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

Table of Notes

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            Cujus quadratum auferendo à rectangulo H G F, quod erat
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              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS</emph>
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            {3/20} quadrati B C, fiet rectangulum G F H = {3/20} b b - {1b4/4 q q}. </s>
            <s xml:id="echoid-s3881" xml:space="preserve">Hoc
              <lb/>
            autem rectangulum, multiplex per numerum particularum
              <lb/>
            ſemiconi A B C, æquatur quadratis diſtantiarum à plano
              <lb/>
            M D O. </s>
            <s xml:id="echoid-s3882" xml:space="preserve">At quadratis diſtantiarum à plano N D æquantur,
              <lb/>
            ut in cono, {3/80} quadrati A B, ſive {3/80} a a, multiplices per
              <lb/>
            numerum particularum ſemiconi A B C. </s>
            <s xml:id="echoid-s3883" xml:space="preserve">Itaque, totum ſpa-
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            tium applicandum, æquabitur hic {3/80} a a + {3/20} b b - {1 b 4/4 q q}.</s>
            <s xml:id="echoid-s3884" xml:space="preserve"/>
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            <s xml:id="echoid-s3885" xml:space="preserve">Unde quidem centrum agitationis invenitur in omni ſuſpen-
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            ſione ſemiconi, dummodo ab axe qui ſit parallelus baſi trianguli
              <lb/>
            à ſectione A B. </s>
            <s xml:id="echoid-s3886" xml:space="preserve">Notandum vero, cum figura S Z Y ſit ignotæ
              <lb/>
            prorſus naturæ, ſubcentricam tamen G H, cunei ſuper ipſa ab-
              <lb/>
            ſciſſi plano per S Y, hinc inveniri. </s>
            <s xml:id="echoid-s3887" xml:space="preserve">Nam, quia rectangulum H G F
              <lb/>
            æquale erat {3/20} b b, ſive quadrati B C, & </s>
            <s xml:id="echoid-s3888" xml:space="preserve">G F æqualis {1b b/2 q},
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            fit inde G H æqualis {3/10} q.</s>
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            <s xml:id="echoid-s3890" xml:space="preserve">Porro, etiam ſemicylindri, & </s>
            <s xml:id="echoid-s3891" xml:space="preserve">ſemiconoidis parabolici,
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            centra agitationis inveniri poſſunt, atque aliorum inſuper ſe-
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            miſolidorum; </s>
            <s xml:id="echoid-s3892" xml:space="preserve">quæ aliis inveſtiganda relinquimus.</s>
            <s xml:id="echoid-s3893" xml:space="preserve"/>
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            <s xml:id="echoid-s3894" xml:space="preserve">Quemadmodum autem in figuris planis, ita & </s>
            <s xml:id="echoid-s3895" xml:space="preserve">hic in ſo-
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            lidis figuris locum habet, quod de obliquarum centris agi-
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            tationis illic diximus, quæ veluti luxatione rectarum conſti-
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            tuuntur, quarum centra oſcillationis non differunt à centris
              <lb/>
            oſcillationis rectarum. </s>
            <s xml:id="echoid-s3896" xml:space="preserve">Sic, ſi coni duo fuerunt A B C, A F G,
              <lb/>
              <note position="right" xlink:label="note-0247-02" xlink:href="note-0247-02a" xml:space="preserve">TAB. XXVII.
                <lb/>
              Fig. 1.</note>
            alter rectus, alter ſcalenus; </s>
            <s xml:id="echoid-s3897" xml:space="preserve">quorum & </s>
            <s xml:id="echoid-s3898" xml:space="preserve">diametri & </s>
            <s xml:id="echoid-s3899" xml:space="preserve">baſes
              <lb/>
            æquales; </s>
            <s xml:id="echoid-s3900" xml:space="preserve">hi ex vertice ſuſpenſi, vel à quibuſcunque axibus,
              <lb/>
            æqualiter à centris eorum gravitatis diſtantibus, iſochroni
              <lb/>
            erunt; </s>
            <s xml:id="echoid-s3901" xml:space="preserve">dummodo axis, unde conus ſcalenus ſuſpenſus eſt,
              <lb/>
            rectus ſit ad planum trianguli per diametrum, quod planum
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            baſi eſt ad angulos rectos.</s>
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