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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[284] Pro Lunæ ortu. Ad lati .45.
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[286] Pro Lunæ occaſu. Ad lati .45.
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                <head xml:id="echoid-head424" xml:space="preserve">NOVA SOLVTIO PROBLEMATIS DE VASE
                  <lb/>
                pleno liquoris.</head>
                <head xml:id="echoid-head425" style="it" xml:space="preserve">Nicolao Caluxio Serenißimi Ducis Sabaudia à ſecretis.</head>
                <p>
                  <s xml:id="echoid-s3577" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  à me poſtulas eſt problema ab alijs iam ſcriptum, ſed illud tibialio
                    <lb/>
                  medio ſoluam.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3578" xml:space="preserve">Proponitur vas
                    <reg norm="plenum" type="context">plenũ</reg>
                  liquore aliquo, puta aqua,
                    <reg norm="quod" type="simple">ꝙ</reg>
                  tres habeat fiſtulas
                    <lb/>
                  ad baſim, quarum vnaquæque poſſit euacuare ipſum vas, inæquales ta-
                    <lb/>
                  men, ita quod prima tam lata ſit, vt ſpatio vnius horæ poſſit ipſum euacuare to-
                    <lb/>
                  tum; </s>
                  <s xml:id="echoid-s3579" xml:space="preserve">ſecunda vero ſpatio duarum horarum, tertia autem ſpatio trium hora-
                    <unsure/>
                  -
                    <lb/>
                  rum. </s>
                  <s xml:id="echoid-s3580" xml:space="preserve">Tunc quæritur quanto tempore omnes tres fiſtulæ ſimul apertæ euacua-
                    <lb/>
                  bunt ipſum vas. </s>
                  <s xml:id="echoid-s3581" xml:space="preserve">Ad hoc volo vt quæratur primo quanta pars aquæ vnaquęquę fi-
                    <lb/>
                  ſtula euacuabit in aliquo dato tempore, quod facilè eſt, vt puta, prima fiſtu-
                    <lb/>
                  la, ſpatio dimidiæ horæ euacuabit dimidium vas, eo quod ſpatio integræ horæ po-
                    <lb/>
                  teſt totum euacuare, ſecunda fiſtula, eodem temporis ſpatio, euacuabit quartam
                    <lb/>
                  partem ipſius vaſis, tertia verò fiſtula, eodemmet ſpatio temporis dimidiæ horæ,
                    <lb/>
                  euacuabit ſextam partem ipſius vaſis, quæ omnia fracta ſimul collecta faciunt vnde-
                    <lb/>
                  cim duodecimas partes totius vaſis, vnde manifeſtum erit, quod omnes fiſtulæ pari-
                    <lb/>
                  ter apertæ, ſpatio dimidię horæ euacuabunt vndecim duodecimas partes totius a-
                    <lb/>
                  quæ, ſed nos cupimus ſcire, quanto tempore, totum vas euacuabitur, apertis omni
                    <lb/>
                  bus fiſtulis, quapropter dicemus ita; </s>
                  <s xml:id="echoid-s3582" xml:space="preserve">Si vndecim duodecimæ partes conſumunt mi-
                    <lb/>
                  nuta .30. temporis, quantum conſument omnes partes aquæ? </s>
                  <s xml:id="echoid-s3583" xml:space="preserve">quæ ſunt .12. quare ex
                    <lb/>
                  regula de tribus prouenient nobis minuta .32. cum .8. vndecimis vnius minuti, hoc
                    <lb/>
                  eſt cum .43. ſecundis horæ ferè, vel ſiaccipiemus tres quartas vnius horæ, </s>
                  <s xml:id="echoid-s3584" xml:space="preserve">tunc pri-
                    <lb/>
                  ma fiſtula emittet tres quartas partes totius aquæ, ſecunda, tres octauas
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                  aquę,
                    <lb/>
                  tertia verò, quarta pars, tunc omnia, hæc collecta, faciunt vnum integrum cum tri
                    <lb/>
                  bus octauis. </s>
                  <s xml:id="echoid-s3585" xml:space="preserve">Si dixerimus igitur quando vnum integrum cum tribus octauis abſu-
                    <lb/>
                  mit .45. minuta temporis, ergo illud ſolum integrum abſumet idem vt ſupra hoc eſt
                    <lb/>
                  min .32. cum .8. vndecimis vnius minuti vel .43. ſecundis. </s>
                  <s xml:id="echoid-s3586" xml:space="preserve">Cuius rei ſpeculatio
                    <reg norm="tam" type="context">tã</reg>
                  con
                    <lb/>
                  iuncta eſt operationi, quòd vna cognita, reliqua ſtatim cognoſcitur.</s>
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                <p>
                  <s xml:id="echoid-s3587" xml:space="preserve">Idem eueniet de implendo vaſe tribus ſimilibus fiſtulis mediantibus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3588" xml:space="preserve">Secundum quæſitum ab alijs traditum, tuum etiam, aliter quoque poteſt ſolui,
                    <lb/>
                  propterea non prętermittam tibi ſatisfacere.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3589" xml:space="preserve">Problema itaque tale eſt, vt ſit vas aliquod in
                    <reg norm="quod" type="wordlist">qđ</reg>
                  infunditur aqua per tres fiſtu-
                    <lb/>
                  las, ſed dum infunditur aqua, eadem egreditur per duas alias fiſtulas in fundo
                    <lb/>
                  vaſis poſitas, ſed tres ſuperiores ſint inuicem proportionatæ, vt ſupradictum
                    <lb/>
                  eſt, primaq́ue inferiorum talis ſit, vt ſpatio .4. horarum poſſit totum vas euacua-
                    <lb/>
                  re, ſecunda autem poſſit ſpatio .6. horarum idem facere, vnde ex ſupradictis, vas im
                    <lb/>
                  plebitur à tribus fiſtulis ſuperioribus, clauſis exiſtentibus inferioribus, ſpatio tempo
                    <lb/>
                  ris
                    <reg norm="minutorum" type="context">minutorũ</reg>
                  .32.
                    <reg norm="cum" type="context">cũ</reg>
                  .8. vndecimis hoc eſt min .32. cum .43. ſecundis, deinde per duas
                    <lb/>
                  fiſtulas inferiores poſſet euacuari ſpatio
                    <reg norm="temporis" type="context">tẽporis</reg>
                  horarum .2. et. mi .24. exſupradictis.</s>
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                <p>
                  <s xml:id="echoid-s3590" xml:space="preserve">Supponamus igitur omnes fiſtulas operari ſpatio temporis minutorum .32. cum
                    <lb/>
                  ſecundis .43. </s>
                  <s xml:id="echoid-s3591" xml:space="preserve">tunc manifeſtum eſt quod vas non implebitur, eo ſpatio min .32. cum
                    <lb/>
                  ſecundis .43. ſed tanta aqua deficiet, quanta ab inferioribus fiſtulis eo ſpatio tempo
                    <lb/>
                  ris min .32. ſecun .43. poteſt euacuari, </s>
                  <s xml:id="echoid-s3592" xml:space="preserve">quare proportio partis vaſis vacuæ, ad totum
                    <lb/>
                  vas, erit vt min .33. ferè ad horas .2. min .24. quod per ſe patet, </s>
                  <s xml:id="echoid-s3593" xml:space="preserve">tunc ſi demptum fue- </s>
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