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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IO. BAPT. BENED.
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<
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xml:space
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">I Dem etiam poteſt dici de .15. problemate (ſicut de alijs multis) vbi ponit tres
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homines habentes .40. aureos quorum primus habet duas quintas partes ſecun-
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di,
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verò
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octauas tertij,
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quot ducatos habeat vnuſquiſque.</
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<
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xml:space
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">Quis non videt quæſo,
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omnes partes erunt .15. quare cum dixerimus ſi .15. dat
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nobis .2. (pro prima portione primi hominis) quid dabit .40? </
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<
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xml:space
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">vnde nobis proueniet
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5. cum tertia parte.</
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<
s
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xml:space
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">Et de .29. ſimiliter aſſero, vbi ponit
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emiſſe tria fruſta panni pro ducatis .48.
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quarum ſecundam habuit pro dimidio precio primæ, tertiam autem pro quarta
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parte ipſius ſecundæ, </
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<
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xml:space
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">quare omnes partes erunt .13. quapropter precium tertiæ pe-
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tiæ erit tertiadecima pars ipſius .48. hoc eſt .3. cum .9. tertijs decimis.</
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<
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xml:space
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">Adhuc duo exempla videtur mihi proponere, quorum primum eſt .38. eiuſdem
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lib. vbi ſupponitur operarium quendam velle perficere opus quoddam ſpacio die-
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rum .36. tali pacto, quod qualibet die, in qua ipſe operaturus ſit lucretur ſolidos
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16.</
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qualibet verò die, in qua nihil agat perdat ſolidos .24. </
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termino
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opere, tantum lucratus ſit, quantum perdiderit. </
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quot fuerint dies lucri, quotúe perditionis.</
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<
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">Huiuſmodi problematis operatio breuiſſima abſque vlla falſa poſitione ita erit,
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hoc eſt diuidendo productum .36. in .24. per .40. ideſt per aggregatum ipſius .24.
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16. & prouentus erit .21. cum tribus quintis pro diebus lucri, vnde reliquum ex .36.
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erit .14. cum duabus quintis pro diebus perditionis.</
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<
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">Cuius operationis ratio ex ſe ſatis patet, cum duo producta, vnum lucri, alterum
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vero perditio-
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nis æqualia eſſe
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debeant, vnde
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ex duodecima,
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& vigeſimaſepti
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mi ex regula de
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tribus reperiun
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tur partes ipſius
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36. eodem mo- </
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