My father-in-law recently taught me the Chinese phrases for first quarter and third quarter moons, they are :
下 弦 Down Bow string = third quarter
上 弦
Up Bow string = first quarter
Now, why would westerners think of quarter moons being left to right or right to left while the Chinese think of them up to down or down to up? Both kinds of moons occur during difference times of year, based on the relative orientation of where you are standing on Earth, where the moon is in the sky, and where the Sun is.
Describing the moon as a "bow" in this phase is better than "quarter" for sure though, right? We call it quarter because of where it is in the 29 day cycle.
In either case, everyone in the southern hemisphere sees their right hand side lit when we see the left hand side. 'Cause they are upside down in the southern hemisphere! Crazy business this is, living on the surface of sphere!
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