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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          <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">
                <p>
                  <s xml:id="echoid-s3569" xml:space="preserve">
                    <pb o="288" rhead="IO. BAPT. BENED." n="300" file="0300" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0300"/>
                  f. toto ſuo pondere, </s>
                  <s xml:id="echoid-s3570" xml:space="preserve">propterea quod pondus diuiditur proportionaliter ſupra ba-
                    <lb/>
                  ſim vaſis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3571" xml:space="preserve">Sit exempli
                    <reg norm="gratia" type="wordlist">gr̃a</reg>
                  vas aliquod
                    <var>.b.d.n.m.</var>
                  conicæ figuræ, ſeu
                    <reg norm="truncus" type="context">trũcus</reg>
                  coni concaui aqua
                    <lb/>
                  plenus, cuius orificij diameter ſit
                    <var>.b.d.</var>
                  & multiplex diametro
                    <var>.m.n.</var>
                  infimæ baſis. </s>
                  <s xml:id="echoid-s3572" xml:space="preserve">co-
                    <lb/>
                  gitemus etiam
                    <var>.b.d.</var>
                  diuiſum in tot partes, quarum
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                  æqualis ſit
                    <var>.m.n.</var>
                  imagi-
                    <lb/>
                    <reg norm="nemurque" type="simple">nemurq́;</reg>
                  tot lineas perpendiculares deſcendere verſus mundi centrum ad puncta
                    <var>r.
                      <lb/>
                    c.m.</var>
                  et
                    <var>.t.x.m.</var>
                  vt in ſubſcripta hic figura videre eſt, per quas cogitemus tot ſuperfi-
                    <lb/>
                  cies curuas
                    <reg norm="conicasque" type="simple">conicasq́;</reg>
                  , inter quas, mente concipienda eſt aqua, quę pondere ſuo quie
                    <lb/>
                  ſcet ſupra maiorem ſuperficiem illa, quæ æque diſtans eſſet mundi centro, ſeu quam
                    <lb/>
                  ſupra baſim
                    <var>.m.n.</var>
                  vt exempli gratia conſideretur aqua inter
                    <var>.g.m.</var>
                  et
                    <var>.s.r.</var>
                  cuius pondus
                    <lb/>
                  diſtribuitur fecundum latitudinem
                    <var>.m.r.</var>
                  quæ maior eſt
                    <var>.g.s.</var>
                  cogitemus igitur
                    <var>.m.c.</var>
                  æ-
                    <lb/>
                  qualem eſſe
                    <var>.g.s.</var>
                  manifeſtum erit, quod
                    <var>.m.c.</var>
                  non ſuſtinebit totum pondus a quæ, quæ
                    <lb/>
                  inter
                    <var>.g.m.</var>
                  et
                    <var>.s.r.</var>
                  reperitur, eo quod omnis pars aquæ ad perpendiculum inclinat ver-
                    <lb/>
                  ſus mundi centrum, quapropter fundus ſeu baſis
                    <var>.m.n.</var>
                  non ſuſtinet aliud pondus
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  aquæ
                    <var>.f.m.</var>
                  ſed ſi quis hoc in dubium reuocaret dicens, quod aqua circunſcribens ſi-
                    <lb/>
                  tum corporis aquei
                    <var>.f.m.</var>
                  impellit lateraliter dictum corpus aqueum, reſpondendum
                    <lb/>
                  eſt, quod ex æquo huius corporis
                    <var>.f.m.</var>
                  aqua impellit etiam aquam circunſtantem,
                    <lb/>
                  eo, quod ſunt corpora homogenea, cum in corporibus homogeneis æquales partes
                    <lb/>
                  habeant æquales vires.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3573" xml:space="preserve">Sed redeundo ad vaſa
                    <var>.a.u.</var>
                  et
                    <var>.f.</var>
                  dico quod ſicut aqua
                    <var>.f.</var>
                  ſufficit ad
                    <reg norm="reſiſtendum" type="context">reſiſtendũ</reg>
                  aquæ
                    <lb/>
                    <var>a.u.</var>
                  ita quodlibet aliud pondus ęquale
                    <var>.f.</var>
                  cuiuſuis materiæ, in fiſtula
                    <var>.f.</var>
                  poſitum, ſuffi-
                    <lb/>
                  ciens erit, dummodo illud corpus ita ſit adæquatum concauitati fiſtulæ
                    <var>.f.</var>
                  quod non
                    <lb/>
                  permittat tranſitum aliquem aquæ vel
                    <lb/>
                    <figure xlink:label="fig-0300-01" xlink:href="fig-0300-01a" number="322">
                      <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0300-01"/>
                    </figure>
                  aeris inter conuexum ipſius corporis,
                    <lb/>
                  & deuexum fiſtulæ
                    <var>.f.</var>
                  & hoc ex ſe ſatis
                    <lb/>
                  patet, ſed in vaſe
                    <var>.a.u.</var>
                  cum ex hypothe
                    <lb/>
                  ſi latius ſit ipſo
                    <var>.f.</var>
                  nullum aliud corpus
                    <lb/>
                  ſufficiens erit ad reſiſtendum aquæ ip-
                    <lb/>
                  ſius
                    <var>.f.</var>
                  quin tam graue ſit, quam tota
                    <lb/>
                  aqua
                    <var>.a.u.</var>
                  exiſtente
                    <var>.a.u.</var>
                  tam alto quam
                    <lb/>
                  f. </s>
                  <s xml:id="echoid-s3574" xml:space="preserve">Vnde ſi aqua ipſius
                    <var>.f.</var>
                  nil plus eſſet
                    <lb/>
                  quam vna tantummodo libra, & vas
                    <var>.a.
                      <lb/>
                    u.</var>
                  exiſteret latius ipſo
                    <var>.f.</var>
                  in decupla pro
                    <lb/>
                  portione, </s>
                  <s xml:id="echoid-s3575" xml:space="preserve">tunc in ipſo
                    <var>.a.u.</var>
                  oporteret
                    <lb/>
                  corpus adæquatum ipſi concauitati po
                    <lb/>
                  nere, cuius pondus eſſet decem libra-
                    <lb/>
                  rum, vt ſufficeret ad ſuſtinendum
                    <reg norm="aquam" type="context">aquã</reg>
                    <lb/>
                  ipſius
                    <var>.f.</var>
                  & ad im
                    <unsure/>
                    <reg norm="pellendum" type="context">pellendũ</reg>
                  ipſam
                    <reg norm="aquam" type="context">aquã</reg>
                    <var>.
                      <lb/>
                    f.</var>
                  deberet eſſe plus quam decem libra-
                    <lb/>
                  rum. </s>
                  <s xml:id="echoid-s3576" xml:space="preserve">Ponamus nunc illud corpus, ita
                    <lb/>
                    <figure xlink:label="fig-0300-02" xlink:href="fig-0300-02a" number="323">
                      <image file="0300-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0300-02"/>
                    </figure>
                  denſius eſſe aqua, vt maius
                    <reg norm="interuallum" type="context">interuallũ</reg>
                    <lb/>
                  non occupet, quam
                    <var>.o.e.</var>
                  corpus igitur
                    <lb/>
                    <var>o.e.</var>
                  ſufficiens erit ad impellendum
                    <lb/>
                  aquam
                    <var>.f.</var>
                  & non eo minus.</s>
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