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

Table of contents

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[151.] Fournier in Hydrographia 1. 12. C. 35.
[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
[154.] II.
[155.] III.
[156.] IV.
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
[159.] VII. Mari invenire horam diei.
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
[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.
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        <div xml:id="echoid-div166" type="section" level="1" n="61">
          <pb o="97" file="0145" n="157" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s2154" xml:space="preserve">Et apparet, ſi dimidiam cycloidem, ipſi A B C gemel-
              <lb/>
              <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" 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">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            lam, contrario ſitu ab altera parte lineæ C G diſponamus,
              <lb/>
            velut C N, ejus evolutione, vel etiam dum filum, jam
              <lb/>
            extenſum in C F, circa eam replicatur, alteram ſemicy-
              <lb/>
            cloidem F N fili extremitate deſcriptum iri, quæ ſimul
              <lb/>
            cum priore A E F integram conſtituat.</s>
            <s xml:id="echoid-s2155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2156" xml:space="preserve">Atque ex his, & </s>
            <s xml:id="echoid-s2157" xml:space="preserve">propoſitione 25 de deſcenſu gravium, ma-
              <lb/>
            nifeſtum jam eſt quod ſupra in Conſtructione Horologii de
              <lb/>
            æquabili penduli motu dictum fuit. </s>
            <s xml:id="echoid-s2158" xml:space="preserve">Patet enim perpendicu-
              <lb/>
            lum, inter laminas binas, ſecundum ſemicycloidem inflexas,
              <lb/>
            ſuſpenſum agitatumque, motu ſuo cycloidis arcum deſcri-
              <lb/>
            bere, ac proinde æqualibus temporibus quaſlibet ejus reci-
              <lb/>
            procationes abſolvi. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">Non refert enim utrum in ſuperficie,
              <lb/>
            ſecundum cycloidem curvata, mobile feratur, an filo alliga-
              <lb/>
            tum lineam ipſam in aëre percurrat, cum utrobique eandem
              <lb/>
            libertatem, eandemque in omnibus curvæ punctis inclina-
              <lb/>
            tionem ad motum habeat.</s>
            <s xml:id="echoid-s2160" xml:space="preserve"/>
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        <div xml:id="echoid-div169" type="section" level="1" n="62">
          <head xml:id="echoid-head86" xml:space="preserve">PROPOSITIO VII.</head>
          <p style="it">
            <s xml:id="echoid-s2161" xml:space="preserve">Cyclois linea ſui axis, ſive diametri circuli ge-
              <lb/>
            nitoris, quadrupla eſt.</s>
            <s xml:id="echoid-s2162" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2163" xml:space="preserve">Repetita enim figura præcedenti: </s>
            <s xml:id="echoid-s2164" xml:space="preserve">cum poſt totam ſemi-
              <lb/>
              <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">TAB. XVI.
                <lb/>
              Fig. 1.</note>
            cycloidem A B C evolutam, filum occupet rectam C F,
              <lb/>
            quæ dupla eſt A D, proptarea quod axes cycloidum A B C,
              <lb/>
            A E F ſunt æquales; </s>
            <s xml:id="echoid-s2165" xml:space="preserve">apparet ſemicycloidem ipſam A B C,
              <lb/>
            filo ſibi circum applicito æqualem, duplam eſſe ſui axis A D,
              <lb/>
            ac totam proinde cycloidem axis ſui quadruplam.</s>
            <s xml:id="echoid-s2166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2167" xml:space="preserve">Apparet etiam tangentem B E, quæ refert partem fili ex-
              <lb/>
            tenſam, antea curvæ parti B A applicatam, huic ipſi longi-
              <lb/>
            tudine æquari. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Eſt autem B E dupla ipſius B K, ſive A H,
              <lb/>
            quoniam in propoſitione quinta oſtenſum eſt K E ipſi A H
              <lb/>
            æqualem eſſe. </s>
            <s xml:id="echoid-s2169" xml:space="preserve">Itaque pars cycloidis A B rectæ A H, ſive
              <lb/>
            B K, dupla erit: </s>
            <s xml:id="echoid-s2170" xml:space="preserve">exiſtente nimirum B H parallela baſi
              <lb/>
            cycloidis: </s>
            <s xml:id="echoid-s2171" xml:space="preserve">idque ubicunque in ea punctum B ſumptum fue-
              <lb/>
            rit.</s>
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