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-s8954" xml:space="preserve">
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            diverſitatem alterius diverſitas ritè conſequatur accommodeturque.
              <lb/>
            </s>
            <s xml:id="echoid-s8955" xml:space="preserve">U
              <unsure/>
            t e. </s>
            <s xml:id="echoid-s8956" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8957" xml:space="preserve">ſi recta ZA ſemper per rectam AY ſibi parallela feratur
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            motu quolibet uniformi, vel difformi (creſcente, vel decreſcente
              <lb/>
            vel alternante ſecundum velocitatem, juxta rationem quamvis ima-
              <lb/>
            ginabilem) et in ea punctum aliquod M deferatur, ità tamen ut
              <lb/>
            puncti motus lineæ rectæ motibus per ſingulas quasque temporis
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            partes eaſdem proportionentur, producetur utique linea recta. </s>
            <s xml:id="echoid-s8958" xml:space="preserve">Nem-
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            pe ſi fuerit ſemper AB. </s>
            <s xml:id="echoid-s8959" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s8960" xml:space="preserve">: BM. </s>
            <s xml:id="echoid-s8961" xml:space="preserve">Cμ. </s>
            <s xml:id="echoid-s8962" xml:space="preserve">vell
              <unsure/>
            AB, MX:</s>
            <s xml:id="echoid-s8963" xml:space="preserve">: AM,
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            X μ (poſitâ ſcilicet MX ad AC parallelâ) liquet puncta A, M
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            μ in una recta verſari. </s>
            <s xml:id="echoid-s8964" xml:space="preserve">Eſt enim rectæ lineæ proprietas in Ele-
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              <note position="left" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">Fig. 17.</note>
            mento VI. </s>
            <s xml:id="echoid-s8965" xml:space="preserve">demonſtrata, quòd ad eam parallelωs applicatæ rectæ
              <lb/>
            lineæ ſuis ad deſignatum in ea punctum diſtantiis proportionales in
              <lb/>
            rectam lineam terminantur. </s>
            <s xml:id="echoid-s8966" xml:space="preserve">Quòd ſi motus hi ſic inter ſe contem-
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            perentur, ut aſſumptâ quâdam lineâ D habeat rectangulum ex diffe-
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            rentia lineæ D, & </s>
            <s xml:id="echoid-s8967" xml:space="preserve">ipſius BM (à puncto mobili decurſæ in recta
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            AZ) & </s>
            <s xml:id="echoid-s8968" xml:space="preserve">ipſa BM ad quadratum ex AB (eodem tempore decurſa
              <lb/>
            à linea AZ) rationem ſemper eandem progignetur _ellipſis aut cir-_
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            _culus;_ </s>
            <s xml:id="echoid-s8969" xml:space="preserve">circulus quidem ſi ratio propoſita fuerit æqualitas, & </s>
            <s xml:id="echoid-s8970" xml:space="preserve">an-
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            gulus ZAY rectus, _ellipſis_ ſi ſecùs; </s>
            <s xml:id="echoid-s8971" xml:space="preserve">& </s>
            <s xml:id="echoid-s8972" xml:space="preserve">in his erit D una _diame-_
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            _trorum_, ſitum habens in linea AZ primò poſitâ, à vertice A por-
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            recta verſus partes Z. </s>
            <s xml:id="echoid-s8973" xml:space="preserve">Sin ità ſe habeant, ut rectangulum ex ſumma
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            linearum D, & </s>
            <s xml:id="echoid-s8974" xml:space="preserve">BM & </s>
            <s xml:id="echoid-s8975" xml:space="preserve">ipſa BM ſemper eandem cum quadrato
              <lb/>
            e
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            x AB proportionem ſervet, eo compoſito motu procreabitur _by-_
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            _perbole_; </s>
            <s xml:id="echoid-s8976" xml:space="preserve">quadrata quidem illa (vel æquilatera rectangula) ſi _ratio_
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            deſignata fuerit æqualitatis, & </s>
            <s xml:id="echoid-s8977" xml:space="preserve">angulus ZAY rectus; </s>
            <s xml:id="echoid-s8978" xml:space="preserve">ſin aliter,
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            alterius, pro rationis aſſignatæ quantitate, ſpeciei; </s>
            <s xml:id="echoid-s8979" xml:space="preserve">cujus _tranſverſa_
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            _diameter_ æquabitur ipſi D, ſitum habens in ZA primò poſita à
              <lb/>
            vertice A protenſa verſus partes averſas ab Z; </s>
            <s xml:id="echoid-s8980" xml:space="preserve">& </s>
            <s xml:id="echoid-s8981" xml:space="preserve">parameter ex
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            ratione data determinatur. </s>
            <s xml:id="echoid-s8982" xml:space="preserve">Quòd ſi perpetuò rectangulum ex ipſa
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            D, & </s>
            <s xml:id="echoid-s8983" xml:space="preserve">decurſa BM ad quadratum ex AB eandem perpetuò ra-
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            tionem obtinet, conſtabit effici _lineam parabolicam_, cujus _para-_
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            _meter_ ex rectæ D, datæque rationis propoſitæ quantitate facilè
              <lb/>
            definietur. </s>
            <s xml:id="echoid-s8984" xml:space="preserve">Et in horum primo quidem caſu ſi motus tranſverſus
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            per AY ponatur uniformis, etiam motus deſcendens per AZ unifor-
              <lb/>
            mis erit; </s>
            <s xml:id="echoid-s8985" xml:space="preserve">in ſecundo & </s>
            <s xml:id="echoid-s8986" xml:space="preserve">tertio ſi motus per AY ſit uniformis, erit motus
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            deſcendens perpetuò creſcens; </s>
            <s xml:id="echoid-s8987" xml:space="preserve">eodemque poſito quoad ultimum caſum,
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            in quo parabola fit; </s>
            <s xml:id="echoid-s8988" xml:space="preserve">punctum M continuò velocitate creſcet æqualiter.
              <lb/>
            </s>
            <s xml:id="echoid-s8989" xml:space="preserve">Nec abſimili modo quævis alia linea tali motûs compoſitione producta
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            concipi poteſt. </s>
            <s xml:id="echoid-s8990" xml:space="preserve">Sed ut eò quo tendimus aliquando perveniamus; </s>
            <s xml:id="echoid-s8991" xml:space="preserve">
              <lb/>
            agedum videamus ecquid in _rem Mathematicam_ utilitatis ex </s>
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