Disputatio:Algebra

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Rename Proposal[fontem recensere]

On the advice of Iustinus, I am proposing that we rename this page from Algebraica to simply Algebra. The former should be an adjective, the latter a noun.

Any objections?

Translations[fontem recensere]

I need to figure out good translations for the following

  • Group - it must be distinct from set. It's basically a set with an addition operator defined on it that satisfies a few sensible properties.
    • sugg. Group = caterva, Set = collectio?
  • Ring - I'm not sure what the motivation was for calling this a "ring" in English. There is nothing I know of more "circular" about it than with other algebraic structures. It's basically a group with multiplication.
  • Field - These are kind of like well-behaved rings; and yet not quite so pleasant as to conjure an image of a field full of flowers.
    • From a previous version of the en:Ring article: "The term ring (Zahlring) was coined by David Hilbert in the article Die Theorie der algebraischen Zahlkörper, Jahresbericht der Deutschen Mathematiker Vereiningung, Vol. 4, 1897." Apparently it had to do with some cyclical structure (a finite ideal?). Fields were originally called "Körper" in German, meaning "body". In French and Portuguese it is "corps" and "corpo" also meaning "body". I guess it would be "corpus" in Latin.
OK, if you look at the interwikis at the relevant English articles, it quickly becomes clear that "field" should be corpus and "ring" should be anellus. --Iustinus 17:42 aug 18, 2005 (UTC)

Continuing: "group" and "set" are, however, much more difficult:

  • ca: Grup
  • da: Gruppe
  • de: Gruppentheorie
  • es: Grupo
  • eo: Grupo
  • fi: Ryhmä
  • fr: Groupe
  • ko: 군론
  • id: Grup
  • it: Gruppo
  • he: חבורה
  • hu: Csoport
  • nl: Groep
  • ja: 群論
  • no: Gruppe
  • pl: Grupa
  • pt: Grupo
  • ro: Grup
  • ru: Группа
  • sk: Grupa
  • sl: grupa
  • sv: Grupp
  • th: กรุป
  • tr: Grup Teorisi
  • zh: &#32676
  • ar: مجموعة
  • bg: Множество
  • cs: Množina
  • de: Menge
  • en: Set (<secta)
  • es: Conjunto (<coniunctus -us or coniunctum -i)
  • eo: Aro (Presumably from "array", which is from Proto-Romance arredare)
  • fa: مجموعه
  • fr: Ensemble (< Vulgar Latin insimul)
  • ko: 집합
  • io: Ensemblo (< V.L. insimul)
  • it: Insieme (< V.L. insimul)
  • he: קבוצה
  • hu: Halmaz
  • lt: Aibė
  • nl: Verzameling (the *zamel- root is, I think, also from Latin simul)
  • ja: 集合
  • no: Mengde
  • pl: Zbiór
  • pt: Conjunto (<coniunctus -us or coniunctum -i)
  • ro: Mulţime
  • ru: Множество
  • sq: Bashkësitë
  • sk: Množina
  • sl: Množica
  • fi: Joukko
  • sv: Mängd
  • uk: Множина
  • zh: 集合

So "Group" is almost universally a cognate or borrowing of the original French term. Which is a real pain for us, because it has no cognate in Latin, possibly not even in Proto-Romance.

Set is done in various ways. The ones that have a Latin origin are so marked.

--Iustinus 18:24 aug 18, 2005 (UTC)

I propose the translation coniunctus for the english word set, because in portuguese set is translated as conjunto. And it makes sense because one of the translations of the verb coniungo is "place side-by-side", and that is what happens when you list the elements of a set, see e.g. numerus primus and numerus naturalis.--Mafrius 18:04 aug 18, 2005 (UTC)

See my additions to the previous remark. --Iustinus 18:24 aug 18, 2005 (UTC)

Mathematicians continued to write in Latin well into the 20th century; surely the bona fide mathematicians among you will soon be able to find Latin terms for these concepts already in use. In the meantime, I think the best policy for translating technical terms like these is to stick close to the vernacular terms. So (building on previous comments) I would propose -- group: coetus || set: synthesis (cf. Martial and Statius, of a set of dishes) || ring: annulus || field: corpus or campus (both notions are used in major European languages for naming this). Of various Latin terms for groups, flocks, herds, bands, etc., "coetus" perhaps reproduces best the neutrality of "group," "Menge." The problem with the terms "conjuctus" or "conjunctum" is that they are used of a connection, rather than a group of things connected. Mar. 23, 2006.

