Physiologia Kircheriana Experimentalis

the surface, the remaining surface from B and D toward C, or from B and D toward A, would tend upward, and would express something mountainous; and thus men at H and M, even in opposite places, would ascend upward on the elliptical surface until they stood upon a straight surface at the four mentioned points A, B, C, D.

Hence it is evident that if any bridge of a square or prismatic shape were made around the center of the earth, it would likewise remain suspended in the air. For since the center of gravity of a square and an equilateral triangle is the same as the center of magnitude, as Kircher demonstrated in the aforementioned work, a bridge constructed according to the laws of such bodies must necessarily hang in the air. For in this way, with all and individual parts of the mass inclining toward the center with equal force, the bridge will remain in equilibrium, since there is no reason why it should incline more toward the center on one side than on the other; but it declines, if it can, with the portion A B D M of the bridge N B H M more toward the center I than the portion N H A D. Therefore, in this case, the equal would overcome the equal, and therefore those parts would counterbalance and would not counterbalance; which, since it is absurd and contrary to the hypothesis, it follows that with the parts balancing each other round about and converging toward the center with equal force, a bridge of square figure will remain suspended in the air, which was to be demonstrated. The same must be said of the triangular bridge A B C D E F; however, the difference between the circular part and the square or triangular is this: that a man walking across a square bridge would find a straight surface in only four places, A, C, D, E, since from A he would continuously ascend toward B, but from B he would continuously descend toward C. By the same logic, in the triangular bridge A B C D E F, we must imagine a plane at points B, D, and F, from which points A, C, and E would be reached by perpetually ascending or descending from the points E, B, and D. So, indeed, the four corners of the square structure, or the three of the triangular one, behave like mountains whose roots are in the places, or in the triangular B D F; but their peaks are at the points B, N, H, M in the square, and in the triangular, at A, E, C, since the recession from the circular plane is nothing other than either an ascent from a plane to a height, or a descent from a height to a plane. This ratio also appears in the surface of the terrestrial globe on mountains, which, the steeper they are, the more the line of direction, along which we walk, forms a sharper angle with the slope of the mountain, and consequently, a man must violently contort his whole body toward the line of direction; but this contortion, as it is violent, is so against nature that therefore...