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-div399" type="section" level="1" n="42">
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          <p>
            <s xml:id="echoid-s13528" xml:space="preserve">XXI. </s>
            <s xml:id="echoid-s13529" xml:space="preserve">Porrò, ſit _circuli_ (cujus centrum C) ſegmentum BAE, cu-
              <lb/>
            jus axis AD, & </s>
            <s xml:id="echoid-s13530" xml:space="preserve">_gravitatis centrum_ K; </s>
            <s xml:id="echoid-s13531" xml:space="preserve">ponatur autem AD =
              <lb/>
            {_s_/_t_} CA, & </s>
            <s xml:id="echoid-s13532" xml:space="preserve">HD = {2 _t_ - _s_/5 _t_ - 3 _s_} AD; </s>
            <s xml:id="echoid-s13533" xml:space="preserve">erit HD major ipsâ KD.</s>
            <s xml:id="echoid-s13534" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13535" xml:space="preserve">Nam per H ducatur recta OP ad BE parallela; </s>
            <s xml:id="echoid-s13536" xml:space="preserve">éſtque punctum
              <lb/>
              <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">Fig. 146.</note>
            H centrum _gravitatis paraboliformis_, (puta AF B) ad baſin B
              <note symbol="(_a_)" position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve">2 _hujus ap._</note>
            conſtitutæ, cujus exponens {_t_ - _s_/2 _t_ - _s_} & </s>
            <s xml:id="echoid-s13537" xml:space="preserve"> quæ proinde circulum
              <note symbol="(_b_)" position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">8. _hujus ap._</note>
            tangit; </s>
            <s xml:id="echoid-s13538" xml:space="preserve">(nam ſi {_t_ - _s_/2 _t_ - _s_} = {_n_/_m_}; </s>
            <s xml:id="echoid-s13539" xml:space="preserve">erit {2 _t_ - _s_/5 _t_ - 3 _s_} = {_m_/_n_ + 2 _m_}) & </s>
            <s xml:id="echoid-s13540" xml:space="preserve">pro-
              <lb/>
            inde H erit centrum gravitatis _paraboliformis_ iſti coordinatæ per O, P tranſeuntis, & </s>
            <s xml:id="echoid-s13541" xml:space="preserve">ad baſin BE pertingentis. </s>
            <s xml:id="echoid-s13542" xml:space="preserve">Hæc autem ſupra O
              <lb/>
            P extra _circulum_ cadit, & </s>
            <s xml:id="echoid-s13543" xml:space="preserve">infra OP intra ipſum; </s>
            <s xml:id="echoid-s13544" xml:space="preserve">
              <note symbol="(_c_)" position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">10. _hujus ap_</note>
              <note symbol="(_d_)" position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve">11 _hujus ap_</note>
              <note symbol="(_e_)" position="left" xlink:label="note-0278-06" xlink:href="note-0278-06a" xml:space="preserve">4. _hujus ap._</note>
            punctum H ſupra K ſitum eſt.</s>
            <s xml:id="echoid-s13545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13546" xml:space="preserve">XXII. </s>
            <s xml:id="echoid-s13547" xml:space="preserve">Sin punctum L ſit _centrum gravitatis parabolæ_, erit L infra
              <lb/>
              <note position="left" xlink:label="note-0278-07" xlink:href="note-0278-07a" xml:space="preserve">Fig. 146.</note>
            K ſitum; </s>
            <s xml:id="echoid-s13548" xml:space="preserve">adeóque KD &</s>
            <s xml:id="echoid-s13549" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13550" xml:space="preserve">{2/5} AD. </s>
            <s xml:id="echoid-s13551" xml:space="preserve">Patet ex 4, & </s>
            <s xml:id="echoid-s13552" xml:space="preserve">17 hujus appen-
              <lb/>
            diculæ.</s>
