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

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          <p>
            <s xml:id="echoid-s13186" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s13187" xml:space="preserve">_Hyperbolam_ AEB, cujus _Centrum_ C, tangant duæ rectæ
              <lb/>
            BT, ES, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">reliqua ponantur ut in proximè præcedente; </s>
            <s xml:id="echoid-s13189" xml:space="preserve">erit T D:
              <lb/>
            </s>
            <s xml:id="echoid-s13190" xml:space="preserve">
              <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">Fig. 137.</note>
            A D &</s>
            <s xml:id="echoid-s13191" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13192" xml:space="preserve">SP. </s>
            <s xml:id="echoid-s13193" xml:space="preserve">AP.</s>
            <s xml:id="echoid-s13194" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13195" xml:space="preserve">Nam eſt CA. </s>
            <s xml:id="echoid-s13196" xml:space="preserve">CD:</s>
            <s xml:id="echoid-s13197" xml:space="preserve">: CT. </s>
            <s xml:id="echoid-s13198" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13199" xml:space="preserve">unde CA - CT. </s>
            <s xml:id="echoid-s13200" xml:space="preserve">CD -
              <lb/>
            CA:</s>
            <s xml:id="echoid-s13201" xml:space="preserve">: CT. </s>
            <s xml:id="echoid-s13202" xml:space="preserve">CA; </s>
            <s xml:id="echoid-s13203" xml:space="preserve">hoceſt TA. </s>
            <s xml:id="echoid-s13204" xml:space="preserve">AD:</s>
            <s xml:id="echoid-s13205" xml:space="preserve">: CT. </s>
            <s xml:id="echoid-s13206" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">ſuppare diſ-
              <lb/>
            curſu, eſt SA. </s>
            <s xml:id="echoid-s13208" xml:space="preserve">AP:</s>
            <s xml:id="echoid-s13209" xml:space="preserve">: CS. </s>
            <s xml:id="echoid-s13210" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13211" xml:space="preserve">Verùm eſt CT. </s>
            <s xml:id="echoid-s13212" xml:space="preserve">CA &</s>
            <s xml:id="echoid-s13213" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13214" xml:space="preserve">CS.
              <lb/>
            </s>
            <s xml:id="echoid-s13215" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s13216" xml:space="preserve">quare TA. </s>
            <s xml:id="echoid-s13217" xml:space="preserve">AD &</s>
            <s xml:id="echoid-s13218" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13219" xml:space="preserve">SA. </s>
            <s xml:id="echoid-s13220" xml:space="preserve">AP; </s>
            <s xml:id="echoid-s13221" xml:space="preserve">ſeu componendo TD. </s>
            <s xml:id="echoid-s13222" xml:space="preserve">AD
              <lb/>
            &</s>
            <s xml:id="echoid-s13223" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13224" xml:space="preserve">SP. </s>
            <s xml:id="echoid-s13225" xml:space="preserve">AP.</s>
            <s xml:id="echoid-s13226" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13227" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s13228" xml:space="preserve">_Circali_ AEB (cujus _Centrum_ C) & </s>
            <s xml:id="echoid-s13229" xml:space="preserve">_paraboliformis_ AFB
              <lb/>
            communes ſint axis AD, & </s>
            <s xml:id="echoid-s13230" xml:space="preserve">baſis BD; </s>
            <s xml:id="echoid-s13231" xml:space="preserve">ſit autem _paraboliformis_ ex-
              <lb/>
            ponens {_n_/_m_}; </s>
            <s xml:id="echoid-s13232" xml:space="preserve">& </s>
            <s xml:id="echoid-s13233" xml:space="preserve">AD = {_m_ - 2 _n_/_m_ - _n_} CA (vel _m_ - _n_. </s>
            <s xml:id="echoid-s13234" xml:space="preserve">_m_ - 2 _n_:</s>
            <s xml:id="echoid-s13235" xml:space="preserve">:
              <lb/>
            CA. </s>
            <s xml:id="echoid-s13236" xml:space="preserve">AD) _circulum_ verò tangat recta BT; </s>
            <s xml:id="echoid-s13237" xml:space="preserve">hæc quoque _paraboli-_
              <lb/>
            _formem_ AFB continget.</s>
            <s xml:id="echoid-s13238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13239" xml:space="preserve">Nam quia BT _circulum_ tangit, eſt CT CA:</s>
            <s xml:id="echoid-s13240" xml:space="preserve">: CA. </s>
            <s xml:id="echoid-s13241" xml:space="preserve">CD; </s>
            <s xml:id="echoid-s13242" xml:space="preserve">unde TA.
