Fabri, Honoré, Tractatus physicus de motu locali, 1646
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1137F">
            <p id="N1548F" type="main">
              <s id="N15491">
                <pb pagenum="67" xlink:href="026/01/099.jpg"/>
                <emph type="italics"/>
              acquiſitum
                <emph.end type="italics"/>
              : </s>
              <s id="N154A3">ſint duæ lineæ IK IL, mobili ſcilicet ſtatuto in I; </s>
              <s id="N154A7">
                <lb/>
              haud dubiè noua linea erit IM; </s>
              <s id="N154AC">& quo angulus KIL, erit acutior (ſup­
                <lb/>
              poſitis æqualibus ſemper lateribus IK IL) Diagonalis IM, erit ma­
                <lb/>
              ior; </s>
              <s id="N154B4">donec tandem IL & IK coeant in eandem lineam; </s>
              <s id="N154B8">tunc enim li­
                <lb/>
              nea erit dupla IK per Th. ſuperius: </s>
              <s id="N154BE">quandiu verò eſt aliquis angulus in
                <lb/>
              I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen
                <lb/>
              propiùs ſemper accedit; quæ omnia conſtant ex elementis. </s>
            </p>
            <p id="N154C6" type="main">
              <s id="N154C8">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              140.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N154D4" type="main">
              <s id="N154D6">
                <emph type="italics"/>
              Si lineæ duplicis impetus faciunt angulum obtuſum, ſpatium acquiſitum erit
                <lb/>
              breuius, & eò breuius quò angulus eſt obtuſior
                <emph.end type="italics"/>
              ; </s>
              <s id="N154E1">ſint enim
                <emph type="sup"/>
              c
                <emph.end type="sup"/>
              duæ lineæ AD
                <lb/>
              AB mobili ſtatuto in A, noua linea erit AC per Th. 137. & ſi accipia­
                <lb/>
              tur angulus obtuſior HEF; </s>
              <s id="N154EF">noua linea erit EG, eo rectè breuior,
                <lb/>
              quò angulus eſt obtuſior, non tamen iuxta rationem angulorum; </s>
              <s id="N154F5">donec
                <lb/>
              tandem deſinat angulus, & ED EF coëant in vnam lineam; </s>
              <s id="N154FB">tunc enim
                <lb/>
              nullum erit ſpatium, quia ſiſter omninò mobile per Th.133.quæ omnia
                <lb/>
              ipſa luce clariora eſſe conſtat; </s>
              <s id="N15503">quippe quæ cum certis experimentis, &
                <lb/>
              clariſſimis principiis conſentiant; ſed de his plura infrà. </s>
            </p>
            <p id="N15509" type="main">
              <s id="N1550B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              141.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N15517" type="main">
              <s id="N15519">
                <emph type="italics"/>
              Ex his neceſſaria ducitur ratio, cur impetus duplus ad diuerſas lineas de­
                <lb/>
              terminatus non habeat motum duplum, & conſequenter ſpatium duplum
                <emph.end type="italics"/>
              ; </s>
              <s id="N15524">nec
                <lb/>
              enim AE eſt dupla AB, vt conſtat; </s>
              <s id="N1552A">nam ſi lineæ ſint oppoſitæ ex
                <lb/>
              diametro vt BA BE totus deſtruitur impetus, per Th.133. ſi verò vna
                <lb/>
              in
                <expan abbr="eãdem">eandem</expan>
              lineam coëat cum aliâ, nihil impetus deſtruitur, nec impedi­
                <lb/>
              tur per Th.138. igitur quà proportione propiùs accedet ad oppoſitas; </s>
              <s id="N15538">
                <lb/>
              plùs deſtruetur, & minus erit ſpatium; & quâ proportione accedent
                <lb/>
              propiùs ad coëuntes, minùs deſtruetur, & maius erit ſpatium, vt conſtat
                <lb/>
              ex dictis. </s>
            </p>
            <p id="N15541" type="main">
              <s id="N15543">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              142.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1554F" type="main">
              <s id="N15551">
                <emph type="italics"/>
              Hinc impetus ad diuerſas lineas determinati it a pugnant pro rata, vt mi­
                <lb/>
              nùs pugnent, quorum lineæ propiùs accedunt ad coëuntes; plùs verò, quorum
                <lb/>
              lineæ propiùs accedunt ad oppoſitas, idque iuxta proportiones Diagonalium,
                <emph.end type="italics"/>
                <lb/>
              quod totum ſequitur ex dictis. </s>
            </p>
            <p id="N1555F" type="main">
              <s id="N15561">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1556D" type="main">
              <s id="N1556F">Obſeruabis vt faciliùs concipias duos impetus ad duas lineas deter­
                <lb/>
              minatos; </s>
              <s id="N15575">finge tibi nauim à diuerſis ventis impulſam, ſeu lapidem pro­
                <lb/>
              jectum è naui mobili; ſed de his plura in lib.4. cum de motu mixto. </s>
            </p>
            <p id="N1557B" type="main">
              <s id="N1557D">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              143.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N15589" type="main">
              <s id="N1558B">
                <emph type="italics"/>
              Impetus ſemel productus, quamdiu durat motus, conſeruatur.
                <emph.end type="italics"/>
              </s>
              <s id="N15592"> Probatur,
                <lb/>
              quia non poteſt eſſe effectus, niſi ſit eius cauſa per Ax. 8. igitur ſi eſt mo­
                <lb/>
              tus, eſt impetus. </s>
            </p>
            <p id="N15599" type="main">
              <s id="N1559B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              144.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N155A7" type="main">
              <s id="N155A9">
                <emph type="italics"/>
              Impetus non conſeruatur à cauſa primò productiua.
                <emph.end type="italics"/>
              </s>
              <s id="N155B0"> Probatur; quia proii-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum