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-s8677" xml:space="preserve">
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            planis laterum alicui parallelis ſecentur, communes ſectiones erunt
              <lb/>
            _Parallelogramma_ (quale eſt EEBB.) </s>
            <s xml:id="echoid-s8678" xml:space="preserve">Quin, ut paucis complectar
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            multa, quæ _de Superficiebus aut Solidis Priſmaticis ac Cylindricis_
              <lb/>
            _ſtrictè dictis generatim enunciantur aut probantur uſpiam,_ quòd ea
              <lb/>
            pleraque juſtam analogiam obſervando, univerſis congruunt hoc modo
              <lb/>
            progenitis quantis. </s>
            <s xml:id="echoid-s8679" xml:space="preserve">Neque jam de progreſſivo motu quidpiam ſuccur-
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            rit adjiciendum; </s>
            <s xml:id="echoid-s8680" xml:space="preserve">quædam enim {δυ}
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            σ{δί}ήγητα conſultò videntur reticen-
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            da. </s>
            <s xml:id="echoid-s8681" xml:space="preserve">Porrò ſimplicis motûs alterum genus, quod adhibet _Matheſis,_
              <lb/>
            eſt _circumlatio, ſeu motus converſivus_; </s>
            <s xml:id="echoid-s8682" xml:space="preserve">qui tum ſcilicet efficitur, cùm
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            dimotæ magnitudinis quiddam (ut punctum aliquod puta lineæ, vel
              <lb/>
            Superficiei linea) fixum & </s>
            <s xml:id="echoid-s8683" xml:space="preserve">immotum conſiſtit, dum ei velut innodata
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            ac adſtricta tota reliqua magnitudo, juxta quamvis aſſignatam di-
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            rectionem, circumagitur. </s>
            <s xml:id="echoid-s8684" xml:space="preserve">Cujuſmodi motûs generaliſſima proprie-
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            tas eſt, ut quæque mobilis puncta dum in uno aliquo plano tranſversè
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            moventur, circulares ſingula peripherias deſcribant; </s>
            <s xml:id="echoid-s8685" xml:space="preserve">& </s>
            <s xml:id="echoid-s8686" xml:space="preserve">quidem
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            omnia, quæ in eodem uno, per fixum punctum tranſeunte plano
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            moventur parallelas, ſeu concentricas, & </s>
            <s xml:id="echoid-s8687" xml:space="preserve">ſimiles inter ſe; </s>
            <s xml:id="echoid-s8688" xml:space="preserve">quæ verò
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            in diverſis planis ſimiles, aut diſſimiles, prout hypotheſium exigit
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            arbitraria diverſitas. </s>
            <s xml:id="echoid-s8689" xml:space="preserve">Præ cæteris autem propria, maximéque na-
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            turalis eſt circumlatio, cùm ſingula mobilis puncta circulares unius
              <lb/>
            ejuſdem circuli peripherias deſcribunt, hoc eſt cùm in uno cuncta
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            plano circumferuntur; </s>
            <s xml:id="echoid-s8690" xml:space="preserve">qualem certè tum ipſa natura ſponte concipit
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            atque proſequitur, cùm nè rectos ſuos quos præſertim aſſectat motus
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            exequatur ab immobili retinaculo prohibere; </s>
            <s xml:id="echoid-s8691" xml:space="preserve">velut in pendulorum,
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            & </s>
            <s xml:id="echoid-s8692" xml:space="preserve">libris appenſorum motibus videre eſt; </s>
            <s xml:id="echoid-s8693" xml:space="preserve">imò cùm objectâ quâvis
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            reſiſtentiâ non ſatìs facilè recto tramiti valet in@ærere; </s>
            <s xml:id="echoid-s8694" xml:space="preserve">ſicut in _rota-_
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            _rum, & </s>
            <s xml:id="echoid-s8695" xml:space="preserve">vorticum, & </s>
            <s xml:id="echoid-s8696" xml:space="preserve">turbinum, & </s>
            <s xml:id="echoid-s8697" xml:space="preserve">in ipſorum fortaſſe ſyderum_,
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            _motibuus adparet_. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">Verùm hujuſmodi motuum generalem indolem
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            haud ità promptum eſt verbis explicare. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">Præſtat ipſas quas accipiunt
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            præcipuas hypotheſes percenſere. </s>
            <s xml:id="echoid-s8700" xml:space="preserve">Aſſumunt primo rectam lineam in
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            plano circa punctum quodvis in ipſa fixum poſſe circumferri; </s>
            <s xml:id="echoid-s8701" xml:space="preserve">cujuſ-
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            modi motu patet omnia lineæ motæ puncta circulares peripherias de-
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            ſcribere; </s>
            <s xml:id="echoid-s8702" xml:space="preserve">ſingulas ab uno quovis deſcriptas ſingulis ab altero quolibet
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            ſimul eodem tempore deſcriptis parallelas, & </s>
            <s xml:id="echoid-s8703" xml:space="preserve">ſimiles. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">Ut ſi linea
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            recta AB manente fixo puncto C circumferatur, ſingula puncta A,
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              <note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">Fig. 7</note>
            E, B peripherias circulares AA, EE, BB ſibi parallelas, & </s>
            <s xml:id="echoid-s8705" xml:space="preserve">ſimiles
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            omnes (iiſdem nimirum, aut æqualibus angulis ſubtenſas, quorum
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            commune centrum, aut vertex C) deſcribent. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">Hoc autem modo
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            conſtat procreari circulos, & </s>
            <s xml:id="echoid-s8707" xml:space="preserve">ſectorum circulares areas (quales ACA,
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            BCB,) ſed & </s>
            <s xml:id="echoid-s8708" xml:space="preserve">annulos planos; </s>
            <s xml:id="echoid-s8709" xml:space="preserve">qualis eſt is qui reſtat, ſi è </s>
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