Disquisitiones Arithmeticae (Classic Reprint) - Hardcover

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Excerpt from Disquisitiones Arithmeticae

Disquisitiones in hoc Opere contentae ad eam Matheseos partem pertinent, quae circa numeros integros*versatur, fractis plerumque, surdis semper exclusis. Analysis indeterminata quam vocaînt seu diophantea, quae ex infinitis solutioni bus problemati indeterminato satisfaeientibus eas seligere docet, quae per nume ros integros aut saltem rationales absolvuntur (plerumque ea quoque conditione adiecta ut si1it positivi), non est illa disciplina ipsa, sed potins pars eius valde spe cialis, ad eamque ita fere se habet, ut ars aequationes reducendi et solvendi (al gebra) ad universam Analysin. 'nimirum quemadmodum ad And'lyseos ditionem referuntur omnes quae circa quantitatum affectiones generales institui possunt dis quisitiones: itanumeri integri.(fractique quatenus per'integros'determinantur) obiectumpr0prium arithmeticae cohstituunt. Sed' quum' ea quae Arithmetices nomine vulgo traduntur, vix ultra artem nume1andi et calculandi (i. E. Numeros per signa idonea e. G. Secundum systema decadicum exhibendi, operationesque arithmeticas perficiendi) extendantu1, adiectis nonnullis quae vel ad Arithmeticam omnino non pertinent (ut'doctrina de logarithmis) vel saltem numeris integris non sunt propria - sed ad omnes quantitates patent: e re esse videtur duas Arithmeti cac partes distinguere, illaque ad Arithmeticam elementarem referre, omnes autem disquisitiones generales de' numerorum integrorum affeètionibus propriis Amit/ume tz'cae de qua sola hic sermo erit, Vindicare.

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