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I am a beginner in Latin and I write most of my math lectures in Latin. I searched at Wikipedia and other sites but I can't find any translation of these words.

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    This is an interesting question. I don't think the Roman authors have much to say about such things. A good place to look is Gauss's Disquisitiones Arithmeticae of 1801,
    – fdb
    Commented Oct 4, 2021 at 16:07

1 Answer 1

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The quotient is quotus, the remainder is residuum.

This textbook titled Elementa arithmeticae singularis et universalis lays it out in very simple terms:

Dividere est ex producto duorum factorum et ex uno eorundem alterum invenire.

Productum cognitum vocatur dividendus.
Factor cognitus vocatur divisor.
Factor incognitus vocatur quotus.

(Click the link and read on, it is really an elementary introduction. I did not find an equally explicit definition of residuum in the book, but it is clear from context.)

I think they're all masculine because numerus is implied. ​The same terminology is also definitely used by Euler.

Instead of quotus, you are also liable to encounter, surprise, quotiens. See this definition by Leibniz:

Divisio est subtractio aequalium [...] in divisione, dato facto sive numero rerum, seu dividendo, quaeritur numerus repetitionum alterius rei seu divisoris; is numerus dicitur quotiens.

Of course, if you have a fractio, the dividend is the numerator and the divisor the denominator.

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  • A happy find. Is there any indication of who is the author of this primer?
    – fdb
    Commented Oct 4, 2021 at 19:29
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    @fdb A fellow named Johann Conrad Blank, who sadly is not primarily remembered for his pedagogical works but for being the victim in a sensational murder case. Commented Oct 4, 2021 at 19:47
  • I wonder if there may be circumstances where quotus (/ quotiens) will be mistaken as a ordinary interrogative word Commented May 15, 2023 at 10:27

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