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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EPISTOL AE.
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<
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xml:space
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">NOVA SOLVTIO PROBLEMATIS DE VASE
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pleno liquoris.</
head
>
<
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style
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xml:space
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">Nicolao Caluxio Serenißimi Ducis Sabaudia à ſecretis.</
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<
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emph
>
à me poſtulas eſt problema ab alijs iam ſcriptum, ſed illud tibialio
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medio ſoluam.</
s
>
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<
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>
<
s
xml:id
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xml:space
="
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">Proponitur vas
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liquore aliquo, puta aqua,
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reg
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="
quod
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>
tres habeat fiſtulas
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ad baſim, quarum vnaquæque poſſit euacuare ipſum vas, inæquales ta-
<
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men, ita quod prima tam lata ſit, vt ſpatio vnius horæ poſſit ipſum euacuare to-
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tum; </
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>
<
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xml:space
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">ſecunda vero ſpatio duarum horarum, tertia autem ſpatio trium hora-
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unsure
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-
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rum. </
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>
<
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xml:space
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">Tunc quæritur quanto tempore omnes tres fiſtulæ ſimul apertæ euacua-
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bunt ipſum vas. </
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<
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xml:space
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">Ad hoc volo vt quæratur primo quanta pars aquæ vnaquęquę fi-
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ſtula euacuabit in aliquo dato tempore, quod facilè eſt, vt puta, prima fiſtu-
<
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la, ſpatio dimidiæ horæ euacuabit dimidium vas, eo quod ſpatio integræ horæ po-
<
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/>
teſt totum euacuare, ſecunda fiſtula, eodem temporis ſpatio, euacuabit quartam
<
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/>
partem ipſius vaſis, tertia verò fiſtula, eodemmet ſpatio temporis dimidiæ horæ,
<
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/>
euacuabit ſextam partem ipſius vaſis, quæ omnia fracta ſimul collecta faciunt vnde-
<
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/>
cim duodecimas partes totius vaſis, vnde manifeſtum erit, quod omnes fiſtulæ pari-
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ter apertæ, ſpatio dimidię horæ euacuabunt vndecim duodecimas partes totius a-
<
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quæ, ſed nos cupimus ſcire, quanto tempore, totum vas euacuabitur, apertis omni
<
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bus fiſtulis, quapropter dicemus ita; </
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<
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xml:space
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">Si vndecim duodecimæ partes conſumunt mi-
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nuta .30. temporis, quantum conſument omnes partes aquæ? </
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xml:space
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">quæ ſunt .12. quare ex
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regula de tribus prouenient nobis minuta .32. cum .8. vndecimis vnius minuti, hoc
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eſt cum .43. ſecundis horæ ferè, vel ſiaccipiemus tres quartas vnius horæ, </
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<
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xml:space
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ma fiſtula emittet tres quartas partes totius aquæ, ſecunda, tres octauas
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aquę,
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tertia verò, quarta pars, tunc omnia, hæc collecta, faciunt vnum integrum cum tri
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bus octauis. </
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<
s
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xml:space
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">Si dixerimus igitur quando vnum integrum cum tribus octauis abſu-
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mit .45. minuta temporis, ergo illud ſolum integrum abſumet idem vt ſupra hoc eſt
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min .32. cum .8. vndecimis vnius minuti vel .43. ſecundis. </
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<
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xml:space
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">Cuius rei ſpeculatio
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con
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iuncta eſt operationi, quòd vna cognita, reliqua ſtatim cognoſcitur.</
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<
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<
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xml:space
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<
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xml:space
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">Secundum quæſitum ab alijs traditum, tuum etiam, aliter quoque poteſt ſolui,
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propterea non prętermittam tibi ſatisfacere.</
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<
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<
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xml:space
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">Problema itaque tale eſt, vt ſit vas aliquod in
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infunditur aqua per tres fiſtu-
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las, ſed dum infunditur aqua, eadem egreditur per duas alias fiſtulas in fundo
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vaſis poſitas, ſed tres ſuperiores ſint inuicem proportionatæ, vt ſupradictum
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eſt, primaq́ue inferiorum talis ſit, vt ſpatio .4. horarum poſſit totum vas euacua-
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re, ſecunda autem poſſit ſpatio .6. horarum idem facere, vnde ex ſupradictis, vas im
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plebitur à tribus fiſtulis ſuperioribus, clauſis exiſtentibus inferioribus, ſpatio tempo
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ris
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.32.
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.8. vndecimis hoc eſt min .32. cum .43. ſecundis, deinde per duas
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fiſtulas inferiores poſſet euacuari ſpatio
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horarum .2. et. mi .24. exſupradictis.</
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<
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xml:space
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">Supponamus igitur omnes fiſtulas operari ſpatio temporis minutorum .32. cum
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ſecundis .43. </
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<
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xml:space
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">tunc manifeſtum eſt quod vas non implebitur, eo ſpatio min .32. cum
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ſecundis .43. ſed tanta aqua deficiet, quanta ab inferioribus fiſtulis eo ſpatio tempo
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ris min .32. ſecun .43. poteſt euacuari, </
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<
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xml:space
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">quare proportio partis vaſis vacuæ, ad totum
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vas, erit vt min .33. ferè ad horas .2. min .24. quod per ſe patet, </
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