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

Table of contents

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[161.] IX.
[163.] XI.
[164.] XII.
[165.] FINIS.
[166.] EXCERPTA EX LITERIS DATIS LONDINI {13/23} JANUARII MDCLXV.
[167.] EXCERPTA EX LITERIS HAGÆ CO-MITUM, DIE XXVI. FEBRUAR MDCLXV. DATIS.
[168.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA.
[169.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA. I. Obſervationes Abbatis Catelani in propoſitio-nem, quæ fundamentum eſt 4æ. partis tra-ctatus de Pendulis, Hugenii.
[170.] II. Domini Abbatis Catelani Examen Ma-thematicum Centri Oſcillationis.
[171.] MONITUM.
[172.] III. Excerpta ex literis Domini Hugenii, quibus re-ſpondet obſervationi Abbatis Catelani in 4am. pro-poſitionem Tractatus de centris Oſcillationis.
[173.] IV. Exceptio Abbatis Catelani ad reſponſionem Hugenii.
[174.] V. Objectio Abbatis Catelani contra motum Pendulorum in Cycloidibus.
[175.] VI. Reſponſio ad objectiones Hugenii adverſus me-thodum Abbatis Catelani de determinan-do Centro Oſcillationis.
[176.] VII. Excerpta ex litteris D. Bernoullii datis Baſileæ ad Autorem Diarii Pariſienſis, de Controverſia, inter Abbatem Catelanum & Hugenium, de Centro Oſcillationis.
[177.] VIII. Excerpta ex literis Dni. Hugenii ad Auctores Diarii Pariſienſis, datis Hagæ 8. Funii 1684. quæ continent ejus reſponſionem ad exceptio-nem Dni. Abbatis Catelani, de cen-tro Oſcillationis.
[178.] IX. Reſponſio Dni. Abbatis Catelani ad literas Dni. Bernoulli de Controverſia ſua cum Dno. Hu-genio de centro Oſcillationis .
[179.] X. Dn. Bernouillii narratio controverſiæ inter Dn. Hugenium & Abbatem Catelanum agitatæ de Centro Oſcillationis, quæ loco Anim-adverſionis eſſe poterit in Reſpon-ſionem Dn. Catelani. Excerpta ex Litteris Dn. Bernoullii Lipſiam miſſis.
[180.] XI. Litteræ Dni Marchionis de l’Hôpital ad Dum Huge-nium, in quibus contendit, ſeregulam hujus Au-ctoris de Centro oſcillationis penduli compoſiti demonſtrare per cauſam Phyſicam, & re-ſpondere ſimul Dno Bernoulli.
[181.] XII. Obſervationes Dni Hugenii in liter as præcedentes & in relationem Dni Bernoulli, cujus in iis fit mentio.
[182.] FINIS.
[183.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM.
[184.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM. I. Excerpta ex Literis Domini Hugenii, novam quan-dam Inventionem Horologiorum exactiſſino-rum ac portatilium concernentibus.
[185.] II. Nova Libella, Teleſcopio inſtructa, propriam ſecum ferens probationem, & quæ in unica ſtatione verificatur, & rectificatur.
[186.] Rectificationis Libellæ Demonſtratio.
[187.] III. Aſtroſcopia Compendiaria, Tubi Optici molimine liberata.
[188.] AUCTARIUM.
[189.] IV. Excerpta ex literis Dni Hugenii de novâ methodo conſtruendi Barometrum.
[190.] V. Nova vis movens mediante pulvere nitrato & aëre.
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            lis eſt ſolido, quod fit ducendo figuram eandem, in
              <lb/>
              <note position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" 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>
              </note>
            altitudinem æqualem diſtantiæ centri gravitatis fi-
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            guræ, ab recta per quam abſciſſus eſt cuneus.</s>
            <s xml:id="echoid-s3012" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3013" xml:space="preserve">Sit, ſuper figura plana A C B, cuneus A B D abſciſſus
              <lb/>
              <note position="right" xlink:label="note-0193-02" xlink:href="note-0193-02a" xml:space="preserve">TAB. XI.
                <lb/>
              Fig. 4.</note>
            plano ad angulum ſemirectum inclinato, ac transeunte per
              <lb/>
            E E, rectam tangentem figuram A C B, inque ejus plano
              <lb/>
            ſitam. </s>
            <s xml:id="echoid-s3014" xml:space="preserve">Centrum vero gravitatis figuræ ſit F, unde in rectam
              <lb/>
            E E ducta ſit perpendicularis F @. </s>
            <s xml:id="echoid-s3015" xml:space="preserve">Dico cuneum A C B æ-
              <lb/>
            qualem eſſe ſolido, quod fit ducendo figuram A C B in al-
              <lb/>
            titudinem ipſi F A æqualem.</s>
            <s xml:id="echoid-s3016" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3017" xml:space="preserve">Intelligatur enim figura A C B diviſa in particulas mini-
              <lb/>
            mas æquales quarum una G. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">Itaque conſtat, ſi harum ſin-
              <lb/>
            gulæ ducantur in diſtantiam ſuam ab recta E E, ſummam
              <lb/>
            productorum fore æqualem ei quod fit ducendo rectam A F
              <lb/>
            in particulas omnes , hoc eſt, ei quod fit ducendo
              <note symbol="*" position="right" xlink:label="note-0193-03" xlink:href="note-0193-03a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            ipſam A C B, in altitudinem æqualem A F. </s>
            <s xml:id="echoid-s3019" xml:space="preserve">Atqui particu-
              <lb/>
            læ ſingulæ ut G, in diſtantias ſuas G H ductæ, æquales
              <lb/>
            ſunt parallelepipedis, vel prismatibus minimis, ſuper ipſas
              <lb/>
            erectis, atque ad ſuperficiem obliquam A D terminatis, qua-
              <lb/>
            le eſt G K; </s>
            <s xml:id="echoid-s3020" xml:space="preserve">quia horum altitudines ipſis diſtantiis G H æ-
              <lb/>
            quantur, propter angulum ſemirectum inclinationis plano-
              <lb/>
            rum A D & </s>
            <s xml:id="echoid-s3021" xml:space="preserve">A C B. </s>
            <s xml:id="echoid-s3022" xml:space="preserve">Patetque ex his parallelepipedis totum
              <lb/>
            cuneum A B D componi. </s>
            <s xml:id="echoid-s3023" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s3024" xml:space="preserve">cuneus ipſe æquabitur ſo-
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            lido ſuper baſi A C B, altitudinem habenti rectæ F A æ-
              <lb/>
            qualem. </s>
            <s xml:id="echoid-s3025" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3026" xml:space="preserve"/>
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          <head xml:id="echoid-head124" xml:space="preserve">PROPOSITIO VIII.</head>
          <p style="it">
            <s xml:id="echoid-s3027" xml:space="preserve">SI figuram planam linea recta tangat, diviſaque
              <lb/>
            intelligatur figura in particulas minimas æqua-
              <lb/>
            les, atque à ſingulis ad rectam illam perpendicula-
              <lb/>
            res ductæ: </s>
            <s xml:id="echoid-s3028" xml:space="preserve">erunt omnium harum quadrata, ſimul
              <lb/>
            ſumpta, æqualia rectangulo cuidam, multiplici ſe-
              <lb/>
            cundum ipſarum particularum numerum; </s>
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