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-s8477" xml:space="preserve">
              <pb o="8" file="0186" n="201" rhead=""/>
            gularem velocitatis cujuſpiam quantitatem nec ex ſola confecti ſpatii, nec
              <lb/>
            ex abſumpti temporis quantitate dignoſci poſle (quælibet enim velocitas
              <lb/>
            aliquo tempore quodvis aſſignatum ſpatium emetiatur) aſt ex ſpatii
              <lb/>
            ſimul ac temporis quantitatibus ad calculum redactis eam innoteſcere;
              <lb/>
            </s>
            <s xml:id="echoid-s8478" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s8479" xml:space="preserve">viciſſim temporis abſumpti quantitas non niſi ſpatii ſimul ac
              <lb/>
            velocitatis agnitis quantitatibus determinetur. </s>
            <s xml:id="echoid-s8480" xml:space="preserve">Quinimo ſpati quo-
              <lb/>
            que quantitas (quatenus hoc modo per motum dignoſcibilis eſt) nec
              <lb/>
            è ſola definitæ velocitatis quantitate, nec ab aſſignato tanto tempore
              <lb/>
            dependet, aſt ab utriuſque ratione conjuncta. </s>
            <s xml:id="echoid-s8481" xml:space="preserve">Et quidem ut hæc quo-
              <lb/>
            modo @e reſpiciant amplius exponamus, ſpatii quatenus hoc modo
              <lb/>
            computatur quantitas eo ferè dignoſcitur modo, quo è dimenſionibus
              <lb/>
            ſuis quanta ſit ſuperficies innoteſcit; </s>
            <s xml:id="echoid-s8482" xml:space="preserve">è quantitate ſcilicet unius lineæ,
              <lb/>
            (quæ longitudinem ejus aut altitudinem oſtentat) & </s>
            <s xml:id="echoid-s8483" xml:space="preserve">è quantitatibus
              <lb/>
            ſingularum invicem ſibi parallelarum linearum, quæ per iſtius lineæ
              <lb/>
            puncta quæque tranſeuntes ſuperficiem totam quodammodo conſti-
              <lb/>
            tuunt, & </s>
            <s xml:id="echoid-s8484" xml:space="preserve">componunt; </s>
            <s xml:id="echoid-s8485" xml:space="preserve">eam ſa@tem limitant atque determinant; </s>
            <s xml:id="echoid-s8486" xml:space="preserve">hoc
              <lb/>
            eſt quaſi per ductum ſingularum ejuſmodi linearum in reſpectiva
              <lb/>
            dictæ lineæ puncta. </s>
            <s xml:id="echoid-s8487" xml:space="preserve">Velocitatis autem, & </s>
            <s xml:id="echoid-s8488" xml:space="preserve">temporis quantitates
              <lb/>
            pariter eo modo diſcernuntur, quo ex ſuperficiei, & </s>
            <s xml:id="echoid-s8489" xml:space="preserve">unius cui appli-
              <lb/>
            catur dimenſionis quantitate diſcernitur quanta ſit reliqua dimenſio
              <lb/>
            (ubivis, inquam, aut ſaltem alicubi quanta, nam fieri poteſt ut re-
              <lb/>
            liqua dimenſio quatenus per omnia prioris dimenſionis puncta diſſundi-
              <lb/>
            tur, ſibi paſſim diſpar & </s>
            <s xml:id="echoid-s8490" xml:space="preserve">diſſormis ſit; </s>
            <s xml:id="echoid-s8491" xml:space="preserve">quid velim è veſtigio conſtabit,
              <lb/>
            nam utilis hæc conſideratio poſtulat enucleatiùs declarari. </s>
            <s xml:id="echoid-s8492" xml:space="preserve">Omni
              <lb/>
            temporis inſtanti, ſeu indefinitè parvæ temporis particulæ (inſtanti
              <lb/>
            dico, vel indefinitæ particulæ, nam utì nihil admodum refert, utrum
              <lb/>
            lineam ex innumeris punctis, an ex indefinitè parvis lineolis compo-
              <lb/>
            ſitam intelligamus, ita perinde eſt, utrum tempus ex inſtantibus,
              <lb/>
            an ex innumeris minutis tempuſculis conſlatum ſupponamus; </s>
            <s xml:id="echoid-s8493" xml:space="preserve">nos ſal-
              <lb/>
            tem brevitati conſulentes pro temporibus quantumlibet exiguis in-
              <lb/>
            ſtantia, hoc eſt pro tempuſcula repræſentantibus lineolis puncta non
              <lb/>
            verebimur uſurpare) cuilibet dico temporis momento competit velo-
              <lb/>
            citatis aliquis gradus, quem mobile tunc habere concipiendum eſt; </s>
            <s xml:id="echoid-s8494" xml:space="preserve">
              <lb/>
            cui gradui reſpondet aliqua decurſi ſpatii longitudo (nam hìc mobile
              <lb/>
            tanquam punctum, & </s>
            <s xml:id="echoid-s8495" xml:space="preserve">ſpa tium proinde tantummodò ceu longum
              <lb/>
            conſideramus) quia veròtemporis momenta quoad rem ipſam neuti-
              <lb/>
            quam à ſe dependent, ſupponi poterit in proximo inſtanti mobile
              <lb/>
            gradum velocitatis alium (alium inquam vel æqualem priori, vel in
              <lb/>
            quavis proportione diverſum) admittere, cui proinde reſpondebit
              <lb/>
            alia ſpatii longitudo, tali proportione reſpiciens priorem, </s>
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