              <lb/>
            </s>
            <s xml:id="echoid-s13243" xml:space="preserve">
              <note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">Fig. 138.</note>
            AD:</s>
            <s xml:id="echoid-s13244" xml:space="preserve">:. </s>
            <s xml:id="echoid-s13245" xml:space="preserve">CACD.</s>
            <s xml:id="echoid-s13246" xml:space="preserve">
              <unsure/>
            componendóque TD. </s>
            <s xml:id="echoid-s13247" xml:space="preserve">AD:</s>
            <s xml:id="echoid-s13248" xml:space="preserve">: CA + CD. </s>
            <s xml:id="echoid-s13249" xml:space="preserve">CD Item, quo-
              <lb/>
            uiam eſt (ex hypotheſi) CA. </s>
            <s xml:id="echoid-s13250" xml:space="preserve">AD:</s>
            <s xml:id="echoid-s13251" xml:space="preserve">: _m_ - _n_. </s>
            <s xml:id="echoid-s13252" xml:space="preserve">_m_ -2 _n_; </s>
            <s xml:id="echoid-s13253" xml:space="preserve">erit per ratio-
              <lb/>
            nis converſionem CA. </s>
            <s xml:id="echoid-s13254" xml:space="preserve">CD:</s>
            <s xml:id="echoid-s13255" xml:space="preserve">: _m_ - _n. </s>
            <s xml:id="echoid-s13256" xml:space="preserve">n_. </s>
            <s xml:id="echoid-s13257" xml:space="preserve">& </s>
            <s xml:id="echoid-s13258" xml:space="preserve">componendo CA +
              <lb/>
            CD. </s>
            <s xml:id="echoid-s13259" xml:space="preserve">CD:</s>
            <s xml:id="echoid-s13260" xml:space="preserve">: _m. </s>
            <s xml:id="echoid-s13261" xml:space="preserve">n_. </s>
            <s xml:id="echoid-s13262" xml:space="preserve">hoc eſt TD. </s>
            <s xml:id="echoid-s13263" xml:space="preserve">AD:</s>
            <s xml:id="echoid-s13264" xml:space="preserve">: _m. </s>
            <s xml:id="echoid-s13265" xml:space="preserve">n_. </s>
            <s xml:id="echoid-s13266" xml:space="preserve">unde palàm
              <note symbol="(_a_)" position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">2 _hujus ap._</note>
            quòd BT _paraboliformem_ AFB tangit.</s>
            <s xml:id="echoid-s13267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13268" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s13269" xml:space="preserve">Subnotetur, quòd inversè, datâ ratione ipſius AD ad CA’
              <lb/>
            deſignabitur hinc _paraboliformis_; </s>
            <s xml:id="echoid-s13270" xml:space="preserve">quæ _Circulum_ AEB ad B contin-
              <lb/>
            get. </s>
            <s xml:id="echoid-s13271" xml:space="preserve">Nempe, ſi AD = {_s_/_t_}, erit {_t_ - _s_/2 _t_ - _s_} dictæ _paraboliformis ex-_
              <lb/>
            ponens. </s>
            <s xml:id="echoid-s13272" xml:space="preserve">Nam poſito fore {_t_ - _s_/2 _t_ - _s_} = {_n_/_m_}; </s>
            <s xml:id="echoid-s13273" xml:space="preserve">erit ideò (juxta crucem
              <lb/>
            multiplicando) _mt_ - _ms_ = 2 _tn_ - _sn_; </s>
            <s xml:id="echoid-s13274" xml:space="preserve">& </s>
            <s xml:id="echoid-s13275" xml:space="preserve">tranſponendo _mt_ -
              <lb/>
            2 _nt_ = _ms_ - _ns_. </s>
            <s xml:id="echoid-s13276" xml:space="preserve">ac ideò (æqualitatem ad analogiſmum redigendo)
              <lb/>
            _m_ - _n. </s>
            <s xml:id="echoid-s13277" xml:space="preserve">m_ - 2 _n_:</s>
            <s xml:id="echoid-s13278" xml:space="preserve">: _t. </s>
            <s xml:id="echoid-s13279" xml:space="preserve">s_:</s>
            <s xml:id="echoid-s13280" xml:space="preserve">: CA. </s>
            <s xml:id="echoid-s13281" xml:space="preserve">AD. </s>
            <s xml:id="echoid-s13282" xml:space="preserve">itaque conſtat ex anteceden-
              <lb/>
            te Propoſitum.</s>
            <s xml:id="echoid-s13283" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13284" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s13285" xml:space="preserve">Manente quoad cætera ſeptimæ hypotheſi, _paraboliformis_
              <lb/>
            AFB extra _circulum_ AEB tota cadet.</s>
            <s xml:id="echoid-s13286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13287" xml:space="preserve">Nam utcunque ducatur recta GEF ad DB parallela; </s>
            <s xml:id="echoid-s13288" xml:space="preserve">quæ ſecet
              <lb/>
              <note position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve">Fig. 139.</note>
            circulum ad E, paraboliformem in F; </s>
            <s xml:id="echoid-s13289" xml:space="preserve">ductæque concipiantur rectæ
              <lb/>
            ES _circulum_, & </s>
            <s xml:id="echoid-s13290" xml:space="preserve">recta FR _paraboliformem_ contingentes; </s>
            <s xml:id="echoid-s13291" xml:space="preserve"/>
          </p>
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    </echo>
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