Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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              <pb o="54" file="0086" n="90" rhead="CHRISTIANI HUGENII"/>
            Atque ita ſpatia quotlibet deinceps conſiderata, quæ æqua-
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
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                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            libus temporibus peracta fuerint, æquali exceſſu, qui ipſi
              <lb/>
            B D æqualis ſit, creſcere manifeſtum eſt; </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ſimulque etiam
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            velocitates per æqualia tempora æqualiter augeri.</s>
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          <head xml:id="echoid-head47" xml:space="preserve">PROPOSITIO II.</head>
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            <s xml:id="echoid-s1151" xml:space="preserve">SPatium peractum certo tempore à gravi, è quie-
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            te caſum inchoante, dimidium eſt ejus ſpatii
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            quod pari tempore transiret motu æquabili, cum
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            velocitate quam acquiſivit ultimo caſus momento.</s>
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            <s xml:id="echoid-s1153" xml:space="preserve">Ponantur quæ in propoſitione præcedenti, ubi quidem
              <lb/>
              <note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">TAB. V.
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              Fig. 1.</note>
            A B erat ſpatium certo tempore, à gravi cadente ex A, per-
              <lb/>
            actum. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">B D vero ſpatium quod pari tempore transiri intel-
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            ligebatur celeritate æquabili, quanta acquiſita erat in fine
              <lb/>
            primi temporis, ſeu in fine ſpatii A B. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Dico itaque ſpatium
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            B D duplum eſſe ad A B.</s>
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            <s xml:id="echoid-s1157" xml:space="preserve">Quum enim ſpatia primis quatuor æqualibus temporibus
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            à cadente transmiſſa ſint A B, B E, E G, G H, quorum
              <lb/>
            inter ſe certa quædam eſt proportio: </s>
            <s xml:id="echoid-s1158" xml:space="preserve">ſi eorum temporum du-
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            pla tempora ſumamus, ut nempe pro primo tempore jam
              <lb/>
            accipiantur duo illa quibus ſpatia A B, B E, peracta fue-
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            re; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">pro ſecundo vero tempore duo reliqua quibus peracta
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            fuere ſpatia E G, G K, oportet jam ſpatia A E, E K,
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            quæ ſunt æqualibus temporibus à quiete peracta, inter ſe
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            eſſe ſicut ſpatia A B, B E, quæ æqualibus item tempori-
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            bus à quiete percurrebantur.</s>
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          <p>
            <s xml:id="echoid-s1161" xml:space="preserve">Quum igitur ſit ut A B ad B E, ita A E ad E K; </s>
            <s xml:id="echoid-s1162" xml:space="preserve">& </s>
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            convertendo, ut E B ſive D A ad A B ita K E ad E A:
              <lb/>
            </s>
            <s xml:id="echoid-s1164" xml:space="preserve">erit quoque, dividendo, D B ad B A ut exceſſus K E ſu-
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            pra E A ad E A. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Quum ſit autem, ex oſtenſis propoſitione
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            præcedenti, K E æqualis tum duplæ A B, tum quintuplæ
              <lb/>
            B D: </s>
            <s xml:id="echoid-s1166" xml:space="preserve">E A vero æqualis tum duplæ A B, tum ſimplici B D; </s>
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            apparet dictum exceſſum K E ſupra E A æquari </s>
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