            <s xml:id="echoid-s13553" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13554" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13555" xml:space="preserve">Sit _Hyperbolæ_ (cujus centrum C) _ſegmentum_ BAE, cujus
              <lb/>
              <note position="left" xlink:label="note-0278-08" xlink:href="note-0278-08a" xml:space="preserve">Fig. 147.</note>
            axis AD, baſis BE; </s>
            <s xml:id="echoid-s13556" xml:space="preserve">gravitatis centrum K; </s>
            <s xml:id="echoid-s13557" xml:space="preserve">ponatur autem AD =
              <lb/>
            {_s_ / _t_} CA, & </s>
            <s xml:id="echoid-s13558" xml:space="preserve">HD = {2 _t_ + _s_/5 _t_ + 3 _s_} AD; </s>
            <s xml:id="echoid-s13559" xml:space="preserve">erit HD minor ipsâ
              <unsure/>
            KD.</s>
            <s xml:id="echoid-s13560" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13561" xml:space="preserve">Nam per H ducatur recta OP ad BE parallela . </s>
            <s xml:id="echoid-s13562" xml:space="preserve">Eſtque
              <note symbol="(_a_)" position="left" xlink:label="note-0278-09" xlink:href="note-0278-09a" xml:space="preserve">2. _hujus. ap._</note>
            H centrum gr. </s>
            <s xml:id="echoid-s13563" xml:space="preserve">_paraboliformis_, puta AFB, ad baſin DB conſtitutæ,
              <lb/>
            cujus exponens {_t_ + _s_/2 _t_ + _s_}; </s>
            <s xml:id="echoid-s13564" xml:space="preserve"> quæ & </s>
            <s xml:id="echoid-s13565" xml:space="preserve">_Hyperbolam_ ad B contingit
              <note symbol="(_b_)" position="left" xlink:label="note-0278-10" xlink:href="note-0278-10a" xml:space="preserve">13. _hujus ap_</note>
            ſi {_t_ + _s_/2 _t_ + _s_} = {_n_/_m_}; </s>
            <s xml:id="echoid-s13566" xml:space="preserve">erit {2 _t_ + _s_/5 _t_ +3 _s_} = {_m_/_n_ + 2_m_} quare H erit cen- trum gravitatis paraboliformis iſti coordinatæ per O, P ductæ, & </s>
            <s xml:id="echoid-s13567" xml:space="preserve">ad BE
              <lb/>
            pertingentis. </s>
            <s xml:id="echoid-s13568" xml:space="preserve">hæc autem ſupra OP intra hyperbolam cadit;</s>
            <s xml:id="echoid-s13569" xml:space="preserve">
              <note symbol="(_c_)" position="left" xlink:label="note-0278-11" xlink:href="note-0278-11a" xml:space="preserve">15. _hujus ap._</note>
            & </s>
            <s xml:id="echoid-s13570" xml:space="preserve">infra OP extra illam; </s>
            <s xml:id="echoid-s13571" xml:space="preserve"> inde pun@um K ſupra
              <note symbol="(_d_)" position="left" xlink:label="note-0278-12" xlink:href="note-0278-12a" xml:space="preserve">16 _hujus ap_</note>
              <note symbol="(_e_)" position="left" xlink:label="note-0278-13" xlink:href="note-0278-13a" xml:space="preserve">4. _hujus ap._</note>
            exiſtit.</s>
            <s xml:id="echoid-s13572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13573" xml:space="preserve">XXIV. </s>
            <s xml:id="echoid-s13574" xml:space="preserve">Parabolæ centrum gr. </s>
            <s xml:id="echoid-s13575" xml:space="preserve">(puta L) ſupra K exiſtit, adeóque
              <lb/>
            KD &</s>
            <s xml:id="echoid-s13576" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13577" xml:space="preserve">{2/3} AD. </s>
            <s xml:id="echoid-s13578" xml:space="preserve">Patet ex 4, & </s>
            <s xml:id="echoid-s13579" xml:space="preserve">18 hujus appendiculæ.</s>
            <s xml:id="echoid-s13580" xml:space="preserve"/>
          </p>
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