Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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          <pb o="65" file="0569" n="627" rhead="MATHEMATICA LIB. III. CAP. XV."/>
          <p>
            <s xml:id="echoid-s14485" xml:space="preserve">Specula ſphærica ſunt aut cava aut convexa.</s>
            <s xml:id="echoid-s14486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14487" xml:space="preserve">Prima formantur ex portione ſphæræ cavæ & </s>
            <s xml:id="echoid-s14488" xml:space="preserve">politæ.</s>
            <s xml:id="echoid-s14489" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14490" xml:space="preserve">Secunda ſunt portiones ſphærarum ab exteriori parte po-
              <lb/>
            litarum.</s>
            <s xml:id="echoid-s14491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14492" xml:space="preserve">Radius in ſpeculum quodcunque ſphæricum impingens, cum
              <lb/>
              <note position="right" xlink:label="note-0569-01" xlink:href="note-0569-01a" xml:space="preserve">804.</note>
            ſuo reflexo, dantur in plano, quod continuatum per ſphæræ cen-
              <lb/>
            trum tranſit , eſt enim tale planum ad ſuperficiem
              <note symbol="*" position="right" xlink:label="note-0569-02" xlink:href="note-0569-02a" xml:space="preserve">782;</note>
            perpendiculare. </s>
            <s xml:id="echoid-s14493" xml:space="preserve">Linea, quæ per centrum ſphæræ & </s>
            <s xml:id="echoid-s14494" xml:space="preserve">punctum
              <lb/>
              <note position="right" xlink:label="note-0569-03" xlink:href="note-0569-03a" xml:space="preserve">805.</note>
            incidentiæ ducitur, continuata, cum radio incidente & </s>
            <s xml:id="echoid-s14495" xml:space="preserve">re-
              <lb/>
            flexo angulos æquales format ; </s>
            <s xml:id="echoid-s14496" xml:space="preserve">nam linea hæc eſt
              <note symbol="*" position="right" xlink:label="note-0569-04" xlink:href="note-0569-04a" xml:space="preserve">784.</note>
            dicularis ad ſuperficiem & </s>
            <s xml:id="echoid-s14497" xml:space="preserve">hi ſunt anguli incidentiæ & </s>
            <s xml:id="echoid-s14498" xml:space="preserve">re-
              <lb/>
            flexionis: </s>
            <s xml:id="echoid-s14499" xml:space="preserve">ideoque radius per centrum tranſiens, aut qui con-
              <lb/>
              <note position="right" xlink:label="note-0569-05" xlink:href="note-0569-05a" xml:space="preserve">806.</note>
            tinuatus per centrum tranſiret, reflexus in ſe redit.</s>
            <s xml:id="echoid-s14500" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">TAB. XII.
            <lb/>
          fig. 5.</note>
          <p>
            <s xml:id="echoid-s14501" xml:space="preserve">Sit b c portio ſpeculi convexi; </s>
            <s xml:id="echoid-s14502" xml:space="preserve">punctum radians A; </s>
            <s xml:id="echoid-s14503" xml:space="preserve">ſint
              <lb/>
            A b, A d, A e, radii incidentes; </s>
            <s xml:id="echoid-s14504" xml:space="preserve">reflexi erunt b f, d g,
              <lb/>
              <note position="right" xlink:label="note-0569-07" xlink:href="note-0569-07a" xml:space="preserve">807.</note>
            e b; </s>
            <s xml:id="echoid-s14505" xml:space="preserve">ſi à puncto radiante A ducatur tangens ad ſpeculum,
              <lb/>
            radius reflexus erit continuatio incidentis, aut potius in
              <lb/>
            puncto contactus terminatur radiorum reflexio.</s>
            <s xml:id="echoid-s14506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14507" xml:space="preserve">Si radii à ſpeculo convexo reflexi b f, d g, e b continuentur,
              <lb/>
              <note position="right" xlink:label="note-0569-08" xlink:href="note-0569-08a" xml:space="preserve">808.</note>
            cum omnibus intermediis, interſectionibus ſuis formant cur-
              <lb/>
            vam a a, quam omnes hi radii tangunt, & </s>
            <s xml:id="echoid-s14508" xml:space="preserve">radii vicini ſeſe
              <lb/>
            mutuo interſecant in ipſa periferia curvæ; </s>
            <s xml:id="echoid-s14509" xml:space="preserve">ita ut ſemper ocu-
              <lb/>
            lum intrent quaſi à puncto periferiæ procederent; </s>
            <s xml:id="echoid-s14510" xml:space="preserve">in qua
              <lb/>
            ideò punctum A ſemper apparet , quamdiu reflexi ad
              <note symbol="*" position="right" xlink:label="note-0569-09" xlink:href="note-0569-09a" xml:space="preserve">737.</note>
            lum pervenire poſſunt, & </s>
            <s xml:id="echoid-s14511" xml:space="preserve">oculus movetur in plano, quod
              <lb/>
            per centrum ſphæræ tranſit: </s>
            <s xml:id="echoid-s14512" xml:space="preserve">remoto verò oculo ex hoc pla-
              <lb/>
            no, in aliâ curvâ apparet radians, quia tales curvæ dantur in
              <lb/>
            ſingulis planis, quæ per A & </s>
            <s xml:id="echoid-s14513" xml:space="preserve">C concipi poſſunt.</s>
            <s xml:id="echoid-s14514" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14515" xml:space="preserve">Cùm omnes hæ curvæ & </s>
            <s xml:id="echoid-s14516" xml:space="preserve">quidem integræ dentur poſt
              <lb/>
            ſpeculum, omnia etiam objecta poſt ſpeculi ſuperficiem appa-
              <lb/>
              <note position="right" xlink:label="note-0569-10" xlink:href="note-0569-10a" xml:space="preserve">809.</note>
            rent.</s>
            <s xml:id="echoid-s14517" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14518" xml:space="preserve">Objecta etiam apparent erecta. </s>
            <s xml:id="echoid-s14519" xml:space="preserve">Nam ſi punctum A mo-
              <lb/>
              <note position="right" xlink:label="note-0569-11" xlink:href="note-0569-11a" xml:space="preserve">810.</note>
            veatur circa ſpeculum, eodem motu fertur tota curva a a;
              <lb/>
            </s>
            <s xml:id="echoid-s14520" xml:space="preserve">quod probat, quantum ad ſitum erectum aut inverſum, pun-
              <lb/>
            cta repræſentationis eandem inter ſe habere relationem,
              <lb/>
            quam ipſius objecti puncta.</s>
            <s xml:id="echoid-s14521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14522" xml:space="preserve">Recedente puncto A à ſpeculo, recedit & </s>
            <s xml:id="echoid-s14523" xml:space="preserve">tota curva </s>
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