Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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THEOR. ARITH.
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quoque ſumma par nunquam exiſtet, cuius medietatem aliquod medium ſemper
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ingredietur, & hanc ob cauſam poſterior ſumma cum fracto ſemper erit, & nume-
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rum deſumptum maiorem eſſe multiplici ad quatuor per duo ſignificabit.</
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<
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<
s
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xml:space
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">At verò ſi inter impares reponatur, aut eorum erit qui ſuperant multiplicem
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ipſius quatuor per vnum, ſeu per tria, quod hinc innoteſcet, nempe, quia ſi eorum
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erit qui dictum multiplicem per vnum tantum vincunt, ſua medietate ipſi numero
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addita, & præter hanc medietatem medio etiam integro adiuncto, tota hæc prior
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ſumma in numerum parem ſemper euadet, vnde in poſteriori ſumma nullus nume-
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rus fractus conſpicietur, & hanc ob
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multiplici ipſius .4. vnitas ſemper addetur.</
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<
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<
s
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xml:space
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">Sed ſi numerus deſumptus, in ſerie eorum, qui multiplicem ipſius .4. pertria ſu-
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perant, collocabitur, hinc compræhendetur, quia primæ ſummæ numerus cum
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media vnitate ſemper impar erit, vnde ſecunda ſumma præter integras cum me-
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dia vnitate nobis ſemper occur ret.</
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<
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">Quod autem nobis prodere faciamus an in prima diuiſione, & ſecunda numerus
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aliquis fractus conſiſtat, eò tantum nobis inſeruit, quò deueniamus in cognitionem
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an numerus animo conceptus multiplicem ipſius .4. per vnum, per duo, aut tria ſupe
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ret. </
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<
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">Quòd etiam medias eas vnitates ad integros reducere faciamus, eò tantum re
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fertur, vt minori labore eum, qui numerum imaginatione compræhendit, onere-
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mus, quia reuera numerus impar nunquam mente concipi poteſt, quin aliquis fra-
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ctus in prima diuiſione, aut in ſecunda ſequatur: </
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<
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xml:id
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xml:space
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">vnde à numeris imparibus, qui mul
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tiplicem ipſius .4. unitatis tantum exceſſu
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, poſterior ſumma
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cum
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type
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quarta parte
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vnitatis, præter integros numeros, & ab imparibus qui dictum multiplicem ipſius
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4.</
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per tria vincunt, cum tribus quartis vnius integri præter integras vnitates ; </
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<
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xml:space
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">& à
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numeris paribus, qui multiplicem ipſius .4. per duo cum medietate vnitatis præter
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integros ſemper procedit. </
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<
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xml:space
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">Ita cum is qui numerum ſecum conſiderat, ſi in nume-
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xlink:href
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ris fractis verſatus eſſet, qui eum in-
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terrogat prudenter ſe gereret, ſi ſibi
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declarari curaret, quis nam ex fractis
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ſu per integros
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remane
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ret, quia
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quot quarta integros
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dæ</
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ſummæ ſuperaret, per
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inte
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gros numerus mente conceptus multiplicem ipſius .4. ſuperaret.</
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<
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.</
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<
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xml:space
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">VNDE fiat, vt ſi ali quis quemuis numerum animo compræhendat, eique
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numero alium etiam quemlibet numerum propoſitum addat, & à tertia par
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te huius ſummæ tertiam partem numeri imaginati detrah et, reſiduum ſecundi nu-
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meri adiuncti, ideſt propoſiti, tertia pars erit.</
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<
s
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">Vt exempli gratia, ſi aliquis de numero denario cogitaſſet,
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.24. adderet,
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vnde triginta quatuor efficerent, detra hendo nunc tertiam partem numeri de na-
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rij cogitatione concepti, ideſt .3. cum tertia parte vnius, à tertia parte huius ſum mæ
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ideſt ab vndecim & vna tertia parte remanerent .8. ideſt tertia pars numeri additi.
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<
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xml:space
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">Id quod mihi inter iocos in honeſtorum hominum cætu in mentem venit.</
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<
s
xml:id
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xml:space
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">Pro cuius ratione, prior numerus ima
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xlink:href
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ginatus mediante linea
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et is, qui ad-
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ditus eſt
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linea
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è directo </
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