Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Page concordance

< >
Scan Original
411 293
412 294
413 295
414 296
415 297
416 298
417 299
418 300
419 301
420 302
421 303
422 304
423 305
424 306
425 307
426 308
427
428
429
430
431
432
433
< >
page |< < (299) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div480" type="section" level="1" n="197">
          <p>
            <s xml:id="echoid-s6592" xml:space="preserve">
              <pb o="299" file="0385" n="417" rhead="MECHANICAM."/>
            particulæ ſimul impingerent; </s>
            <s xml:id="echoid-s6593" xml:space="preserve">unde triplâ exiſtente velocitate,
              <lb/>
            maſſâ etidem triplâ, potentia aut vis erit noncupla; </s>
            <s xml:id="echoid-s6594" xml:space="preserve">ex quo
              <lb/>
            patet maſſam augeri in eadem ratione, qua velocitas auge-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s6595" xml:space="preserve">& </s>
            <s xml:id="echoid-s6596" xml:space="preserve">cum unaquæque pars etiam fortius impingat in ratio-
              <lb/>
            ne auctæ velocitatis, potentia aut vis venti in velum, eſt in
              <lb/>
            ratione duplicata celeritatum venti, id eſt, in ratione qua-
              <lb/>
            dratorum velocitatum venti in velum. </s>
            <s xml:id="echoid-s6597" xml:space="preserve">Agnoſcit hocce prin-
              <lb/>
            cipium Cl. </s>
            <s xml:id="echoid-s6598" xml:space="preserve">Hugenius; </s>
            <s xml:id="echoid-s6599" xml:space="preserve">reſtat ergo tantum, ut illud ap-
              <lb/>
            plicemus.</s>
            <s xml:id="echoid-s6600" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6601" xml:space="preserve">Prima applicatio oſtendet, quare vis venti in velum, cum
              <lb/>
            ventus velo perpendicularis eſt, ſeſe habeat ad vim ejuſdem
              <lb/>
            venti in velum, quando illud inclinatum vento opponitur,
              <lb/>
            ut quadratum radii ad quadratum ſinûs anguli incidentiæ;
              <lb/>
            </s>
            <s xml:id="echoid-s6602" xml:space="preserve">aut, quod idem eſt, cur vires ejuſdem venti in vela varia in-
              <lb/>
            clinatione ipſi obtenſa, ſint inter ſe in ratione quadratorum
              <lb/>
            ſinuum angulorum incidentiæ, quod demonſtravi Articulis
              <lb/>
            7. </s>
            <s xml:id="echoid-s6603" xml:space="preserve">8. </s>
            <s xml:id="echoid-s6604" xml:space="preserve">& </s>
            <s xml:id="echoid-s6605" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">Cap. </s>
            <s xml:id="echoid-s6607" xml:space="preserve">1.</s>
            <s xml:id="echoid-s6608" xml:space="preserve">, & </s>
            <s xml:id="echoid-s6609" xml:space="preserve">quod etiam hoc modo nunc demonſtro. </s>
            <s xml:id="echoid-s6610" xml:space="preserve">
              <lb/>
            Probatum dedi in Theoria Manuariæ Nauticæ, Artic. </s>
            <s xml:id="echoid-s6611" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6612" xml:space="preserve">Cap. </s>
            <s xml:id="echoid-s6613" xml:space="preserve">
              <lb/>
            1. </s>
            <s xml:id="echoid-s6614" xml:space="preserve">corpus motum ab A in B non occurrere ſuperficiei C D
              <lb/>
            niſi ſecundum determinationem ſuam A V, ponendo ſcilicet
              <lb/>
            A V perpendicularem ipſi D C productæ, & </s>
            <s xml:id="echoid-s6615" xml:space="preserve">in illam ſuper-
              <lb/>
            ficiem nullam vim exſerere niſi ſecundum hanc determinatio-
              <lb/>
            nem; </s>
            <s xml:id="echoid-s6616" xml:space="preserve">quod agnoſcit D
              <emph style="super">nus</emph>
            Hugenius. </s>
            <s xml:id="echoid-s6617" xml:space="preserve">Hoc poſito, ventus A B
              <lb/>
            in velum non agit, niſi ſecundum hanc determinationem, id
              <lb/>
            eſt, cum velocitate A V. </s>
            <s xml:id="echoid-s6618" xml:space="preserve">Si velum C D vento A B per-
              <lb/>
            pendiculare eſſet, ventus in velum ageret velocitate A B; </s>
            <s xml:id="echoid-s6619" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s6620" xml:space="preserve">per conſequens ex principio quod ſtatim adſtruxi, vis
              <lb/>
            cum qua ventus in velum ageret, ſi vento eſſet perpendicula-
              <lb/>
            re, eſt ad vim venti in velum D, quod inclinatè vento ob-
              <lb/>
            tenditur, ut quadratum A B ad quadratum A V, id eſt,
              <lb/>
            ut quadratum radii ad quadratum ſinûs anguli incidentiæ.</s>
            <s xml:id="echoid-s6621" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6622" xml:space="preserve">Secunda applicatio inſervit ſolvendæ quæſtioni, de qua
              <lb/>
            lis eſt inter D
              <emph style="super">num</emph>
            Hugenium & </s>
            <s xml:id="echoid-s6623" xml:space="preserve">me, id eſt oſtendit, quod,
              <lb/>
            velo conſtituto in ſitu C D, & </s>
            <s xml:id="echoid-s6624" xml:space="preserve">navi in ſitu B K, vis, qua
              <lb/>
            ventus ope veli, navim ſecundum B G propellit, ſit ad vim,
              <lb/>
            qua idem ventus, ope ejuſdem veli navim propellit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum