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

Table of contents

< >
[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.
< >
page |< < (95) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div160" type="section" level="1" n="59">
          <pb o="95" file="0141" n="152" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s2106" xml:space="preserve">Sunto lineæ A B C, A D E, in partem unam inflexæ,
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" 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>
            & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">quarum uttraque in eaſdem partes cava exiſtat, habeant-
              <lb/>
            que communem terminum A punctum. </s>
            <s xml:id="echoid-s2108" xml:space="preserve">Omnes autem rectæ
              <lb/>
            tangentes lineam A B C, velut B D, C E, occurrant
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">TAB. XII.
                <lb/>
              Fig. 4.</note>
            lineæ A D E ad angulos rectos. </s>
            <s xml:id="echoid-s2109" xml:space="preserve">Dico evolutione ipſius
              <lb/>
            A B C, à termino A incepta, deſcribi A D E.</s>
            <s xml:id="echoid-s2110" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2111" xml:space="preserve">Si enim fieri poteſt, deſcribatur dicta evolutione alia
              <lb/>
            quædam curva A F G. </s>
            <s xml:id="echoid-s2112" xml:space="preserve">Ergo lineæ rectæ quælibet, evolu-
              <lb/>
            tam A B C tangentes, ut B D, C E, occurrent ipſi A F G
              <lb/>
            ad angulos rectos, puta in F & </s>
            <s xml:id="echoid-s2113" xml:space="preserve">G. </s>
            <s xml:id="echoid-s2114" xml:space="preserve">Sed eædem
              <note symbol="*" position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            etiam ad rectos angulos occurrere ponuntur lineæ A D E.
              <lb/>
            </s>
            <s xml:id="echoid-s2115" xml:space="preserve">Sunt igitur lineæ curvæ A D E, A F G, eodem puncto
              <lb/>
            A terminatæ, inque partem unam flexæ, & </s>
            <s xml:id="echoid-s2116" xml:space="preserve">ambæ in ean-
              <lb/>
            dem partem cavæ, quippe utraque in eandem atque ipſa
              <lb/>
            A B C; </s>
            <s xml:id="echoid-s2117" xml:space="preserve">nam de linea A D E conſtat ex hypotheſi, de
              <lb/>
            A F G vero ex propoſitione prima hujus; </s>
            <s xml:id="echoid-s2118" xml:space="preserve">& </s>
            <s xml:id="echoid-s2119" xml:space="preserve">omnes quæ
              <lb/>
            uni earum occurrunt ad angulos rectos, etiam alteri ſimili-
              <lb/>
            ter occurrunt. </s>
            <s xml:id="echoid-s2120" xml:space="preserve">quod quidem fieri non poſſe antea oſtenſum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s2121" xml:space="preserve">Quare conſtat ipſam A D E deſcriptum iri
              <note symbol="*" position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">Prop. 3.
                <lb/>
              huj.</note>
            lineæ A B C. </s>
            <s xml:id="echoid-s2122" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2123" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div163" type="section" level="1" n="60">
          <head xml:id="echoid-head84" xml:space="preserve">PROPOSITIO V.</head>
          <p style="it">
            <s xml:id="echoid-s2124" xml:space="preserve">SI Cycloidem recta linea in vertice contingat, ſu-
              <lb/>
            per qua, tanquam baſi, alia cyclois priori ſimi-
              <lb/>
            lis & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">æqualis conſtituatur, initium ſumens à pun-
              <lb/>
            cto dicti verticis; </s>
            <s xml:id="echoid-s2126" xml:space="preserve">recta quælibet inferiorem cycloi-
              <lb/>
            dem tangens, occurret ſuperioris portioni, ſibi ſu-
              <lb/>
            perpoſitæ, ad angulos rectos.</s>
            <s xml:id="echoid-s2127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2128" xml:space="preserve">Tangat cycloidem A B C in vertice A recta A G, ſuper
              <lb/>
              <note position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">TAB. XVI.
                <lb/>
              Fig. 1.</note>
            qua, tanquam baſi, ſimilis alia cyclois conſtituta ſit A E F,
              <lb/>
            cujus vertex F. </s>
            <s xml:id="echoid-s2129" xml:space="preserve">Cycloidem autem A B C tangat recta B K
              <lb/>
            in B. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">Dico eam productam occurrere cycloidi A E F ad an-
              <lb/>
            gulos rectos.</s>
            <s xml:id="echoid-s2131" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2132" xml:space="preserve">Deſcribatur enim circa A D, axem cycloidis A B C, </s>
          </p>
        </div>
      </text>
    </echo>