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-div512" type="section" level="3" n="7">
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                <p>
                  <s xml:id="echoid-s3252" xml:space="preserve">
                    <pb o="259" rhead="EPISTOL AE." n="271" file="0271" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0271"/>
                  reducere putat, nullo fundamento nititur, quia non eſt ſemper dicendum, quod
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  to velocior ſit quædam pila, tanto rectius moueatur, quia ei dici poſſet, vſque ad cer
                    <lb/>
                  tum quendam terminum velocitatis, per tantum ſpatij eam aptam eſſe, vt recta per
                    <lb/>
                  fectè moueatur, ſed ſi velocius iret, non tamen futurum, vt per idem ſpatium re-
                    <lb/>
                  ctius moueretur, ſed quod per longius ſpatium recta motum perageret, & ſic nihil
                    <lb/>
                  haberet quod replicaret, præter quam quod ipſe ſupponit id quod in 18. quæſito
                    <lb/>
                  negat, in quo ait pilam uicinam orificio, non adeo uelocem eſſe, quam cum aliquan-
                    <lb/>
                  tulum ab eodem eſt rem ota, ratione reſiſtentiæ ſui cyllindriaerei. </s>
                  <s xml:id="echoid-s3253" xml:space="preserve">Sed quod pila,
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                  recta eat quanto altior, aut depreſſior
                    <reg norm="bombarda" type="context">bõbarda</reg>
                  erit,
                    <reg norm="ion" type="context">iõ</reg>
                  fit, quia linea inclinationis na
                    <lb/>
                  turalis cum linea inclinationis uiolentæ angulum rectum non facit, </s>
                  <s xml:id="echoid-s3254" xml:space="preserve">unde quanto lon
                    <lb/>
                  gius diſtat à recto huiuſmodi
                    <reg norm="angulus" type="simple">angulꝰ</reg>
                  , ſiue ſit acutus ſiue obtuſus, tanto minorem uim
                    <lb/>
                  habet, eodem planè ferè modo quem tertio capite mei tractatus de rebus mechani
                    <lb/>
                  cis deſcripſi. </s>
                  <s xml:id="echoid-s3255" xml:space="preserve">Quia in ictibus eleuatis, iter inclinationis violentæ ipſius pilæ verſus
                    <lb/>
                  terminum ad quem, incipiendo à loco ipſius pilæ cum itinere inclinationis natura-
                    <lb/>
                  lis, angulum obtuſum, & in ictibus inclinatis acutum conſtituit. </s>
                  <s xml:id="echoid-s3256" xml:space="preserve">Neque etiam hic
                    <lb/>
                  prætermittam notatu dignum errorem, quem Tartalea eodem loco committit,
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  putet indifferenter aliquod corpus impellere, aut percutere maiori
                    <reg norm="cum" type="context">cũ</reg>
                  impetu cum
                    <lb/>
                  eſt in itinere recto. </s>
                  <s xml:id="echoid-s3257" xml:space="preserve">Quia ſequeretur quod aliquod corpus graue perpendiculari-
                    <lb/>
                  ter ſurſum verſus proiectum, in qualibet parte ſui itineris, ſemper fortius percute-
                    <lb/>
                  ret, quam in qualibet parte itineris alterius cuiuſuis eleuationis obliquæ, quod
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  ſit falſum, tibi conſiderandum relinquo.</s>
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                <p>
                  <s xml:id="echoid-s3258" xml:space="preserve">Eſt etiam falſa ea ratio, quam in quarto quæſito idem adducit, quia aer in motu
                    <lb/>
                  non tantum durat, quantum ipſe putat, imò huiuſmodi violenta agitatio, citò ceſſat
                    <lb/>
                  & citius etiam, quam ſi extra aliquam bombardam cum tanta violentia impulliſſet
                    <lb/>
                  ſaceum plumis plenum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3259" xml:space="preserve">Ratio etiam quam in .18. quæſito de eo, quod pila pertran ſeat illud corpus cyllin
                    <lb/>
                  dricum aereum adducit, eſt planè vana, quia ſtatim aer, qui prius in
                    <reg norm="bombarda" type="context">bõbarda</reg>
                  erat
                    <lb/>
                  incluſus, extra ipſam
                    <reg norm="erumpit" type="context">erũpit</reg>
                  , cedit, à
                    <reg norm="pilaque" type="simple">pilaq́;</reg>
                  diuiditur, vt ſi nunquam eam figuram in-
                    <lb/>
                  duiſſet, neque aer ambiens ei reſiſtit. </s>
                  <s xml:id="echoid-s3260" xml:space="preserve">Sed quod velocior ſit in certa quadam diſtan
                    <lb/>
                  tia, quam in principio erat, ſi hoc
                    <reg norm="verum" type="context">verũ</reg>
                  eſſet, ab alia cauſa dependeret, quæ partim ſi
                    <lb/>
                  milis eſſet ei, quæ efficit, vt corpora in motibus naturalibus, cum longius diſtant à ter
                    <lb/>
                  mino vnde naturaliter ſeſe mouerunt, ſint velociora, quia per aliquod ſpatium hu-
                    <lb/>
                  iuſmodi corpus moueretur quemadmodum motu naturali cietur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3261" xml:space="preserve">Ratio autem eius quare pila, aut globus bombardæ ſibiletab eodem in ſeptimo
                    <lb/>
                  quæſito nil valet, quia hoc fit cum pila aliquam paruam concauitatem habet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3262" xml:space="preserve">In .27. autem quæſito ait, quod retrotrahendo ſignum, ictus altius tenderet, quod
                    <lb/>
                  poteſt etiam eſſe falſum, cum hocnon ſit neceſſarium, quia pila dum deſcendit, for-
                    <lb/>
                  taſſe tangeret ſcopum.</s>
                </p>
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