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-s8540" xml:space="preserve">
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            ſingillatim ſpectantur; </s>
            <s xml:id="echoid-s8541" xml:space="preserve">nihil refert quinam angulus ſtatuatur) hæc,
              <lb/>
            inquam, è parallelogrammorum natura liquent, & </s>
            <s xml:id="echoid-s8542" xml:space="preserve">ex iis quæ
              <lb/>
            poſuimus ſponte conſectantur; </s>
            <s xml:id="echoid-s8543" xml:space="preserve">ut nullam aliam demonſtrationem re-
              <lb/>
            quirere videantur. </s>
            <s xml:id="echoid-s8544" xml:space="preserve">Et ſanè quoad omnes Mathematicæ {ακ}
              <unsure/>
            @ψΗ
              <unsure/>
            ſubditas
              <lb/>
            (hoc eſt utcunque quantitatem involventes) materias cùm magnâ fa-
              <lb/>
            cilitate Theoremata perſpicere, tum ſummo eadem compendio de-
              <lb/>
            monſtrare poterit, quiſquis contemplationi ſuæ ſubjecta cujuſcunque
              <lb/>
            generis quanta ad analogicas magnitudines ritè congruéque novit re-
              <lb/>
            digere. </s>
            <s xml:id="echoid-s8545" xml:space="preserve">Quòd ſi porrò velocitatis gradus continuò per ſingula tempo-
              <lb/>
            ris inſtantia ſupponantur æqualiter adaugeri, vel imminui, à gradu
              <lb/>
            minimo, ſeu quiete, definitum ad velocitatis gradum, vel à definito
              <lb/>
            tali gradu ad quietem; </s>
            <s xml:id="echoid-s8546" xml:space="preserve">conſimili pacto poterit aggregata velocitas per
              <lb/>
            quamvis ſuperficiem æqualiter à puncto creſcentem ad definitam mag-
              <lb/>
            nitudine lineam; </s>
            <s xml:id="echoid-s8547" xml:space="preserve">vel eodem retrogradè paſſu decreſcentem, exhiberi;
              <lb/>
            </s>
            <s xml:id="echoid-s8548" xml:space="preserve">ſimpliciſſimè verò, & </s>
            <s xml:id="echoid-s8549" xml:space="preserve">optimè per triangulum rectilineum; </s>
            <s xml:id="echoid-s8550" xml:space="preserve">ut puta per
              <lb/>
            triangulum AEY, in quo crus AE tempus denotat; </s>
            <s xml:id="echoid-s8551" xml:space="preserve">ejúſque punctis
              <lb/>
              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">Fig. I.</note>
            applicatæ lineæ parallelæ BY, CY, DY, EY gradus velocitatis ſin-
              <lb/>
            gulis inſtantibus congruos à puncto A (quod quietem, vel infimam
              <lb/>
            velocitatem refert) ad definitum gradum lineâ maximâ EY repræſen-
              <lb/>
            tatum æqualiter increſcentes; </s>
            <s xml:id="echoid-s8552" xml:space="preserve">vel ab eadem EY retrò ad punctum A
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            quietis repræſentativum declinantes. </s>
            <s xml:id="echoid-s8553" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s8554" xml:space="preserve">pari jure, quo priùs,
              <lb/>
            trigona ABY, ACY, ADY, AEY per reſpectiva ab initio tem-
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            pora decurſis ſpatiis repræſentandis inſervient. </s>
            <s xml:id="echoid-s8555" xml:space="preserve">Et conſequenter, ſi
              <lb/>
            velocitas æqualiter à definito gradu ad gradum definitum ſupponatur
              <lb/>
            augeri, vel diminui, repræſentabitur tam aggregata velocitas, quàm
              <lb/>
            ſpatium ei reſpondens à figura quadrangula Trapezia, qualis eſt CYYE,
              <lb/>
            in ſigura priùs adhibita. </s>
            <s xml:id="echoid-s8556" xml:space="preserve">Hinc, non ſecùs quàm in præcedentibus, hu-
              <lb/>
            juſmodi motûs quem uniformiter acceleratum nomine perquam apto
              <lb/>
            _Galilæus_ nuncupavit) aſſectiones omnes præcipuæ facilimè deprehen-
              <lb/>
            dentur, atque demonſtrabuntur; </s>
            <s xml:id="echoid-s8557" xml:space="preserve">cujuſmodi ſunt:</s>
            <s xml:id="echoid-s8558" xml:space="preserve">Quòd æ quali tem-
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            pore conficietur æquale ſpatium per motum à quiete uniformiter acce-
              <lb/>
            leratum, ac per ipſum motum uniformem, modò velocitas hujus ſub-
              <lb/>
            dupla ſit velocitatis, quam ille maximam habet. </s>
            <s xml:id="echoid-s8559" xml:space="preserve">Quòd ſpatia motu
              <lb/>
            à quiete uniformiter accelerato peracta, ſeſe habent ut _Quadr @ta tem-_
              <lb/>
            _porum_ (vel in duplicata temporum proportione.) </s>
            <s xml:id="echoid-s8560" xml:space="preserve">Et diverſos hoc
              <lb/>
            modo acceleratos motus comparando: </s>
            <s xml:id="echoid-s8561" xml:space="preserve">Quòd ab illis tranſacta ſpatia
              <lb/>
            habeant rationem è rationibus temporum, & </s>
            <s xml:id="echoid-s8562" xml:space="preserve">velocitatum maxima-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s8563" xml:space="preserve">Et ſimilia talia vel his connexa, vel indè conſequentia, quæ
              <lb/>
            triangulis conveniunt inter ſe quoad ſuas, & </s>
            <s xml:id="echoid-s8564" xml:space="preserve">quoad laterum rationes
              <lb/>
            comparatis; </s>
            <s xml:id="echoid-s8565" xml:space="preserve">quæ ex poſitis haud diſſicilè perſpìciantur, ac </s>
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