Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div475" type="section" level="1" n="46">
          <head xml:id="echoid-head49" xml:space="preserve">APPENDICULA 2.</head>
          <p>
            <s xml:id="echoid-s14542" xml:space="preserve">B Revitati ſimul ac perſpicuitati (huic autem præcipuè) conſulentes
              <lb/>
            præcedentia recto diſcurſu comprobata dedimus; </s>
            <s xml:id="echoid-s14543" xml:space="preserve">qualinon mo-
              <lb/>
            do veritas, opinor, ſatis ſirmatur, at ejuſdem origo limpidiùs appa-
              <lb/>
            ret. </s>
            <s xml:id="echoid-s14544" xml:space="preserve">Verùm nè quis, minùs hujuſmodi ratiociniis adſuetus, hæreat,
              <lb/>
            iſta paucula ſubdemus, quibus tales diſcurſus communiantur, quorum-
              <lb/>
            que ſubſidio non difficilè conficiantur _Propoſitorum demonſtrationes a-_
              <lb/>
            _pagogicœ_.</s>
            <s xml:id="echoid-s14545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14546" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14547" xml:space="preserve">Sint quotlibet _rationes_ A ad X, B ad Y, C ad Z, ſingulæ deſig-
              <lb/>
            natâ quâ piam ratione R ad S majores; </s>
            <s xml:id="echoid-s14548" xml:space="preserve">erit _omnium antecedentium_
              <lb/>
            (ſimul acceptarum) ad _omnes conſequentes ratio_ major ratione
              <lb/>
            R ad S.</s>
            <s xml:id="echoid-s14549" xml:space="preserve"/>
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          <note position="right" xml:space="preserve">
            <lb/>
          A. X. # A. M.
            <lb/>
          B. Y. # B. N.
            <lb/>
          C. Z. # C. O.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s14550" xml:space="preserve">Nam ſint rationes A ad M, B ad N, C ad O ſingulæ æquales ra-
              <lb/>
            tioni R ad S. </s>
            <s xml:id="echoid-s14551" xml:space="preserve">ergò X &</s>
            <s xml:id="echoid-s14552" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s14553" xml:space="preserve">M; </s>
            <s xml:id="echoid-s14554" xml:space="preserve">& </s>
            <s xml:id="echoid-s14555" xml:space="preserve">Y &</s>
            <s xml:id="echoid-s14556" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s14557" xml:space="preserve">N; </s>
            <s xml:id="echoid-s14558" xml:space="preserve">ac Z &</s>
            <s xml:id="echoid-s14559" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s14560" xml:space="preserve">O. </s>
            <s xml:id="echoid-s14561" xml:space="preserve">patet igitur
              <lb/>
            fore A + B + C. </s>
            <s xml:id="echoid-s14562" xml:space="preserve">X + Y + Z &</s>
            <s xml:id="echoid-s14563" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s14564" xml:space="preserve">A + B + C. </s>
            <s xml:id="echoid-s14565" xml:space="preserve">M + N + O.
              <lb/>
            </s>
            <s xml:id="echoid-s14566" xml:space="preserve">hoc eſt A + B + C. </s>
            <s xml:id="echoid-s14567" xml:space="preserve">X + Y + Z &</s>
            <s xml:id="echoid-s14568" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s14569" xml:space="preserve">R. </s>
            <s xml:id="echoid-s14570" xml:space="preserve">S.</s>
            <s xml:id="echoid-s14571" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14572" xml:space="preserve">II. </s>
            <s xml:id="echoid-s14573" xml:space="preserve">Hinc patet, ſi quotlibet rationes ſingulæ deſignabili quâcunque
              <lb/>
            majores ſint, _antecedentium ſummam ad ſummam conſequentium_ eti-
              <lb/>
            am deſignabili quâcunque majorem rationem habere.</s>
            <s xml:id="echoid-s14574" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14575" xml:space="preserve">III. </s>
            <s xml:id="echoid-s14576" xml:space="preserve">Sit curva quævis ADB, cujus axis AD, & </s>
            <s xml:id="echoid-s14577" xml:space="preserve">ad hunc </s>
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