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

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            <s xml:id="echoid-s9015" xml:space="preserve">I. </s>
            <s xml:id="echoid-s9016" xml:space="preserve">Hoc modo (per motum nempe tranſverſum uniformem, & </s>
            <s xml:id="echoid-s9017" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">Fig. 19.</note>
            deſcenſivum continuo creſcentem) progenita linea per omnes ſui partes
              <lb/>
            curva evadet.</s>
            <s xml:id="echoid-s9018" xml:space="preserve">‖ Accipiantur enim in ipſa tria quælibet puncta M,
              <lb/>
            N, O; </s>
            <s xml:id="echoid-s9019" xml:space="preserve">per quæ tranſeant BZ, CZ, DZ ad AZ parallelæ, & </s>
            <s xml:id="echoid-s9020" xml:space="preserve">per
              <lb/>
            puncta M, N ducatur recta MNK. </s>
            <s xml:id="echoid-s9021" xml:space="preserve">Et quia recta MN gignitur è
              <lb/>
            motu compoſito tranſverſo per BC (vel huic parallelam MG) & </s>
            <s xml:id="echoid-s9022" xml:space="preserve">
              <lb/>
            deſcendente per AZ, uniformi utroque; </s>
            <s xml:id="echoid-s9023" xml:space="preserve">tranſverſus autem per MG
              <lb/>
            eſt prorſus idem cum tranſverſo, quo linea propoſita MNO de-
              <lb/>
            ſcribitur; </s>
            <s xml:id="echoid-s9024" xml:space="preserve">patet velocitatem deſcendentis motûs uniformis rectam MN
              <lb/>
            gignentis minorem eſſe velocitate, quam motus itidem deſcendens,
              <lb/>
            lineam MNO deſcribens, habet in N (etenim niſi motus hic velo-
              <lb/>
            cior jam ſit illo, cùm continuò creſcere ponatur, in toto tempore
              <lb/>
            deſcenſus per GN illo tardior fuiſſet, adeóque nunquam eodem tem-
              <lb/>
            pore ſpatium æquale tranſegiſſet, nec unà cum eo pertigiſſet ad
              <lb/>
            punctum N) ergò motus hîc inæqualis & </s>
            <s xml:id="echoid-s9025" xml:space="preserve">increſcens per tempus
              <lb/>
            motûs uniformis CD continuatus (quo nempe gignitur linea NO)
              <lb/>
            majus ſpatium emetitur, quàm uniformis motus deſcendens, quo
              <lb/>
            MN. </s>
            <s xml:id="echoid-s9026" xml:space="preserve">ad K protractus deſcribitur, eodem tempore CD; </s>
            <s xml:id="echoid-s9027" xml:space="preserve">(liquet
              <lb/>
            enim eodem tempore à majore vi creſcente majus ſpatium peragi, quàm
              <lb/>
            à minore neutiquam creſcente) quare linea HO major eſt quàm HK;
              <lb/>
            </s>
            <s xml:id="echoid-s9028" xml:space="preserve">adeóque tria puncta M, N, O non exiſtunt in eadem recta linea; </s>
            <s xml:id="echoid-s9029" xml:space="preserve">
              <lb/>
            quod cùm tribus quibuſvis lineæ MNO punctis conveniat, abunde
              <lb/>
            patet eam eſſe nullibi rectam, ſed per omnes ſui partes incurvatam, & </s>
            <s xml:id="echoid-s9030" xml:space="preserve">
              <lb/>
            inflexam.</s>
            <s xml:id="echoid-s9031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9032" xml:space="preserve">II. </s>
            <s xml:id="echoid-s9033" xml:space="preserve">Hinc emergit _Corollarium_; </s>
            <s xml:id="echoid-s9034" xml:space="preserve">velocitas motûs uniformis deſcen-
              <lb/>
            dentis, quo curvæ MNO ſubtenſa quævis (ut MN) deſcribitur,
              <lb/>
            exiſtente ſcilicet communi tranſverſo motu uniformi quo ipſa, ejúſque
              <lb/>
            arcus fiunt, minor eſt velocitate, quàm motus deſcenſivus increſcens
              <lb/>
            habet ad communem utriuſque terminum N.</s>
            <s xml:id="echoid-s9035" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9036" xml:space="preserve">III. </s>
            <s xml:id="echoid-s9037" xml:space="preserve">Hujuſce curvæ _ſubtenſa_ quælibet (ut MO) intra _ſuum arcum_
              <lb/>
            (verſus partes AZ) tota cadit, & </s>
            <s xml:id="echoid-s9038" xml:space="preserve">producta tota cadit extra lineam
              <lb/>
            MNO.</s>
            <s xml:id="echoid-s9039" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9040" xml:space="preserve">Nam ſi ſumatur in arcu MO punctum quodvis N, & </s>
            <s xml:id="echoid-s9041" xml:space="preserve">connectantur
              <lb/>
              <note position="left" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">Elem. III. 2.
                <lb/>
              Apoll. I.
                <lb/>
              Seren. I. 8.</note>
            rectæ MN, NO liquet totam MO intra rectas MN, NO jacere,
              <lb/>
            & </s>
            <s xml:id="echoid-s9042" xml:space="preserve">proinde intra curvam MNO. </s>
            <s xml:id="echoid-s9043" xml:space="preserve">Tota verò, ſi producatur, extra
              <lb/>
            lineam MNO cadit, quia nuſquam alibi ei occurrit, utì mox oſtenſum.</s>
            <s xml:id="echoid-s9044" xml:space="preserve">‖</s>
          </p>
          <p>
            <s xml:id="echoid-s9045" xml:space="preserve">Hoc accidens de circulo ſpeciatim demonſtrat _Euclides, de ſectionibus_
              <lb/>
            conicis Apollenius; </s>
            <s xml:id="echoid-s9046" xml:space="preserve">de cylindricis Serenus
              <unsure/>
            .</s>
            <s xml:id="echoid-s9047" xml:space="preserve"/>
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