The Elements of Hydrostatics

propositions. It is true that we could take the surface of the water as part of the world-surface, and base the following description upon that, but because it would be more difficult, and not more useful to the end, that is, the Hydrostatic act, it is requested that one allow that every surface of water be a plane, parallel to the horizon.

VII. POSTULATE.

Homologa. Corresponding points.

GIVEN that the base and top of a pillar are parallel to the horizon, and the straight lines between *corresponding points of the same are perpendicular to the horizon: That those lines, if extended, meet at the center of the world; also that such base and top are parts of world-surfaces.

EXPLANATION.

A geometric diagram depicts a trapezoidal section labeled ABCD, representing a "pillar." Below it is a point E representing the center of the world. Lines AE and BE converge at point E, intersecting the base line DC at points F and G. This diagram illustrates the divergence between a flat-earth model, where verticals remain parallel, and a spherical model, where verticals converge at the center.

Let A B C D be a pillar whose top A B and base D C are parallel to the horizon, and B C be a straight line perpendicular to the horizon between two corresponding points C, B, but let E be the center of the world; let now be drawn the lines A E, and B E, approaching the base D C at the points F, G, between which let be described the base F G equal to D C. This being so, it appears that the lines B C and A D, if extended, do not meet at E, for those that meet there are A F, and B G; also the planes A B and D C are not parts of world-surfaces, nevertheless we request that it be permitted that B C and A D, if extended, meet there, and that those planes A B, D C are parts of world-surfaces, because in all that we encounter in the Hydrostatic act, such difference is imperceptible, as it also is between the pillar A B C D and Part of a pyramid. *the pyramidal part A B G F, even if it is assumed that A B and F G were parts of world-surfaces. It is indeed so that we could take such a body A B G F in place of the pillar A B C D, and base the following propositions upon that, but for such reasons as are stated under the 6th postulate, it is better left, for just as in * Astronomy Astrology. it would be wrong not to allow the earth to be taken as the center of the world, so too here.