the fixed stars. For they saw that the fixed stars fixed stars: stars that maintain their positions relative to one another, unlike planets maintained their distances from each other, and the locations of their rising and setting did not vary. They thought, therefore, that the fixed stars moved only according to the first [daily] motion. But they concluded the planets were carried by another motion in addition, because they themselves, noted among the fixed stars, seemed after some time to have receded from them toward the east. And since in this motion they did not maintain the same distances from the poles of the world, but declined now indeed to the south, now to the north, it was necessary for a motion of this kind to occur around other poles. But they learned that the declination declination: the angular distance of a body north or south of the celestial equator of the sun and the declinations of the other planets were confined within almost the same limits. From this they maintained it as certain: that they were carried around not upon the poles of the world, but others in a certain circle oblique to the equinoctial This refers to the Ecliptic, the path the sun appears to follow through the zodiac.. ¶ These six conclusions, although they present no difficulty, we have decided to write at the beginning of our work.

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9 3 1 2 This margin contains dense geometric proofs keyed to the diagram below, likely referencing Euclid's Elements. ...angle E equal to angle D from above... ...line BE equals line BD... in square B... the angle equals C D... ...[the calculation] of the parts... angle BF concurs... angle M... angle E... ...twice the...

A geometric diagram showing circular arcs labeled with letters (a, b, c, d, e, f, g) intersected by diagonal and horizontal lines forming angles and triangles. Handwritten notes are interspersed around the lines.

: signs... and two extremes angle... by two measures it is necessary equal... proposition 32 degrees 32 . 13 if thus they understand the two triangles D E R total and B D R partial... total is equal to... and angle F T S... two sides... Proposition 32... two sides E C and E D... continue angle E in totality... so the two sides D E and E B... are continued...