Bibliography[fontem recensere]

Here is a list of Latin texts on Algebra which I can find on line (other users should feel free to contribute). Note that I found most of these simply by looking for the string algebr in their titles, which is far from a perfect criterion. I have left works that appear to be about something else (e.g. one of the Leibnix 1710 items seems to be about calculus) just in case:

p. 155, LebnitiiMonitum de Characteribus Algebraicis prima pagina
p. 160 Lebnitii Symbolismus memorabilis calculi Algebraici et Infinitesimalis, in comparatione potentiarum et differentiarum; et de Lege Homogeneorum Transcendentali: prima pagina
p. 166 Philippi Naudaei Iunioris Regulae, qua inveniuntur omnes cuiuslibetcunque producti Algebraici divisores... prima pagina
  • 1723 Miscellanea Berolinensia ad incrementum scientiarum II
p. 66 Philippi Naudaei Iunioris Regula, qua inveniuntur, omnes divisores cuiuscunque producti Algebraïci... prima pagina

Suggestion[fontem recensere]

Suggestion: rather than opening with what most people wrongly think algebra is, wouldn't it be better to start with a good, correct definition of algebra? Such a definition surely can be found in some of the Latin texts which have very helpfully been listed here. I have reedited the first few sentences to improve the Latin; I hope the mathematicians (who are to be thanked for coming up with this article) will look carefully to make sure the content hasn't been affected. Mar. 26, 2006.

Set, Superset, Subset[fontem recensere]

(Copied from Taberna discussion since pertinent here--Rafaelgarcia 00:26, 28 Decembris 2007 (UTC))

Verba latina quaero pro "Menge, Obermenge, Untermenge" (in English: set, superset, subset) in contextu mathematicae. Num quis me adiuvare potest? -- Scriptor17 17:42, 8 Decembris 2007 (UTC)

Credo verbum pro set esse recte collectio; ergo superset est supercollectio et subset est subcollectio.--Rafaelgarcia 17:57, 8 Decembris 2007 (UTC)
Equidem puto a vocabulo copiae proficiscendum esse: copia 'Menge', subcopia 'Untermenge', supercopia 'Obermenge'. Neander 03:40, 9 Decembris 2007 (UTC)
Cave, quod in mathematica set potest significare et elementi multitudinem {A,B,C,...} et solum unum elementum {A} et nihil elementi {}. Copia non potest mea sententia significare {A} et {}. --Rafaelgarcia 04:07, 9 Decembris 2007 (UTC)
Meum profecto non est tecum de mathematica altercari! Sed si 'empty set' Germanice leere Menge dici potest, non video, cur etiam de vacua copia loqui non possimus. Mea quidem sententia nihil obstat, quin copiam putemus tamquam involucrum quoddam abstractum membrorum quorum numerus a zero ad infinitum extenditur. Sed ut dixi, de hisce rebus tu me melius cognovisti. --Neander 04:36, 9 Decembris 2007 (UTC)
Post unos dies illum pensando, assentio cum Neandro quod copia sensum set aptior capit quam collectio. Causa est quod copia (grammaticali in numero singulari) semper significat numerum rerum similarum quendam, aut abundantia quaedam. Collectio autem significat numerum qui colligitur quemquam etsi dissimilares sint. Ita collectio' est generalior quam copia, sicut collectio est generalior quam set.--Rafaelgarcia 00:24, 28 Decembris 2007 (UTC)