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-s8513" xml:space="preserve">
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            ſtantaneus, eò recurrendum ut per inſtantias nil aliud, quàm inde-
              <lb/>
            finitas temporis particulas intelligamus; </s>
            <s xml:id="echoid-s8514" xml:space="preserve">quibus reſpondeant certo
              <lb/>
            velocitatis gradu, alio atque alio, percurſa indefinitè minuta ſpatiola
              <lb/>
            velocitatis gradibus adproportionata; </s>
            <s xml:id="echoid-s8515" xml:space="preserve">tum autem repræſentando
              <lb/>
            ſingulo cuipiam velocitatis gradui per tempuſculum aliquod retento,
              <lb/>
            loco lineæ rectæ ſubſtituatur oportet exiguum rectangulum dicto tem-
              <lb/>
            puſculo applicatum. </s>
            <s xml:id="echoid-s8516" xml:space="preserve">Perinde fuerit, ac eodem recidet hoc an illo
              <lb/>
            modo ſe res habeat, aſt ſimplicior & </s>
            <s xml:id="echoid-s8517" xml:space="preserve">clarior videtur iſte modus, quem
              <lb/>
            priùs expoſuimus, cui proinde poſthac inſiſtemus. </s>
            <s xml:id="echoid-s8518" xml:space="preserve">Ut redeam, & </s>
            <s xml:id="echoid-s8519" xml:space="preserve">
              <lb/>
            recolligam; </s>
            <s xml:id="echoid-s8520" xml:space="preserve">ſicuti per omnia lineæ rectæ puncta traduci poſſunt pa-
              <lb/>
            rallelæ rectæ, magnitudine pro lubitu pares, vel impares, è qui-
              <lb/>
            bus aggregatis ſuperficiale planum exurgat, ità ad ſingula temporis
              <lb/>
            inſtantia applicari poſſunt velocitatis gradus diverſi, pares vel impares,
              <lb/>
            prout mobile per totam ſuam lationem vel eundem impetum retmere,
              <lb/>
            vel aliquando varium adſciſſere ſupponatur, utcunque creſcendo vel
              <lb/>
            decreſcendo. </s>
            <s xml:id="echoid-s8521" xml:space="preserve">Si velocitatem ſemper eandem conſervare dicatur, fa-
              <lb/>
            cilè patet è dictis velocitatem aggregatam definito cuivis tempori con-
              <lb/>
            venientem rectiſſimè per figuram parallelogrammam exprimi, qua-
              <lb/>
              <note position="left" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">Fig. I.</note>
            lis eſt AZZE, in qua latus AE temporis deſiniti vicem obit, re-
              <lb/>
            liquum AZ, eíque parallelæ rectæ omnes BZ, CZ, DZ, EZ
              <lb/>
            velocitatis gradus ſingulos per ſingula temporis momenta penetrantes,
              <lb/>
            in hoc ſcilicet caſu pares, exhibent. </s>
            <s xml:id="echoid-s8522" xml:space="preserve">Poſſunt etiam, ut dictum, pa-
              <lb/>
            rallelogramma AZZB, AZZC, AZZD, AZZE ſpatia re-
              <lb/>
            ſpectivis temporibus AB, AC, AD, AE decurſa appoſitè deſignare.
              <lb/>
            </s>
            <s xml:id="echoid-s8523" xml:space="preserve">E qua conſideratione ſola, vel intuitu primo motûs hujuſmodi, quem
              <lb/>
            æquabilem, & </s>
            <s xml:id="echoid-s8524" xml:space="preserve">uniformem vocitant, omnia ſymptomata deduci
              <lb/>
            poſſunt. </s>
            <s xml:id="echoid-s8525" xml:space="preserve">Quales ſunt: </s>
            <s xml:id="echoid-s8526" xml:space="preserve">quòd æquali perpetuò velocitate tranſmiſſa
              <lb/>
            ſpatia ſeſe habent ut tempora: </s>
            <s xml:id="echoid-s8527" xml:space="preserve">Quod æquali tempore peracta
              <lb/>
            ſpatia ſeſe habent ut velocitates; </s>
            <s xml:id="echoid-s8528" xml:space="preserve">& </s>
            <s xml:id="echoid-s8529" xml:space="preserve">viciſſim: </s>
            <s xml:id="echoid-s8530" xml:space="preserve">Si ſpatia ſunt ut
              <lb/>
            velocitates tempora fore æqualia; </s>
            <s xml:id="echoid-s8531" xml:space="preserve">ſi ut tempora, velocitates
              <lb/>
            æquari. </s>
            <s xml:id="echoid-s8532" xml:space="preserve">Et ſi æqualia ſpatia fuerint, tempora velocitatibus propor-
              <lb/>
            tione reciprocari; </s>
            <s xml:id="echoid-s8533" xml:space="preserve">contráque, ſi tempora velocitatibus proportione
              <lb/>
            reciprocentur, ſpatia ſibimet exæquari. </s>
            <s xml:id="echoid-s8534" xml:space="preserve">Spatia denique quælibet
              <lb/>
            compoſitam habere rationem è rationibus velocitatum & </s>
            <s xml:id="echoid-s8535" xml:space="preserve">temporum; </s>
            <s xml:id="echoid-s8536" xml:space="preserve">
              <lb/>
            nec non, ſubducendo rationem temporum è ratione ſpatiorum reſiduam
              <lb/>
            manere rationem velocitatum; </s>
            <s xml:id="echoid-s8537" xml:space="preserve">vel ſubducendo rationem velocitatum
              <lb/>
            relinqui rationem temporum. </s>
            <s xml:id="echoid-s8538" xml:space="preserve">Hæc enim parallelogrammorum inter
              <lb/>
            ſe comparatorum aſſectiones ſunt (æquiangulorum intelligo paralle-
              <lb/>
            logrammorum; </s>
            <s xml:id="echoid-s8539" xml:space="preserve">nam ubi repræſentativa, hæc parallelogramma con-
              <lb/>
            feruntur inter ſe, æquiangula conſtituantur oportet; </s>
            <s xml:id="echoid-s8540" xml:space="preserve">alioqui </s>
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