Two problems in Aristarchus's treatise \textit{On the sizes and distances of the Sun and Moon} (Q2435326)

Distinguishing between the \textit{light line} and the \textit{visibility line} in Aristarchus' \textit{On the sizes and distances of the Sun and Moon}, the author shows that five inconsistencies pointed out by \textit{J. L. Berggren} and \textit{N. Sidoli} [Arch.\ Hist.\ Exact Sci.\ 61, No. 3, 213--254 (2007; Zbl 1123.01004)] and by \textit{N. Sidoli} [Ann.\ Sci.\ 64, No. 4, 525--547 (2007; Zbl 1183.01004)], turn out to be only apparent inconsistencies. The author then turns to the second topic of the paper, an attempt to explain why Aristarchus took the Moon's apparent size to be \(2^{\circ}\), which is four times greater than the correct value. The solution proposed is that ``Aristarchus took the greatest value for the Moon's apparent size that still guarantees that the difference between the dividing line and the diameter of the Moon is imperceptible and so allows him the geometrical construction for the distance proportion calculations'' (p.\ 55).