Perhaps it should be mentioned that while normalis did mean perpendicular in classical Latin, it was not the only possible (and perhaps not the preferred) choice of words.
I asked about expressing perpendicularity in classical Latin at the new Latin Language SE site. The answer given there lists a number of expressions, mainly from Vitruvius:
- πρὸς ὀρθᾶς — yes, this Greek expression was used in Latin.
- ad normam — according to norma, a square employed by carpenters, masons, etc., for making right angles.
- ad perpendiculum — according to perpendiculum, a plumb-line
- ad perpendiculum et normam — combination of the previous two
- directus — "straight", essentially the same as rectus used in the medieval commentary Carlo mentions
There is a finite amount of extant Latin literature and perpendicularity is not the most common of subjects, so it is difficult to tell what exactly are the differences between these phrases in usage or frequency. The examples listed above, apart from directus, mean "orthogonally". For the adjective "orthogonal" one might use directus, rectus or indeed normalis. Vitruvius does not use the word normalis at all.
Notice that norma and perpendiculum are two different tools used to create straight angles, not geometrical descriptions of the angle itself.
I am not aware of any ancient mathematical texts in Latin, either original or translations. It would be interesting to see which expression would be chosen in mathematical context. If you know any suitable sources, consider answering "Where to find ancient mathematics in Latin?".
(The phrase mentioned in Carlo's answer can be found in the Perseus service together with an English translation in a more readable and searchable form.)
