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

Table of Notes

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            E A G, quia omnes F L æquales totidem G A . </s>
            <s xml:id="echoid-s3072" xml:space="preserve">Et
              <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">
                <emph style="sc">Decentro</emph>
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                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
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            que quadrata L F æquantur totidem rectangulis H A G , hoc eſt, totidem quadratis A G cum totidem rectangulis
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">Prop. 2.
                <lb/>
              huj.</note>
            A G H. </s>
            <s xml:id="echoid-s3073" xml:space="preserve">Ergo quadrata omnia F K æqualia erunt totidem
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            quadratis E A, cum totidem duplis rectangulis E A G, at-
              <lb/>
            que inſuper totidem quadratis A G cum totidem rectangulis
              <lb/>
            A G H. </s>
            <s xml:id="echoid-s3074" xml:space="preserve">Atqui tria iſta; </s>
            <s xml:id="echoid-s3075" xml:space="preserve">nempe quadratum E A cum duplo
              <lb/>
            rectangulo E A G & </s>
            <s xml:id="echoid-s3076" xml:space="preserve">quadrato A G; </s>
            <s xml:id="echoid-s3077" xml:space="preserve">faciunt quadratum E G.
              <lb/>
            </s>
            <s xml:id="echoid-s3078" xml:space="preserve">Ergo apparet quadrata omnia F K æquari totidem quadratis
              <lb/>
            E G, una cum totidem rectangulis A G H. </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s3080" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3081" xml:space="preserve">Porro in reliquis omnibus caſibus, quadrata omnia F K
              <lb/>
              <note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">TAB. XX.
                <lb/>
              Fig. 1. 2.</note>
            æquantur totidem quadratis K L, minus bis totidem rectan-
              <lb/>
            gulis K L F, plus totidem quadratis L F; </s>
            <s xml:id="echoid-s3082" xml:space="preserve">hoc eſt, toti-
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            dem quadratis E A, minus totidem duplis rectangulis E A G,
              <lb/>
            plus totidem quadratis A G, cum totidem rectangulis A G H.
              <lb/>
            </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Atqui, omnibus hiſce caſibus, fit quadratum E A, plus qua-
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            drato A G, minus duplo rectangulo E A G, æquale qua-
              <lb/>
            drato E G. </s>
            <s xml:id="echoid-s3084" xml:space="preserve">Ergo rurſus quadrata omnia F K æqualia erunt
              <lb/>
            totidem quadratis E G, una cum totidem rectangulis A G H. </s>
            <s xml:id="echoid-s3085" xml:space="preserve">
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            Quare conſtat propoſitum.</s>
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            <s xml:id="echoid-s3087" xml:space="preserve">Hinc ſequitur, rectangulum A G H eadem magnitudine
              <lb/>
            eſſe, utriusvis cunei ſubcentrica fuerit A H; </s>
            <s xml:id="echoid-s3088" xml:space="preserve">hoc eſt, ſive
              <lb/>
            per hanc, ſive per illam tangentium parallelarum A L ab-
              <lb/>
            ſciſſi. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">Itaque A G unius caſus ad A G alterius, ut H G hu-
              <lb/>
            jus ad H G illius. </s>
            <s xml:id="echoid-s3090" xml:space="preserve">Sicut autem rectæ A G inter ſe, ita in
              <lb/>
            utroque caſu cunei per A L abſciſſi, ut colligitur ex prop. </s>
            <s xml:id="echoid-s3091" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s3092" xml:space="preserve">huj. </s>
            <s xml:id="echoid-s3093" xml:space="preserve">Ergo ita quoque reciproce G H ad G H.</s>
            <s xml:id="echoid-s3094" xml:space="preserve"/>
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            <s xml:id="echoid-s3095" xml:space="preserve">Apparet etiam, dato figuræ planæ centro gravitatis G, & </s>
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            ſubcene
              <unsure/>
            rica cunei, per alterutram tangentium parallelarum
              <lb/>
            A L abſciſſi, dari quoque cunei, pertangentem alteram A L
              <lb/>
            abſciſſi, ſubcentricam.</s>
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          <head xml:id="echoid-head126" xml:space="preserve">PROPOSITIO X.</head>
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            <s xml:id="echoid-s3098" xml:space="preserve">Poſitis quæ in propoſitione præcedenti; </s>
            <s xml:id="echoid-s3099" xml:space="preserve">ſi data
              <lb/>
              <note position="left" xlink:label="note-0196-05" xlink:href="note-0196-05a" xml:space="preserve">TAB. XX.
                <lb/>
              Fig. 3.</note>
            recta E D transeat per G, centrum </s>
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