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]

Page concordance

< >
Scan Original
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
291 279
292 280
293 281
294 288
295 283
296 284
297 285
298 286
299 287
300 288
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
< >
page |< < (289) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div551" type="section" level="3" n="15">
              <div xml:id="echoid-div553" type="letter" level="4" n="3">
                <pb o="289" rhead="EPISTOL AE." n="301" file="0301" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0301"/>
              </div>
            </div>
            <div xml:id="echoid-div558" type="section" level="3" n="16">
              <div xml:id="echoid-div558" type="letter" level="4" n="1">
                <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>
                </p>
                <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>
                </p>
                <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>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum