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

Table of contents

< >
[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.
< >
page |< < (104) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div184" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s2321" xml:space="preserve">
              <pb o="104" file="0152" n="164" rhead="CHRISTIANI HUGENII"/>
            portionalis linea H. </s>
            <s xml:id="echoid-s2322" xml:space="preserve">Erit hæc radius circuli qui ſuperficiei
              <lb/>
              <note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLURIO-</emph>
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            ſphæroidis propoſiti æqualis ſit.</s>
            <s xml:id="echoid-s2323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div187" type="section" level="1" n="68">
          <head xml:id="echoid-head92" style="it" xml:space="preserve">Conoidis hyperbolici ſuperficiei curvæ circulum
            <lb/>
          æqualem invenire.</head>
          <p>
            <s xml:id="echoid-s2324" xml:space="preserve">ESto conoides hyperbolicum cujus axis A B, ſectio per
              <lb/>
              <note position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">TAB. XIV.
                <lb/>
              Fig. 4.</note>
            axem hyperbola C A D, cujus latus tranſverſum E A,
              <lb/>
            centrum F, latus rectum A G.</s>
            <s xml:id="echoid-s2325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2326" xml:space="preserve">Sumatur in axe recta A H, æqualis dimidio lateri recto
              <lb/>
            A G. </s>
            <s xml:id="echoid-s2327" xml:space="preserve">& </s>
            <s xml:id="echoid-s2328" xml:space="preserve">ut H F ad A F longitudine ita, ſit A F ad F K
              <lb/>
            potentiâ. </s>
            <s xml:id="echoid-s2329" xml:space="preserve">Et intelligatur vertice K alia hyperbola deſcripta
              <lb/>
            K L M, eodem axe & </s>
            <s xml:id="echoid-s2330" xml:space="preserve">centro F cum priore, quæque late-
              <lb/>
            ra rectum & </s>
            <s xml:id="echoid-s2331" xml:space="preserve">transverſum illi reciproce proportionalia habeat.
              <lb/>
            </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Occurrat autem ipſi producta B C in M, ſitque A L paralle-
              <lb/>
            la B C. </s>
            <s xml:id="echoid-s2333" xml:space="preserve">Erit jam ſicut ſpatium A L M B, tribus rectis lineis
              <lb/>
            & </s>
            <s xml:id="echoid-s2334" xml:space="preserve">curva hyperbolica comprehenſum, ad dimidium quadra-
              <lb/>
            tum ex B C, ita ſuperficies conoidis curva ad circulum ba-
              <lb/>
            ſeos ſuæ, cujus diameter C D. </s>
            <s xml:id="echoid-s2335" xml:space="preserve">Unde conſtructio reliqua
              <lb/>
            facile abſolvetur, poſitâ hyperbolæ quadraturâ.</s>
            <s xml:id="echoid-s2336" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2337" xml:space="preserve">Quum igitur conoidis parabolici ſuperficies ad circulum
              <lb/>
            redigatur, æque ac ſuperficies ſphæræ, ex notis geometriæ
              <lb/>
            regulis; </s>
            <s xml:id="echoid-s2338" xml:space="preserve">in ſuperficie ſphæroidis oblongi, ut idem fiat, po-
              <lb/>
            nendum eſt arcus circumferentiæ longitudinem æquari poſſe
              <lb/>
            lineæ rectæ. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">Ad ſphæroidis vero lati, itemque ad conoidis
              <lb/>
            hyperbolici ſuperficiem eadem ratione complanandam, hy-
              <lb/>
            perbolæ quadratura requiritur. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">Nam parabolicæ lineæ lon-
              <lb/>
            gitudo, quam in ſphæroide hoc adhibuimus, pendet à qua-
              <lb/>
            dratura hyperbolæ, ut mox oſtendemus.</s>
            <s xml:id="echoid-s2341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2342" xml:space="preserve">Verum, quod non indignum animadverſione videtur, in-
              <lb/>
            venimus absque ulla hyperbolicæ quadraturæ ſuppoſitione,
              <lb/>
            circulum æqualem conſtrui ſuperficiei utrique ſimul, ſphæ-
              <lb/>
            roidis lati & </s>
            <s xml:id="echoid-s2343" xml:space="preserve">conoidis hyperbolici.</s>
            <s xml:id="echoid-s2344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2345" xml:space="preserve">Dato enim ſphæroide quovis lato, poſſe inveniri conoi-
              <lb/>
            des hyperbolicum, vel contra, dato conoide hyperbolico,
              <lb/>
            poſſe inveniri ſphæroides latum ejusmodi, ut utriusque </s>
          </p>
        </div>
      </text>
    </echo>