Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.002412">
                <pb pagenum="459" xlink:href="010/01/467.jpg"/>
                <arrow.to.target n="marg619"/>
                <lb/>
              quæ moles ab infimo eiuſdem fiſtulæ orificio egredi­
                <lb/>
              untur, & propterea vna, & eadem velocitate deter­
                <lb/>
              minata ab eius ſumma altitudine aqua fluit, (ſi tamen
                <lb/>
              ſemper fiſtula repleta ſupponatur); ergo æqualibus
                <lb/>
              temporibus tanta aquæ moles ſupernè infunditur,
                <lb/>
              quanta inferiùs ab eadem fiſtula egreditur, quare in
                <lb/>
              progreſſu motus intra fiſtulam
                <expan abbr="eadẽ">eadem</expan>
              velocitate à qua
                <lb/>
              excurrit, qua infernè egreditur, cùmque hæc veloci­
                <lb/>
              tas ab altitudine caſus, ſeu longitudine penduli, vel
                <lb/>
              fiſtulæ determinetur, igitur velocitas aquæ intra ca­
                <lb/>
              nalem fiſtulæ ſemper eumdem gradum habet, æqua­
                <lb/>
              lem ſcilicèt ei, qui fiſtulæ longitudini competit. </s>
              <s id="s.002413">po­
                <lb/>
              ſtea, vt ſubſequentes propoſitiones demonſtrari com­
                <lb/>
              modiùs poſſint; Primò ſupponendum eſt vt euidens,
                <lb/>
                <arrow.to.target n="marg620"/>
                <lb/>
              quòd ab eodem fiſtulæ orificio,
                <expan abbr="perpẽdicularitèr">perpendicularitèr</expan>
              ta­
                <lb/>
              men erecto ad directionem aquæ fluentis, duæ moles
                <lb/>
              æquales aquæ æqualibus temporibus egreſſæ neceſ­
                <lb/>
              ſariò æqualibus velocitatibus egredi debent; & è
                <expan abbr="cõ-uerſo">con­
                  <lb/>
                uerſo</expan>
              ſi velocitates æquales fuerint, paritèr moles a­
                <lb/>
              quæ æqualibus temporibus effluxæ erunt quoque in­
                <lb/>
              ter ſe æquales. </s>
              <s id="s.002414">Vnde colligitur, quòd velocitatę
                <lb/>
              dupla eodem tempore paritèr dupla moles aquæ ab
                <lb/>
              æquali foramine egreditur, idemque dicendum eſt
                <lb/>
              de qualibet æquè multiplici proportione: paritèrque
                <lb/>
              ſi velocitas partes fuerit alterius velocitatis, paritèr
                <lb/>
              moles aquæ ab æqualibus foraminibus eodem tem­
                <lb/>
              pore egredientes eamdem proportionem commen­
                <lb/>
              ſurabilem habebunt, quam habent
                <expan abbr="earũ">earum</expan>
              velocitates.
                <lb/>
                <arrow.to.target n="marg621"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.002415">
                <margin.target id="marg619"/>
              Cap. 11. gra­
                <lb/>
              uia in fluido
                <lb/>
              velocitati­
                <lb/>
              bus inæqua­
                <lb/>
              libus ferri
                <lb/>
              debere.</s>
            </p>
            <p type="margin">
              <s id="s.002416">
                <margin.target id="marg620"/>
              Supp. 1.</s>
            </p>
            <p type="margin">
              <s id="s.002417">
                <margin.target id="marg621"/>
              Supp. 2.</s>
            </p>
            <p type="main">
              <s id="s.002418">Non ſecùs ſi ab eodem foramine eadem velocita-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum