Fabri, Honoré, Tractatus physicus de motu locali, 1646

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      <text>
        <body>
          <chap id="N1EE3A">
            <p id="N2101C" type="main">
              <s id="N2114F">
                <pb pagenum="269" xlink:href="026/01/303.jpg"/>
              vniuerſale eſt, falſum eſſe conſtat; addunt aliqui eſſe mixtam æquiualen­
                <lb/>
              ter. </s>
              <s id="N2115A">Tertiò, cum ſit eadem potentia motrix applicata, tùm in K, tùm in
                <lb/>
              A; </s>
              <s id="N21160">certè debet eſſe idem impetus; </s>
              <s id="N21164">cum autem duæ lineæ K
                <foreign lang="grc">θ</foreign>
              K
                <foreign lang="grc">β</foreign>
              repræ­
                <lb/>
              ſentent duos impetus, qui concurrunt ad motum mixtum per KD (nam
                <lb/>
              hoc ipſi dicunt) certè duo ABAP ſimul ſumpti æquales eſſe deberent
                <lb/>
              duobus K
                <foreign lang="grc">θ</foreign>
              K
                <foreign lang="grc">β</foreign>
              , quod falſum eſt; quia KD ſit 4. ſitque angulus GDK
                <lb/>
              30.grad. </s>
              <s id="N21180">K
                <foreign lang="grc">θ</foreign>
              eſt 2. igitur collecta
                <foreign lang="grc">θ</foreign>
              K
                <foreign lang="grc">β</foreign>
              eſt 6. & eius quadratum 36. at
                <lb/>
              verò quadratum AB eſt 18. ergo quadratum collectæ ex ABAP eſt
                <lb/>
              32. igitur illa maior eſt. </s>
            </p>
            <p id="N21193" type="main">
              <s id="N21195">Sed iam ad aliam propoſitionem venio, in qua dicitur linea reflexio­
                <lb/>
              nis DX eſſe mixta ex D
                <foreign lang="grc">θ</foreign>
              D
                <foreign lang="grc">υ</foreign>
              quod falſum eſt; </s>
              <s id="N211A3">nam primò hoc dicis,
                <lb/>
              hoc proba poſitiuo argumento: </s>
              <s id="N211A9">Dices, quia non poteſt aliter explicari
                <lb/>
              æqualitas anguli reflexionis; </s>
              <s id="N211AF">bellè! nego antecedens; nam licèt nondum
                <lb/>
              verus illius modus explicatus non eſſet, proba tuum eſſe verum. </s>
              <s id="N211B5">Secundò
                <lb/>
              vel aliquid prioris determinationis manet, vel nihil; </s>
              <s id="N211BB">non primum, vt ipſi
                <lb/>
              volunt; </s>
              <s id="N211C1">alioqui DX eſſet mixta ex tribus ſcilicet DQ, D
                <foreign lang="grc">θ</foreign>
              , D
                <foreign lang="grc">υ</foreign>
              , quod
                <lb/>
              abſurdum eſt; </s>
              <s id="N211CF">quod ſi nihil remaneat prioris determinationis; </s>
              <s id="N211D3">ergo ni­
                <lb/>
              hil prioris impetus, quod etiam concedunt; </s>
              <s id="N211D9">igitur producitur nouus, ſci­
                <lb/>
              licet propter compreſſionem aëris, corporis reflexi, & reflectentis; </s>
              <s id="N211DF">ſed
                <lb/>
              profectò, licèt hoc totum verum eſſet, cùm illa compreſſio fieret in linea
                <lb/>
              quæ per centrum globi producitur, ſcilicet à puncto contactus, ſcilicet
                <lb/>
              in linea DG; </s>
              <s id="N211E9">certè per illam fieret repercuſſio; </s>
              <s id="N211ED">Tertiò tunc maxima eſt
                <lb/>
              percuſſio, cum linea incidentiæ eſt perpendicularis; </s>
              <s id="N211F3">igitur tunc eſſe de­
                <lb/>
              bet maxima vis compreſſionis; </s>
              <s id="N211F9">igitur maxima vis repercuſſionis, ſed eſt
                <lb/>
              tantùm vt DG; at verò, ſi linea incidentiæ ſit AD, vis repercuſſionis
                <lb/>
              erit, vt collecta ex DFDP quæ maior eſt priore. </s>
              <s id="N21201">Quartò, cur DX erit
                <lb/>
              potiùs mixta ex duabus D
                <foreign lang="grc">θ</foreign>
              , D
                <foreign lang="grc">υ</foreign>
              , quàm ex duabus aliis? </s>
              <s id="N2120E">Quintò, perinde
                <lb/>
              ſe habet planum reflectens, atque ſi globum ipſum pelleret, cùm nihil de­
                <lb/>
              terminationis prioris remaneat, vt ipſi volunt, ſed pelleret per ipſam
                <lb/>
              DG. Sextò, proba argumento poſitiuo eſſe mixtam DX ex D
                <foreign lang="grc">υ</foreign>
              , D
                <foreign lang="grc">θ</foreign>
              ; nam
                <lb/>
              hoc reuerâ fingis ſine ratione. </s>
              <s id="N21222">Septimò, præterea ſi corpus eſſet duriſſi­
                <lb/>
              mum minùs reflecti poſſet à plano duriſſimo, ſi nulla fieret compreſſio. </s>
              <s id="N21227">
                <lb/>
              Octauò proba mihi impetum priorem deſtrui per ſe; </s>
              <s id="N2122C">nam cùm ſit indif­
                <lb/>
              ferens ad omnes lineas, nunquam deſtruitur, niſi ſit fruſtrà; </s>
              <s id="N21232">hic autem
                <lb/>
              fruſtrà non eſt: </s>
              <s id="N21238">Itaque manifeſtum efficitur, non modò ex his principiis
                <lb/>
              non demonſtrari æqualitatem anguli reflexionis, ſed ne argumento qui­
                <lb/>
              dem probabili comprobari; quia tamen in noſtra demonſtratione multa
                <lb/>
              ſunt, quæ ipſis non probantur, breuiter recenſeo. </s>
            </p>
            <p id="N21242" type="main">
              <s id="N21244">Suppono primò, planum reflectens eſſe principium nouæ determina­
                <lb/>
              tionis, quod nemo inficiebitur. </s>
              <s id="N21249">Secundò, eſſe tantùm principium vnius
                <lb/>
              determinationis quia vnum principium eſt. </s>
              <s id="N2124E">Tertiò, per quamcunque li­
                <lb/>
              neam incidat globus in punctum D plani ſcilicet immobilis, eſt ſemper
                <lb/>
              idem punctum contactus & eadem
                <expan abbr="Tãgens">Tangens</expan>
              . </s>
              <s id="N2125A">Quartò, à puncto contactus
                <lb/>
              globi duci tantùm poſſe vnicam lineam ad centrum. </s>
              <s id="N2125F">Quintò, cum deter­
                <lb/>
              minationis terminus à quo ſit illud punctum contactus, per illam tan-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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