... thosewhich are composed of straight lines, and it is among these that linesconcave in the same direction are identified, it is possible to take, on some line, concave in the same direction, two ... points, so that the line joined to them will fall on neither side of the line, but willcoincide with the line itself. Therefore he says that he calls “concavein the same direction, a line in ... curved lines, whichare either all on the same side as the straight lines joining their limitsor have nothing on the other side.”3 The assertion will be clear if werealize which lines he calls...