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Rupes recta is the name given to a feature on the Moon. This feature is also known as the straight wall or straight cliff.

Is rupes recta the correct Latin phrase for straight wall or straight cliff?

The phrase may have originated during the 1600s.

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Yes, depending on the type of wall.

Rūpēs, -is is a third-declension feminine noun derived from rumpō "break, split". It means a rock which is split apart or has a smooth face; I've seen it translated as "cliff", "canyon", or just plain "rock" (e.g. rūpēs Tarpeia is "the Tarpeian Rock").

Rectus, -a, -um started as the past participle of regō "to keep straight". Eventually rectus became more popular than regō, so it's often analyzed as an independent adjective meaning "straight, perpendicular, horizontal; correct, accurate, proper". Compare English "rectify", "correct", "rectangle".

From the looks of it, the Rūpēs Recta on the moon is definitely a smooth rock face, and is definitely (kind of) straight, so the name seems appropriate.

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    Astronomers say Rupes Recta is a fault, possibly 5 faults, rising about 300 meters, running over 100 kilometers. It is not a sharp cliff, but a shallow slope. However, the name is now official. – KeithSmith Nov 11 '16 at 4:22
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    I mean, early astronomers couldn't see the steepness...so the ambiguity isn't their fault. (Ba-dum tsss) – Draconis Nov 11 '16 at 4:42
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    Sorry. I couldn't resist. – Draconis Nov 11 '16 at 4:42

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