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-s8709" xml:space="preserve">
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            majore AABB detrahatur minor circulus concentricus EEEE. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">E
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            qua geneſi colligitur circulorum, & </s>
            <s xml:id="echoid-s8711" xml:space="preserve">ſectorum circularium areas, è
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            circularibus peripheriis, integris aut partialibus concentricis ac ſimili-
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            bns, conſtare tot numero qu
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            ot radius puncta habet; </s>
            <s xml:id="echoid-s8712" xml:space="preserve">quarum proinde
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            calculum ineundo circularis areæ talis qualis dimenſio quam facillimè
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            reperitur; </s>
            <s xml:id="echoid-s8713" xml:space="preserve">id quod non eſt hujus temporis ulteriùs exponere. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">Quin-
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            etiam ſupponunt lineam quamvis rectam, indeſinitè protenſam, uno
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            manente fixo ipſius puncto circa deſignatam quamvis in alio plano
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            conſtitutam lineam, curvam aut è rectis compoſitam, revolvi, ſic ut
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            ei nempe lineæ ſemper inſiſtat, vel eam quaſi lambat, aut perſtringat.
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            </s>
            <s xml:id="echoid-s8715" xml:space="preserve">
              <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">Fig. 8.</note>
            Sit, exempli causâ, linea recta AB indefinitè protenſa, & </s>
            <s xml:id="echoid-s8716" xml:space="preserve">in ea
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            fixum punctum V; </s>
            <s xml:id="echoid-s8717" xml:space="preserve">& </s>
            <s xml:id="echoid-s8718" xml:space="preserve">per V ſemper feratur linea AB juxta lineam
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            quamlibet BC in alio plano collocatam; </s>
            <s xml:id="echoid-s8719" xml:space="preserve">ità quidem ut aliquod lineæ
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            mobilis punctum continuò lineæ BC inhæreat; </s>
            <s xml:id="echoid-s8720" xml:space="preserve">ex hujuſmodi motu
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            producetur curva Superficies (è planis ſaltem compoſita, quam & </s>
            <s xml:id="echoid-s8721" xml:space="preserve">
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            generali ratione, poſt _Archimedem_, curvam appellare nil vetat)
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            quæ quidem ſi linea directrix tota componatur è definitè magnis rectis
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            lineis, fiet _Superficies py@@m dalis_, è triangulis ad verticem V concur-
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            rentibus aggregata; </s>
            <s xml:id="echoid-s8722" xml:space="preserve">ſin circularis fuerit, aut conicarum ſectionum
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            aliqua, Superficies evadet ſtrictè _conica_; </s>
            <s xml:id="echoid-s8723" xml:space="preserve">ſin alterius generis aliqua,
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            conica ſaltem extenſo latiùs ſignificatu dicatur; </s>
            <s xml:id="echoid-s8724" xml:space="preserve">& </s>
            <s xml:id="echoid-s8725" xml:space="preserve">à quibuſdam di-
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            citur. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">Cujus quidem Superficiei proprietas eſt, ex ipſa generatione
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            maniſeſta, quòd ſi per fixum punctum V plano ſecetur, communis
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            plani cum ipſa ſectio erit angulus rectilineus. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">Nam ſi planum ipſam
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            ſecans per V lineæ directrici occurrat in punctis duobus, ut in D, E
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            (occurret autem in duobus, aliàs Superficiem ipſam non ſecaret) ductæ
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            rectæ VD, VE erunt tam in plano ſecante, quàm in curva Super-
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            ficie; </s>
            <s xml:id="echoid-s8728" xml:space="preserve">in plano, ex plani natura; </s>
            <s xml:id="echoid-s8729" xml:space="preserve">in Superficie, quia genetrix eadem
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            recta per harum terminos tranſit, ipsíſque proinde coincidit. </s>
            <s xml:id="echoid-s8730" xml:space="preserve">In hu-
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            juſmodi verò motu poſito quòd lineæ rectæ à puncto fixo V (ſeu ver-
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            tice) ad directricem lineam BC ductæ ſunt inæquales inter ſe, ſatìs
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            liquet lineam BC non à lineà B delineari, vel perambulari, quia
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            lineæ inæquales (ut VB, VE, VC) ſibi nequeunt congruere; </s>
            <s xml:id="echoid-s8731" xml:space="preserve">ade-
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              <note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">Fig. 8.</note>
            óque punctum B progrediens ſupra, vel infra puncta B, E, C cadet;
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            </s>
            <s xml:id="echoid-s8732" xml:space="preserve">ut nec eâdem inæqualitate ſuppoſitâ punctum quodvis aliud in VB puta
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            G) motu ſuo lineam deſcribet lineæ directrici BC ſimilem (quare
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            linea VB ſupponitur indefinitè protenſa) at verò ſi lineæ omnes, quæ
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            ab V ad BC duci poſſunt (quas Superficiei propoſitæ latera nuncu-
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            pemus licet) proportionaliter ſecentur (id quod fiet à plano per hanc
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            Superſiciem trajecto ad planum, in quo ſita eſt BC, parallelo) </s>
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