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

Table of Notes

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            ducantur autem ab omnibus datis punctis, ad pun-
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              <note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">
                <emph style="sc">Decentro</emph>
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                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            ctum aliquod in circuli illius circumferentia lineæ
              <lb/>
            rectæ erit ſumma quadratorum ab omnibus ſem-
              <lb/>
            per eidem plano æqualis.</s>
            <s xml:id="echoid-s3118" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3119" xml:space="preserve">Sint data puncta A B C D: </s>
            <s xml:id="echoid-s3120" xml:space="preserve">centrumque gravitatis eorum,
              <lb/>
              <note position="left" xlink:label="note-0200-02" xlink:href="note-0200-02a" xml:space="preserve">TAB. XX.
                <lb/>
              Fig. 5.</note>
            ſive magnitudinum æqualium ab ipſis ſuſpenſarum, ſit E;
              <lb/>
            </s>
            <s xml:id="echoid-s3121" xml:space="preserve">& </s>
            <s xml:id="echoid-s3122" xml:space="preserve">centro E deſcribatur circulus quilibet F f, in cujus cir-
              <lb/>
            cumferentia ſumpto puncto aliquo, ut F, ducantur ad id,
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            à datis punctis, rectæ A F, B F, C F, D F. </s>
            <s xml:id="echoid-s3123" xml:space="preserve">Dico earum
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            omnium quadrata, ſimul ſumpta, æqualia eſſe plano cuidam
              <lb/>
            dato, ſemperque eidem, ubicunque in circumferentia pun-
              <lb/>
            ctum F ſumptum fuerit.</s>
            <s xml:id="echoid-s3124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3125" xml:space="preserve">Ducantur enim rectæ G H, G K, angulum rectum con-
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            ſtituentes, & </s>
            <s xml:id="echoid-s3126" xml:space="preserve">quarum unicuique omnia data puncta ſint po-
              <lb/>
            ſita ad eandem partem. </s>
            <s xml:id="echoid-s3127" xml:space="preserve">Et à ſingulis in utramque harum
              <lb/>
            perpendiculares agantur A L, A K; </s>
            <s xml:id="echoid-s3128" xml:space="preserve">B M, B O; </s>
            <s xml:id="echoid-s3129" xml:space="preserve">C N,
              <lb/>
            C P; </s>
            <s xml:id="echoid-s3130" xml:space="preserve">D H, D Q. </s>
            <s xml:id="echoid-s3131" xml:space="preserve">A centro autem gravitatis E, & </s>
            <s xml:id="echoid-s3132" xml:space="preserve">à pun-
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            cto F, in alterutram duarum, G H vel G K, perpendi-
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            culares E R, F S. </s>
            <s xml:id="echoid-s3133" xml:space="preserve">Et item, à datis punctis, in ipſam
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            F S perpendiculares A V, B X, C Y, D Z. </s>
            <s xml:id="echoid-s3134" xml:space="preserve">Et F T per-
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            pendicularis in ipſam E R. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">Porro ſit jam</s>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          A L = a # A K = e # radius # E F = z
            <lb/>
          B M = b # B O = f # # G S = x
            <lb/>
          C N = c # C P = g
            <lb/>
          D H = d # D Q = h
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3136" xml:space="preserve">Quia autem E eſt centrum gravitatis punctorum A, B, C, D;
              <lb/>
            </s>
            <s xml:id="echoid-s3137" xml:space="preserve">ſi addantur in unum perpendiculares A L, B M, C N, D H,
              <lb/>
            compoſitaque ex omnibus dividatur in tot partes, quot ſunt
              <lb/>
            data puncta; </s>
            <s xml:id="echoid-s3138" xml:space="preserve">earum partium uni æqualis erit E R . </s>
            <s xml:id="echoid-s3139" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">Prop. 2.
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              huj.</note>
            terque, divisâ in totidem partes ſummâ perpendicularium
              <lb/>
            A K, B O, C P, D Q, earum uni æqualis erit perpendi-
              <lb/>
            cularis, ducta ex E in rectam G K, ſive ipſa R G . </s>
            <s xml:id="echoid-s3140" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0200-05" xlink:href="note-0200-05a" xml:space="preserve">Prop. 2.
                <lb/>
              huj.</note>
            que, ſi ſumma omnium A L, B M, C N, D H, ſive
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            a + b + c + d vocetur l: </s>
            <s xml:id="echoid-s3141" xml:space="preserve">ſumma vero omnium, A K, B O,
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            C P, D Q ſive e + f + g + h, vocetur m: </s>
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