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

Table of Notes

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            <s xml:id="echoid-s9048" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s9049" xml:space="preserve">Patet curvam propoſitam eſſe convexam, aut concavam ad
              <lb/>
            eaſdem partes (convexam verſus partes ſuperiores vel exteriores AY,
              <lb/>
            concavam introrſum, aut deorſum verſus AZZ) nam hoc ipſum,
              <lb/>
            fore convexum aut concavum ad eaſdem partes, nil omnino deſignat
              <lb/>
            aliud, quàm à nulla recta linea præterquam duobus punctis ſecari;
              <lb/>
            </s>
            <s xml:id="echoid-s9050" xml:space="preserve">nec aliò recidit, quam initio libri de ſphæra & </s>
            <s xml:id="echoid-s9051" xml:space="preserve">cylindro tradit _Ar-_
              <lb/>
            _chimedes,_ lineæ ad eaſdem partes cavæ definitio. </s>
            <s xml:id="echoid-s9052" xml:space="preserve">Perſpicuum eſt
              <lb/>
            v. </s>
            <s xml:id="echoid-s9053" xml:space="preserve">g. </s>
            <s xml:id="echoid-s9054" xml:space="preserve">ut linea MN duobus in punctis M, N curvam MNO ſecans ei
              <lb/>
            rurſus occurrat, ut puta in K, debere curvam MNO reflecti, ver-
              <lb/>
            ſùſque partes AY recurvari; </s>
            <s xml:id="echoid-s9055" xml:space="preserve">id quod modò demonſtratum eſt non
              <lb/>
            poſſe contingere. </s>
            <s xml:id="echoid-s9056" xml:space="preserve">Quapropter ipſa linea verſus eaſdem partes con-
              <lb/>
            vexa eſt, ſeu concava.</s>
            <s xml:id="echoid-s9057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9058" xml:space="preserve">V. </s>
            <s xml:id="echoid-s9059" xml:space="preserve">Apertiſſimè conſtat lineas quaſvis rectas (ut BZ, CZ) gene-
              <lb/>
            trici AZ parallelas propoſitam curvam ſecare (modò contineantur
              <lb/>
            intra terminos motûs per AY; </s>
            <s xml:id="echoid-s9060" xml:space="preserve">quia curva per harum quamvis inde-
              <lb/>
            finitè promotam deſcripta cenſetur) addo quod harum quælibet cur-
              <lb/>
            vam in uno tantùm puncto ſecat.</s>
            <s xml:id="echoid-s9061" xml:space="preserve">‖ Id patet, quia recta genetrix
              <lb/>
            AZ per unicum duntaxat inſtans temporis durat in ſitu quovis uno,
              <lb/>
            ſeu BZ; </s>
            <s xml:id="echoid-s9062" xml:space="preserve">ſimúlque pertingit ipſam BZ, ac deſerit; </s>
            <s xml:id="echoid-s9063" xml:space="preserve">prætérque
              <lb/>
            punctum unum M in BMZ reliqua cuncta lineæ curvæ puncta ſunt
              <lb/>
              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">Apoll. I. 26.
                <lb/>
              Arch. de Con
                <unsure/>
              @id.
                <lb/>
              & Sph. 16.</note>
            in parallelis ad BZ. </s>
            <s xml:id="echoid-s9064" xml:space="preserve">Ergò liquidum eſt ipſam BZ in uno tantùm
              <lb/>
            puncto curvam ſecare.</s>
            <s xml:id="echoid-s9065" xml:space="preserve">‖ Hocipſum de parabola, & </s>
            <s xml:id="echoid-s9066" xml:space="preserve">hiperbola ſpecia-
              <lb/>
            tim oſtendit _Apollonius_; </s>
            <s xml:id="echoid-s9067" xml:space="preserve">de ſectionibus conoideon _Arcbimedes_.</s>
            <s xml:id="echoid-s9068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9069" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s9070" xml:space="preserve">Non diſſimili modo patet ad AY parallelam quamvis, (qualis
              <lb/>
            PG) unico puncto propoſitam curvam attingere.</s>
            <s xml:id="echoid-s9071" xml:space="preserve">‖ Quòd ſemel
              <lb/>
            occurret (modò contineatur intra limites deſcensûs per AZ) patet,
              <lb/>
            quia punctum mobile continuò deſcendens, indefinito progreſſu, eam
              <lb/>
            indefinitè protenſam aliquando trajiciet; </s>
            <s xml:id="echoid-s9072" xml:space="preserve">nec in eo tamen præterquam
              <lb/>
              <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">I. 19.</note>
            ad unum temporis momentum perdurat.</s>
            <s xml:id="echoid-s9073" xml:space="preserve">‖ Videatur hoc de ſectioni-
              <lb/>
            bus conicis oſtendens _Apollonius_.</s>
            <s xml:id="echoid-s9074" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9075" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s9076" xml:space="preserve">Patet omnes curvæ ſubtenſas rectas cum AZ & </s>
            <s xml:id="echoid-s9077" xml:space="preserve">ei parallelis,
              <lb/>
            ſi producantur, concurrere.</s>
            <s xml:id="echoid-s9078" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9079" xml:space="preserve">Quòd enim ſubtenſa quævis, ut MN, uni parallelarum alicui, ut
              <lb/>
            BR, occurrit, ibi ſcilicet ubi ipſa curvam ſecat, exinde manifeſtiſſimum
              <lb/>
            eſt, quòd tota curva per parallelum dictæ rectæ motum deſcribitur.
              <lb/>
            </s>
            <s xml:id="echoid-s9080" xml:space="preserve">Ergò, cùm uni occurrat, omnibus occurret; </s>
            <s xml:id="echoid-s9081" xml:space="preserve">quæ enim uni </s>
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