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Suppose I want to discuss an algorithm in Latin: that is, a series of steps to calculate a result from an input, usually involving mathematical formulae.

How would I say this? The English word came from Arabic through Late Latin, but was its Late Latin meaning at all similar to how it's used now? And even if the Romans didn't do advanced mathematics, they certainly must have had algorithms to calculate everything from festival days to the size of arches.

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  • I suspect the choice of words will be different from ancient Romans doing architectural calculations and people carrying out numerical algorithms some two millennia later. Which one are you more interested in? They are good questions, but I wonder whether they are two separate ones.
    – Joonas Ilmavirta
    May 7, 2018 at 21:24
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    There is a very good discussion in the OED: oed.com/view/Entry/4956#eid7070186 and oed.com/view/Entry/4959#eid7075835
    – fdb
    May 8, 2018 at 11:13
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    They may not have had "the calculus" but I've always considered water clocks to be a physical expression of algorithms (information encoded in physical form that constitutes a mechanical process.) Very interesting question! Have you considered asking on History of Science? I was researching the term "mechanics" recently, and although the application to calculus is late, it might be worth looking at.
    – DukeZhou
    May 8, 2018 at 21:27

2 Answers 2

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I'd propose some form of:

The third form seems most apt, as mathematics can be understood to constitute "tricks to doing things" (not restricted to machination in the pejorative, but as "noun of action from past participle stem of machinari 'contrive skillfully, to design; to scheme, to plot,'--one can plot the course of a celestial body.)

Why the mech- root?

  • Aristotle's Μηχανικά (pre-calculus, but the ball is rolling, as they say;)

See: Mechanical Problems, Aristotle

Machines can absolutely be regarded as algorithms--think not of the physical machine but of the plans that dictate it's construction and function.

See also: Euclid's Algorithm

Derivation, Latin: Mechanica Sive Motus Scientia Analytice Exposita

“For a long time in the past, a discourse on mechanics involved two possible different meanings, and indeed at that time two sciences were called by that name : on the one hand as an account of the principles, or wholly as an account of the interactions of different materials between each other, [as in simple machines and structures]. Indeed the name mechanics is usually applied to that science which deals with the equilibrium of forces, and comparisons between them, rather than to these circumstance in which the nature of the motion, its generation and changes, can also be explained. Although indeed, in these more recent discussions too on the general principles, forces especially are to be considered, since it is from these that motion can be both generated and changed ; yet there is much disagreement in the early science, on account of their derivations. Therefore it is best to avoid all the ambiguity that arises from the comparison and equilibrium of forces, which is to be called Statics here, and truly the name Mechanics alone remains for that science of motion, and for which it is understood that these names are always to be applied.”
EULER'S MECHANICA VOL. 1. Preface. (English) (Latin)

Euler predates computers, but, then again, so does minimax, (at least in the pre-ENIAC sense.) See: Computers (pre-20th century), and note their mechanical nature in the physical sense, and; difference engine in the sense of Babbage.

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Alternately, you could look to Leibniz and his Nova Methodus pro Maximis et Minimis. Leibniz' work on binary arithmetic is credited to be at the foundation of digital computing.

See:

methodus "a way of teaching, mode of proceeding, method (post-class.)"

μέθοδος "mode of prosecuting [the pursuit of knowledge], method, system"; "the doctrine of motion, Pl.Tht.183c."; "mode of treating the subject-matter"; "stratagem".

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Alternatively, you could use:

Medieval Latin algorismus (a mangled transliteration of Arabic al-Khwarizmi "native of Khwarazm";)
Algorithm, Online Etymological Dictionary

See also: Algorism

As important as al-Khwārizmī (محمد بن موسى خوارزمی) is, I would nevertheless go the Euler direction, because algorismus refers to a surname, where mechanica refers to a mathematical concept and the usage predates Caesar.

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The word "algorithm" comes from the Latin words "algorithmus" and "algorismus". These Latin words, in turn, are transliterations of al-Khwarizmi, the name of an Arabic mathematician.

Muhammad al-Khwarizmi wrote a book on algebra in the 9th century CE, which is often called al-Jabr, for short. This book got the title Liber Algebræ et Almucabola in Latin, from which we get the word "algebra".

To honor Muhammad al-Khwarizmi, one of the creators of algebra, we can use the Latin words "algorithmus" or "algorismus", since they are transliterations of the name al-Khwarizmi.

Muhammad al-Khwarizmi also wrote a book on arithmetic that got translated into Latin under the title Algorithmo de Numero Indorum. The phrase "algorithmo numero" is used to translate the Arabic word al-ḥisāb, which means arithmetic or calculation. So we see how al-Khwarizmi's name came to be used as a mathematical term under the Latin transliteration algorithmus. Algorithmo de Numero Indorum can be translated as "On the numerical method of the Indians." [1] [2]


Footnotes:

[1] The Arabic textbook on arithmetic kitāb al-ḥisāb al-hindī can be translated as "the book of Indian arithmetic" or "the book of Indian computation". The Arabic phrase kitāb al-ḥisāb al-hindī contains three nouns in construct state. This grammatical feature (construct state) is found in both Hebrew and Arabic. A possessor noun can follow a possessed noun to indicate possession.

[2] The Arabic textbook kitāb al-ḥisāb al-hindī was written by al-Khwarizmi in the 9th century CE. It was translated into Latin in the 12th century CE. There are Latin translations titled "algorithmo de numero Indorum" and "algoritmi de numero Indorum". There are many ethical ways to translate these titles. The translation used is the choice of the translator.

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    The title of the work is Algoritmi de numero indorum, and the word corresponding to al-ḥisāb is just numero. Algoritmi is just the author's name in the genitive, as is common (and in this case also necessary to distinguish it from several other works by the same title, e.g. by Kushyar Gilani). You had it right the first time.
    – Cairnarvon
    Apr 25, 2023 at 5:16
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    One noun in the construct state, one noun in the genitive case, one adjective.
    – fdb
    Apr 25, 2023 at 16:29

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