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-s8495" xml:space="preserve">
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            velocitatis hic gradus præcedentem. </s>
            <s xml:id="echoid-s8496" xml:space="preserve">Quum enim temporis inſtantia
              <lb/>
            prorſus æqualia ſint inter ſe, ſpatialium longitudinum ratio à ſola
              <lb/>
            velocitatem ratione dependebit, eíque proinde par erit, aut ſimilis
              <lb/>
            (quod niſi pro veriſſimo ſumatur, haud ullo modo menſurari poſſit
              <lb/>
            velocitas; </s>
            <s xml:id="echoid-s8497" xml:space="preserve">nam à ſola ſpatiorum eodem tempore decurſorum (vel
              <lb/>
            eodem inſtanti) proportione velocitatum inter ſe collatarum imme-
              <lb/>
            diatè vel mediatè ratio taxatur, & </s>
            <s xml:id="echoid-s8498" xml:space="preserve">altera alterius reſpectu denomi-
              <lb/>
            natur tanta) ſimiliter ſi per omnia temporis cujuſvis momenta qui
              <lb/>
            conveniunt ipſis velocitatis gradus aſſignentur, aggregabitur ex iis
              <lb/>
            quantum quiddam, cujus partibus quibuſvis decurſorum ſpatiorum
              <lb/>
            partes reſpectivæ, hoc eſt iiſdem temporibus reſpondentes particulæ,
              <lb/>
            juſtè proportionantur, adeóque quantum è gradibus iſtis conſtans
              <lb/>
            repræſentans magnitudo ſpatium quoque decurſum repræſentare poſſit;
              <lb/>
            </s>
            <s xml:id="echoid-s8499" xml:space="preserve">quatenus nempe qualem ſpatii partes temporibus ſingulis peractæ pro-
              <lb/>
            portionem inter ſe ſervant, exactè referat. </s>
            <s xml:id="echoid-s8500" xml:space="preserve">Quum igitur, utpote
              <lb/>
            quàm æquabiliſſimè ſluens per lineam, ut præmonuimus, rectam ap-
              <lb/>
            tiſſimè repræſentetur, & </s>
            <s xml:id="echoid-s8501" xml:space="preserve">qui in ſingulis temporis inſtantibus haben-
              <lb/>
            tur alii ac alii, ſibimet æquales; </s>
            <s xml:id="echoid-s8502" xml:space="preserve">aut inæquales, velocitatis gradus per
              <lb/>
            lineas itidem, ut priùs etiam inſinuatum eſt, rectas exprimantur,
              <lb/>
            & </s>
            <s xml:id="echoid-s8503" xml:space="preserve">cùm hi velocitatis gradus ſingula temporis momenta alii ac alii
              <lb/>
            permeent, independentèr à ſe invicem ac impermixtè; </s>
            <s xml:id="echoid-s8504" xml:space="preserve">itaque ſi per
              <lb/>
            lineæ tempus repræſentantis omnia puncta trajiciantur rectæ ſic
              <lb/>
            diſpoſitæ, ut altera nulla nulli alteri coïncidat, hoc eſt in ſitu pa-
              <lb/>
            rallelo; </s>
            <s xml:id="echoid-s8505" xml:space="preserve">quæ reſultat hinc ſuperficies plana (pro quantitate temporis,
              <lb/>
            & </s>
            <s xml:id="echoid-s8506" xml:space="preserve">poſitorum velocitatis graduum ratione determinata) graduum ve-
              <lb/>
            locitatis aggregatum exactiſſimè referet; </s>
            <s xml:id="echoid-s8507" xml:space="preserve">cujus ſuperficiei partes cùm
              <lb/>
            reſpectivis (ut prædictum) ſpatii peracti partibus proportionales
              <lb/>
            ſint, poterit id ſpatio quoque repræſentando commodiſſimè adaptari. </s>
            <s xml:id="echoid-s8508" xml:space="preserve">
              <lb/>
            Iſta verò ſuperficies brevitatis causâ dehinc appellabitur velocitas ag-
              <lb/>
            gregata, vel ſpatii repræſentativa. </s>
            <s xml:id="echoid-s8509" xml:space="preserve">Neque quenquam aſſiciat, nam
              <lb/>
            ſubmovenda nobis hæc remora, quod diximus in ſingulis temporis
              <lb/>
            inſtantibus longitudinem aliquam confici, quaſi dari poſſe motum
              <lb/>
            inſtantaneum aſſirmarem. </s>
            <s xml:id="echoid-s8510" xml:space="preserve">Nam poſito tempora è momentis com-
              <lb/>
            poni, etiam lineæ componentur è punctis; </s>
            <s xml:id="echoid-s8511" xml:space="preserve">quòd ſi lineæ inæ-
              <lb/>
            quales componantur è punctis infinitis, ſibimet æquinume-
              <lb/>
            ris, neceſſariò ſequitur linearum puncta, juxta ſimilem cum ipſis
              <lb/>
            proportionem inæqualia fore, adeóque per longitudines in æquitem-
              <lb/>
            poraneìs momentis decurſas duntaxat intelligenda ſunt ejuſmodi inæ-
              <lb/>
            qualia puncta, è quibus tota decurſa longitudo quaſi conſlatur. </s>
            <s xml:id="echoid-s8512" xml:space="preserve">Sin
              <lb/>
            hoc abſonum cuipiam videatur, & </s>
            <s xml:id="echoid-s8513" xml:space="preserve">nullo ſenſu motus admittatur </s>
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