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== Theoria numerorum ==
In antiquitate omnes quantitates originabant in geometria et mathematici aequationes solvebant methodis geometricis. Saeculo IV librum ''Arithmetica'' a [[Diophantus|Diophanto]] scriptum notissimum fuit tantum pro numeros considerando sine iustificatione geometrica quantum pro usu symboli permonodico ad quantitatem ignotam designandam.<ref> "According to a generally accepted hypothesis of Heath’s, his sign for this was probably originally a contraction of the first two letters, αρ, of the Greek word for number, αριθµoς." Norbert Schappacher (2005). [http://www-irma.u-strasbg.fr/~schappa/Dioph.pdf Diophantus of Alexandria : a Text and its History (Anglice)].</ref>
 
Diophantus, sicut alii mathematici suae aetatis, ad aequationes solvendas solos numeros naturales intuitur. Et notationes eius erant perprimitivae. Methodos subsequenter mathematici excoluerunt. Saeculo VIII liber celeber de algebra a Machometo ibn Musa al-Kwarizmi scriptus methodos de aequationes gradus secundi solvendo simplices ostendit, systema notationis algebraicum melius monstrans. Etiam ea aetate systema decimale Arabicum magnopere progressum mathematicae adiuvit.
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Res algebrae abstractae sunt numerorum generalizationes classificatae modo axiomatico secundum earum operationes:
* [[Copia]] = rerum elementalium collectio quaedam sine aut cum operationibus inter elementos definitis.
* [[Grex]] = copia clausa sub operatione invertibili associativaque, symbolo "+".
* [[Grex abelianus]] vel commutativus = copia clausa sub operatione invertibili associativaque commuativaque, symbolo "+".
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* Post [[1569]]: [[Franciscus Maurolicus|Francisci Maurolici]] ''Demonstratio Algebrae'': [http://www.dm.unipi.it/pages/maurolic/edizioni/arithmet/algebra/alg.htm textus]
* [[1661]] [[Franciscus a Schooten|Francisci à Schooten]] ''Tractatus de concinnandis Demonstrationibus Geometricis ex Calculo Algebraïco'' [http://visualiseur.bnf.fr/Image/CadresPage?O=NUMM-57483&I=359&Y=Image prima pagina]
* [[1710]] ''Miscellanea Berolinensia ad incrementum scientiarum I''
:p. 155 [[Godefridus Guilielmus Leibnitius|Leibnitii]] ''Monitum de Characteribus Algebraicis'' [http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=01-misc/1&seite:int=179 prima pagina]
:p. 160 [[Godefridus Guilielmus Leibnitius|Leibnitii]] ''Symbolismus memorabilis calculi Algebraici et Infinitesimalis, in comparatione potentiarum et differentiarum; et de Lege Homogeneorum Transcendentali'': [http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=01-misc/1&seite:int=184 prima pagina]
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== Notae ==
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== Vide etiam ==