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

Table of Notes

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              <pb o="145" file="0209" n="229" rhead="HOROLOG. OSCILLATOR."/>
            ris contingit. </s>
            <s xml:id="echoid-s3289" xml:space="preserve">Atque eorum planorum diſtantias cen-
              <lb/>
              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">
                <emph style="sc">De centr@</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
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            tri gravitatis, ſuper tangentibus axi oſcillationis
              <lb/>
            parallelis, datas eſſe neceſſe eſt; </s>
            <s xml:id="echoid-s3290" xml:space="preserve">uti & </s>
            <s xml:id="echoid-s3291" xml:space="preserve">ſubcentri-
              <lb/>
            cas cuneorum, qui ſuper ipſis abſcinduntur, ductis
              <lb/>
            planis per easdem tangentes.</s>
            <s xml:id="echoid-s3292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3293" xml:space="preserve">Veluti, ſi maxima dictarum ſectionum ſit B D, & </s>
            <s xml:id="echoid-s3294" xml:space="preserve">in B
              <lb/>
              <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">Fig. 2</note>
            intelligatur recta parallela axi E, hoc eſt, erecta ad planum
              <lb/>
            quod hic conſpicitur, oportet datam eſſe diſtantiam centri
              <lb/>
            gr. </s>
            <s xml:id="echoid-s3295" xml:space="preserve">ſectionis B D à dicta linea in B, quæ ſit B C; </s>
            <s xml:id="echoid-s3296" xml:space="preserve">itemque
              <lb/>
            ſubcentricam cunei, ſuper ſectione B D abſciſſi, plano du-
              <lb/>
            cto per eandem lineam in B, quæ ſubcentrica ſit B K.</s>
            <s xml:id="echoid-s3297" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3298" xml:space="preserve">Etenim his datis, divisâque P V bifariam in Δ, ſi fiat
              <lb/>
            ſicut Δ P ad P Φ, ita rectangulum B C K ad ſpatium quod-
              <lb/>
            dam Z; </s>
            <s xml:id="echoid-s3299" xml:space="preserve">dico hoc ipſum, multiplex per numerum particu-
              <lb/>
            larum ſolidi A B C D, æquari ſummæ quæſitæ quadrato-
              <lb/>
            rum, à diſtantiis earundem particularum à plano E C.</s>
            <s xml:id="echoid-s3300" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3301" xml:space="preserve">Quadrata enim à diſtantiis particularum planæ ſectionis
              <lb/>
            B D, à plano E C, quod per centrum gravitatis ſuæ tranſit;
              <lb/>
            </s>
            <s xml:id="echoid-s3302" xml:space="preserve">ſive quadrata à diſtantiis particularum ſolidarum ſegmenti
              <lb/>
            B N N D à plano eodem, æquari conſtat rectangulo B C K,
              <lb/>
            multiplici per numerum dictarum particularum . </s>
            <s xml:id="echoid-s3303" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">Prop. 10.
                <lb/>
              huj.</note>
            ſi planæ ſectionis N N diſtantia centri gravitatis, ab recta
              <lb/>
            quæ in N intelligitur axi E parallela, ſit N X; </s>
            <s xml:id="echoid-s3304" xml:space="preserve">ſubcentrica
              <lb/>
            vero cunei ſuper ipſa abſciſſi, plano per eandem rectam, ſit
              <lb/>
            N F; </s>
            <s xml:id="echoid-s3305" xml:space="preserve">erunt quadrata à diſtantiis particularum planarum ſe-
              <lb/>
            ctionis N N à plano E C, ſive quadrata à diſtantiis parti-
              <lb/>
            cularum ſolidarum ſegmenti N M M N, à plano eodem,
              <lb/>
            æqualia rectangulo N X F, multiplici per numerum parti-
              <lb/>
            cularum ipſarum ſectionis N N, vel ſegmenti N M M N.
              <lb/>
            </s>
            <s xml:id="echoid-s3306" xml:space="preserve">Eſt autem B D diviſa ſimiliter in C & </s>
            <s xml:id="echoid-s3307" xml:space="preserve">K, atque N N in X
              <lb/>
            & </s>
            <s xml:id="echoid-s3308" xml:space="preserve">F. </s>
            <s xml:id="echoid-s3309" xml:space="preserve">Ergo rectangulum B C K ad rectangulum N X F,
              <lb/>
            ſicut quadratum B D ad quadratum N N.</s>
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            <s xml:id="echoid-s3311" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s3312" xml:space="preserve">numerus particularum ſectionis B D, ad nu-
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            merum particularum ſectionis N N, ſicut ſectiones ipſæ;</s>
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