In APPENDIX A. of Ptolemy: Syntaxis Mathematica (Almagest), there is a brief explanation that includes the true notion that the distinction between up and down, as well as lateral and vertical, in a true sphere is arbitrary.
Ptolemy appears to be adding a little spin to things. In the real world, up is just up. And down is just down. Of course, not on the globe, which supports arbitrary concepts of place, position, reality, or in other words, relativism. Globers will admit that they think the definitions of words like lateral, vertical, horizontal, curve, straight, level, east, west, up and down are not actually true. That kind of thinking naturally has an effect on one's relationship with truth and it can't be good.