Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

< >
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1C940">
            <p id="N1D714" type="main">
              <s id="N1D747">
                <pb pagenum="211" xlink:href="026/01/243.jpg"/>
              ſunt vt radices AEAT, id eſt tempus quo percurritur AE eſt ad tem­
                <lb/>
              pus, quo percurritur AT, vt AE ad mediam proportionalem inter AE
                <lb/>
              AT, vel vt AD ad mediam proportionalem inter AD AR; quippe AD
                <lb/>
              eſt ad AR vt AE ad AT. </s>
            </p>
            <p id="N1D756" type="main">
              <s id="N1D758">Galileus verò demonſtrat rationem iſtorum temporum eſſe compoſi­
                <lb/>
              tam ex ratione longitudinem planorum & ex ratione ſubduplicata al­
                <lb/>
              titudinum eorumdem permutatim accepta: pro quo obſerua à Galileo
                <lb/>
              rationem duplicatam appellari duplam, & ſubduplicatam appellari ſub­
                <lb/>
              duplam. </s>
            </p>
            <p id="N1D764" type="main">
              <s id="N1D766">Obſeruabis denique plurima ex his colligi poſſe præſertim ex Th. 27.
                <lb/>
              quæ quia ſunt purè geometrica, certè phyſicę minimè competunt; aliqua
                <lb/>
              tamen omittere non poſſum. </s>
            </p>
            <p id="N1D76E" type="main">
              <s id="N1D770">Primò, ſi ſint duo plana inæqualia ad angulum rectum, qui ſuſtinea­
                <lb/>
              tur ab horizontali, determinari poſſunt tempora deſcenſuum ſit enim
                <lb/>
              triangulum orthogonium ABE, ita vt AE ſit horizontalis; </s>
              <s id="N1D778">ducatur B
                <lb/>
              G indefinita perpendicularis in baſim AE; </s>
              <s id="N1D77E">tùm FA perpendicularis in
                <lb/>
              AB; </s>
              <s id="N1D784">tùm FC perpendicularis in BE; </s>
              <s id="N1D788">tùm denique GE in BE; </s>
              <s id="N1D78C">dico BA
                <lb/>
              BFBC percurri temporibus æqualibus, item BE, BG, EG, etiam æqua­
                <lb/>
              libus; </s>
              <s id="N1D794">igitur tempus, quo percurritur BA eſt ad tempus quo percurri­
                <lb/>
              tur BE, vt tempus, quo percurritur BF ad tempus quo percurritur BG;
                <lb/>
              hæc porrò ſunt in ſubduplicata ratione BFBG vel BC, & BE. </s>
            </p>
            <p id="N1D79D" type="main">
              <s id="N1D79F">Secundò, ſi planum ſuſtinens angulum rectum non ſit parallelum
                <lb/>
              horizonti 6. res ſimiliter determinari poterit; </s>
              <s id="N1D7A5">ſit enim triangulum or­
                <lb/>
              thogonium ABC ex B, ducatur perpendicularis deorſum indefinitè BF,
                <lb/>
              tùm EA in AB, tùm DC in CB, tùm EH parallela DC, tùm GC in A
                <lb/>
              C; </s>
              <s id="N1D7AF">denique AG parallela BF; dico quod BABEHE AE percurren­
                <lb/>
              tur æqualibus temporibus item BCCDBD. </s>
            </p>
            <p id="N1D7B5" type="main">
              <s id="N1D7B7">Tertiò, ſiue deſcendat ex B in C per lineam perpendicularem BC,
                <lb/>
              ſiue ex A per inclinatam AC, eodem modo deſcendet ſiue per CD, ſiue
                <lb/>
              per CE; ratio eſt clara, quia acquirit æqualem velocitatem ſiue ex A ſi­
                <lb/>
              ue ex B deſcendat pet Th. 20. erit autem tempus per CE ad tempus per
                <lb/>
              CD, vt CE ad CD per Th.23.& motus per CE ad motum per CD, vt
                <lb/>
              CD ad CE per Th.6. poſito initio motus in C. </s>
            </p>
            <p id="N1D7C6" type="main">
              <s id="N1D7C8">Quartò, præuio motu ex A vel ex B ad C poteſt inueniri inclinata,
                <lb/>
              per quam mobile pergat moueri motu ſcilicet naturaliter accelerato, ita
                <lb/>
              vt æquali tempore illam conficiat; </s>
              <s id="N1D7D0">ſi enim BC conficiet dato tempore; </s>
              <s id="N1D7D4">
                <lb/>
              igitur CF triplum CB conficiet tempore æquali; </s>
              <s id="N1D7D9">ſit autem planum ho­
                <lb/>
              rizontale EDK ad quod ex C ducendum ſit planum inclinatum, quod
                <lb/>
              eodem tempore percurratur, quo CF, diuidatur CF bifariam in H, & ex
                <lb/>
              puncto H fiat arcus CK, ducaturque CK: </s>
              <s id="N1D7E3">Dico CF & CK æquali tem­
                <lb/>
              pore confici per Th. 27. modò ex quiete C procedat motus: </s>
              <s id="N1D7E9">ſimiliter aſ­
                <lb/>
              ſumi poteſt alia horizontalis LM ducto arcu LF ex centro H; </s>
              <s id="N1D7EF">nam CL
                <lb/>
              & CF æquali tempore percurruntur; </s>
              <s id="N1D7F5">ſi verò præſupponatur motus præ­
                <lb/>
              uius ex A vel ex B, haud dubiè CK breuiori tempore percurretur, quàm
                <lb/>
              CF, idem dico de CL; </s>
              <s id="N1D7FD">alioqui CE & CI eodem præuio motu ſuppo </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum