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-s9081" xml:space="preserve">
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            larum æquidiſtat recta, pariter omnibus æquidiſtat, ut in elemento
              <lb/>
            primo demonſtratur.</s>
            <s xml:id="echoid-s9082" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9083" xml:space="preserve">Operæ pretium exiſtimavit _Apollonius_ hoc de _parabola, & </s>
            <s xml:id="echoid-s9084" xml:space="preserve">byper-_
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">I. 22.</note>
            _bola_ ſpeciatim demonſtrare.</s>
            <s xml:id="echoid-s9085" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9086" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s9087" xml:space="preserve">Simili modo patet rectas quaſcunque curvas tangentes una
              <lb/>
            tantùm excipitur, ad extremum lineæ recurrentis. </s>
            <s xml:id="echoid-s9088" xml:space="preserve">Vid. </s>
            <s xml:id="echoid-s9089" xml:space="preserve">18. </s>
            <s xml:id="echoid-s9090" xml:space="preserve">hujus.
              <lb/>
            </s>
            <s xml:id="echoid-s9091" xml:space="preserve">Iiſdem parallelis occurrere.</s>
            <s xml:id="echoid-s9092" xml:space="preserve">‖ Etiam hoc, quoad _ſectiones conicas_, uno
              <lb/>
              <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">I. 24, 25.</note>
            vel altero _Theoremate_ demonſtravit _Apollonius_.</s>
            <s xml:id="echoid-s9093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9094" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s9095" xml:space="preserve">Quinimò rectæ quævis ipſam AZ ſecantes (infra punctum
              <lb/>
            A, ſupráque limitem, ſiquis erit, motûs deſcenſivi) curvam
              <lb/>
            ſecabunt.</s>
            <s xml:id="echoid-s9096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9097" xml:space="preserve">Cùm enim omnes ipſi AZ parallelas ſecent etiam infinitè pro-
              <lb/>
            ductæ curvam ſecent oportet. </s>
            <s xml:id="echoid-s9098" xml:space="preserve">_Hujuſmodi Symptomatis demonſtra-_
              <lb/>
              <note position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">I. 27, 28.</note>
            _tioni in ſectionibus conicis_ laborioſam operam impendit _Apolloniu_.</s>
            <s xml:id="echoid-s9099" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9100" xml:space="preserve">X. </s>
            <s xml:id="echoid-s9101" xml:space="preserve">Porrò liquet applicatas ad rectam AY, ipſi AZ parallelas
              <lb/>
            (quas nempe propoſitæ curvæ ſinus verſos appellare fas erit mi-
              <lb/>
            norem inter ſe rationem habere (minores cum majoribus comparan-
              <lb/>
            do, ſeu minores antecedentium loco ponendo) quàm habent re-
              <lb/>
            ſpectivæ AY partes, iiſdem temporibus decurſæ (quas & </s>
            <s xml:id="echoid-s9102" xml:space="preserve">curvæ
              <lb/>
            propoſitæ ſinus rectos appellare nil dubitem.) </s>
            <s xml:id="echoid-s9103" xml:space="preserve">Nempe BM ad CN
              <lb/>
            minorem rationem habet, quàm AB ad AC, vel BM ad CF; </s>
            <s xml:id="echoid-s9104" xml:space="preserve">quia
              <lb/>
            CN &</s>
            <s xml:id="echoid-s9105" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s9106" xml:space="preserve">CF.</s>
            <s xml:id="echoid-s9107" xml:space="preserve">‖ Hoc de circulis, & </s>
            <s xml:id="echoid-s9108" xml:space="preserve">aliis curvis ſpeciatim reperiatur
              <lb/>
            paſſim oſtenſum.</s>
            <s xml:id="echoid-s9109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9110" xml:space="preserve">Ad ſequentia notandum, quod ſi recta tranſverſim & </s>
            <s xml:id="echoid-s9111" xml:space="preserve">parallelωs
              <lb/>
            mota retrogradè (à D puta verſus A per DA) moveri concipiatur,
              <lb/>
            ab aliquo curvæ propoſitæ puncto, velut O, incipiens; </s>
            <s xml:id="echoid-s9112" xml:space="preserve">eâdemque ſem-
              <lb/>
            per ratione dictum punctum ab O aſcendens quoad velocitatem de-
              <lb/>
            creſcat, quâ ad ipſum O deſcendens increverat, eadem curva pro-
              <lb/>
            ducetur. </s>
            <s xml:id="echoid-s9113" xml:space="preserve">Quidni? </s>
            <s xml:id="echoid-s9114" xml:space="preserve">Cùm idem motus ſit, inversè tantum conſide-
              <lb/>
            ratus.</s>
            <s xml:id="echoid-s9115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9116" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s9117" xml:space="preserve">Supponatur rectam lineam TMS propoſitam curvam in
              <lb/>
            puncto M tangere (ſic ut eam nempe non ſecet) occurrátque tangens
              <lb/>
            hæc rectæ AZ in T, ducatúrque per M recta PMG ad AY parallela;
              <lb/>
            </s>
            <s xml:id="echoid-s9118" xml:space="preserve">dico velocitatem puncti deſcendentis, e
              <unsure/>
            óque motu curvam deſcriben-
              <lb/>
            tis, quam habet ad contactum M, æquari velocitati, quâ recta
              <lb/>
            TP deſcribetur uniformiter eodem tempore, quo recta AZ </s>
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