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PARADOX I.
How a circular, elliptical, square, or triangular wooden bridge, suspended in the air, can be built without any support.
I suppose, first, that the entire earth is concave for many miles around its center. Given this, if a circular or elliptical—or even a triangular—wooden or stone bridge were made around the center of the earth, I claim that it would stand in the air without a support.
Let a wooden bridge be A B C D around the center of the earth I; all and individual parts of which, since they incline toward the center, will terminate at I: being counterpoised, it will necessarily remain in the air, gravitating equally from every side. If anyone should deny this, let him rest at some point among A B C D; but since the center of gravity of the whole mass is not in any of the said points, according to canons 1 & 2, it is also impossible for it to rest there. Instead, according to the laws of isorropics, all parts will accommodate themselves to the center of the medium, or the center of the world—which Kircher, in Mundus Subterraneus, book 1, canon 1, shows amply to coincide with the center of gravity—so that they may obtain a firm state there; since it is impossible for it to subsist otherwise. Therefore, a circular wooden bridge, or one constructed from any other material, will necessarily subsist in the air around the center of the earth without a support, which was to be demonstrated. The same would happen if a huge ring or wheel were cast into the center of the earth. The same would happen with a bridge constructed in an elliptical shape, with this difference, however, that only four places, A B C D, would have a flat