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-div551" type="section" level="3" n="15">
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                <p>
                  <s xml:id="echoid-s3560" xml:space="preserve">
                    <pb o="287" rhead="EPISTOL AE." n="299" file="0299" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0299"/>
                  nem & impetum motus, ita vt ſeparatum à virtute mouente per aliquod temporis
                    <lb/>
                  ſpatium ex ſeipſo moueatur. </s>
                  <s xml:id="echoid-s3561" xml:space="preserve">nam ſi ſecundum naturam motu cieatur, ſuam veloci-
                    <lb/>
                  tatem ſemper augebit, cum in eo, impetus & impreſſio ſemper augeantur, quia
                    <lb/>
                  coniunctam habet per petuò virtutem mouentem. </s>
                  <s xml:id="echoid-s3562" xml:space="preserve">Vnde manu mouendo rotam, ab
                    <lb/>
                    <reg norm="eaque" type="simple">eaq́;</reg>
                  eam remouendo rota ſtatim non quieſcet, ſed per aliquod temporis ſpatium
                    <lb/>
                  circunuertetur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3563" xml:space="preserve">Secunda cauſa eſt, quia quoduis gr aue corpus, aut per naturam, aut per vim mo-
                    <lb/>
                  tum, rectitudinem itineris naturaliter appetat, quod clarè cognoſcere poſſumus,
                    <lb/>
                  proijciendo lapides funda, & circunducentes brachium, nam funes tanto maius
                    <lb/>
                  pondus acquirunt, & manum tanto magis onerant, quanto velocius voluitur funda,
                    <lb/>
                  & incitatur motus, quod ab appetitu naturali inſito ei corpori per
                    <reg norm="lineam" type="context">lineã</reg>
                  rectam pro-
                    <lb/>
                  grediendi procedit. </s>
                  <s xml:id="echoid-s3564" xml:space="preserve">Vnde fit, vt pondus circunferentiæ ipſius rotæ, tanto facilius cir-
                    <lb/>
                  cunuoluatur, & ex ſeipſo tanto longiori tempore moueatur, quanto longius diſtat à
                    <lb/>
                  centro, cum eius iter tanto minus ſit curuum. </s>
                  <s xml:id="echoid-s3565" xml:space="preserve">Hanc igitur ob cauſam, rota, quanto
                    <lb/>
                  maior erit,
                    <reg norm="eiuſque" type="simple">eiuſq́;</reg>
                  pondus tanto magis vicinum circunferentiæ, tanto magis durabit
                    <lb/>
                  impetus motus aſſumptus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3566" xml:space="preserve">Tertia cauſa eſt, quod funis dum circunuoluitur, vicinius axi mathematico reuo-
                    <lb/>
                  lutionis, quam corpus graue circunferentiæ rotæ, ratione vectis, cum rota eſt in mo
                    <lb/>
                  tu, eius impetus non obtinet reſiſtentiam æqualem à contrario pondere aquæ in ſitu
                    <lb/>
                  la poſitæ.</s>
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              <div xml:id="echoid-div553" type="letter" level="4" n="3">
                <head xml:id="echoid-head422" style="it" xml:space="preserve">De machina, qua aquam impellit & ſubleuat.</head>
                <head xml:id="echoid-head423" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3567" xml:space="preserve">VNde ſit vt in fonte mandauerim,
                    <lb/>
                    <figure xlink:label="fig-0299-01" xlink:href="fig-0299-01a" number="320">
                      <image file="0299-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0299-01"/>
                    </figure>
                  vas ſeu mortarium in quod in-
                    <lb/>
                  greditur inſtrumentum, quod aquam
                    <lb/>
                  impellit, diametrum ſuæ concauitatis,
                    <lb/>
                  habere non oportere maiorem dia-
                    <lb/>
                  metro fiſtulæ, per quam debet aſcende
                    <lb/>
                  re aqua, ratio eſt, quia ſi maius eſſet,
                    <lb/>
                  neceſſarium eſſet aliquod inſtrumen-
                    <lb/>
                  tum quo aqua impelleretur multo gra
                    <lb/>
                  uius toto corpore aqueo, quod aptum
                    <lb/>
                  eſſet implere aliquam fiſtulam adeo
                    <lb/>
                  altam, vt eſt fons, quæ tamen eſſet
                    <lb/>
                  adeo lata vt eſt mortarium.</s>
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                <p>
                  <s xml:id="echoid-s3568" xml:space="preserve">Sit exempli gratia, tota fiſtula, ſeu
                    <lb/>
                  hirundo, per quam aſcendit aqua
                    <var>.f.</var>
                    <lb/>
                  mortarium verò ſit
                    <var>.a.u.</var>
                  quod tam
                    <reg norm="altum" type="context">altũ</reg>
                    <lb/>
                  ſit vt
                    <var>.f.</var>
                  ſed
                    <var>.f.</var>
                  anguſtior ipſo
                    <var>.a.u</var>
                  . </s>
                  <s xml:id="echoid-s3569" xml:space="preserve">Nunc
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                    <figure xlink:label="fig-0299-02" xlink:href="fig-0299-02a" number="321">
                      <image file="0299-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0299-02"/>
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                  cum repleta fuerint hæc duo vaſa, ma-
                    <lb/>
                  nifeſtum erit, quod aqua ipſius
                    <var>.f.</var>
                  ſuffi-
                    <lb/>
                  ciens erit ad
                    <reg norm="reſiſtendum" type="context">reſiſtẽdum</reg>
                  toti aquæ
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                    <lb/>
                    <var>a.u.</var>
                  & aqua
                    <var>.a.u.</var>
                  reſiſtet aquæ
                    <var>.f.</var>
                  quam-
                    <lb/>
                  uis aqua
                    <var>.a.u.</var>
                  maioris quantitatis ſit, &
                    <lb/>
                  ponderis ipſa
                    <var>.f.</var>
                  hoc autem euenit ex
                    <lb/>
                  eo quod aqua
                    <var>.a.u.</var>
                    <reg norm="non" type="context">nõ</reg>
                  impellit aquam </s>
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