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Consider the word quinquies/quinquiens ("five times"). It has two alternative spellings. Having the options -ies and -iens seems to be common for numerals of this kind. What is the origin of these forms? Why are there two alternatives? I don't recall seeing any analogous spelling variants elsewhere in Latin; faciens and facies are very different things, for example.

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The etymologically expected form is -iens, but since the vowel preceding the ns was regularly lengthened, the pronunciation would be [ie:ns], in which the vowel was secondarily nasalized to [iẽ:ns]. This would naturally lead to sometimes omitting the [n] altogether, i.e. [iẽ:s]* (still probably phonemically /iens/), and possibly denasalized to [ie:s]**.

In words like faciens, the other declensional forms reinforced the pronunciation and spelling of the n, but in forms like quinquiens/quinquies, there was no such reinforcement, hence a more or less random pattern of the replacement from becoming the norm.

* This stage is like that of modern French, where syllable-final n or m is not pronounced itself, but serves as an indicator that the previous vowel is nasalized.

** This ultimately became the regular development in Spanish, as exemplified by L. mensa -> Sp. mesa.

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