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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                <p>
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                    <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-
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                  ſim vaſis.</s>
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                  <s xml:id="echoid-s3571" xml:space="preserve">Sit exempli
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                  vas aliquod
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                  conicæ figuræ, ſeu
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                  coni concaui aqua
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                  plenus, cuius orificij diameter ſit
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                  & multiplex diametro
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                  infimæ baſis. </s>
                  <s xml:id="echoid-s3572" xml:space="preserve">co-
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                  gitemus etiam
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                  diuiſum in tot partes, quarum
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                  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-
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                  cies curuas
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                  , inter quas, mente concipienda eſt aqua, quę pondere ſuo quie
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                  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
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                  quæ maior eſt
                    <var>.g.s.</var>
                  cogitemus igitur
                    <var>.m.c.</var>
                  æ-
                    <lb/>
                  qualem eſſe
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                  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-
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                  ſus mundi centrum, quapropter fundus ſeu baſis
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                  non ſuſtinet aliud pondus
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                    <lb/>
                  aquæ
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                  ſed ſi quis hoc in dubium reuocaret dicens, quod aqua circunſcribens ſi-
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                  tum corporis aquei
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                  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>
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                <p>
                  <s xml:id="echoid-s3573" xml:space="preserve">Sed redeundo ad vaſa
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                  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-
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                  ciens erit, dummodo illud corpus ita ſit adæquatum concauitati fiſtulæ
                    <var>.f.</var>
                  quod non
                    <lb/>
                  permittat tranſitum aliquem aquæ vel
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0300-01a" xlink:href="fig-0300-01"/>
                  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
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                  corpus adæquatum ipſi concauitati po
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                  nere, cuius pondus eſſet decem libra-
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                  rum, vt ſufficeret ad ſuſtinendum
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                    <lb/>
                  ipſius
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                  & ad im
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                    <reg norm="pellendum" type="context">pellendũ</reg>
                  ipſam
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                    <var>.
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                    f.</var>
                  deberet eſſe plus quam decem libra-
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                  rum. </s>
                  <s xml:id="echoid-s3576" xml:space="preserve">Ponamus nunc illud corpus, ita
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                    <anchor type="figure" xlink:label="fig-0300-02a" xlink:href="fig-0300-02"/>
                  denſius eſſe aqua, vt maius
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                    <lb/>
                  non occupet, quam
                    <var>.o.e.</var>
                  corpus igitur
                    <lb/>
                    <var>o.e.</var>
                  ſufficiens erit ad impellendum
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                  aquam
                    <var>.f.</var>
                  & non eo minus.</s>
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                  <figure xlink:label="fig-0300-02" xlink:href="fig-0300-02a">
                    <image file="0300-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0300-02"/>
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