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.
Page: 299
[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
Page: 299
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
Page: 300
[154.] II.
Page: 300
[155.] III.
Page: 300
[156.] IV.
Page: 300
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
Page: 301 (196)
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
Page: 307 (202)
[159.] VII. Mari invenire horam diei.
Page: 309 (204)
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
Page: 310 (205)
[161.] IX.
Page: 314 (209)
[162.] X.
Page: 314 (209)
[163.] XI.
Page: 315 (210)
[164.] XII.
Page: 315 (210)
[165.] FINIS.
Page: 316 (211)
[166.] EXCERPTA EX LITERIS DATIS LONDINI {13/23} JANUARII MDCLXV.
Page: 316 (211)
[167.] EXCERPTA EX LITERIS HAGÆ CO-MITUM, DIE XXVI. FEBRUAR MDCLXV. DATIS.
Page: 318 (213)
[168.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA.
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[169.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA. I. Obſervationes Abbatis Catelani in propoſitio-nem, quæ fundamentum eſt 4æ. partis tra-ctatus de Pendulis, Hugenii.
Page: 322
[170.] II. Domini Abbatis Catelani Examen Ma-thematicum Centri Oſcillationis.
Page: 324 (219)
[171.] MONITUM.
Page: 327 (222)
[172.] III. Excerpta ex literis Domini Hugenii, quibus re-ſpondet obſervationi Abbatis Catelani in 4am. pro-poſitionem Tractatus de centris Oſcillationis.
Page: 327 (222)
[173.] IV. Exceptio Abbatis Catelani ad reſponſionem Hugenii.
Page: 330 (225)
[174.] V. Objectio Abbatis Catelani contra motum Pendulorum in Cycloidibus.
Page: 332 (227)
[175.] VI. Reſponſio ad objectiones Hugenii adverſus me-thodum Abbatis Catelani de determinan-do Centro Oſcillationis.
Page: 333 (228)
[176.] VII. Excerpta ex litteris D. Bernoullii datis Baſileæ ad Autorem Diarii Pariſienſis, de Controverſia, inter Abbatem Catelanum & Hugenium, de Centro Oſcillationis.
Page: 335 (230)
[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.
Page: 337 (232)
[178.] IX. Reſponſio Dni. Abbatis Catelani ad literas Dni. Bernoulli de Controverſia ſua cum Dno. Hu-genio de centro Oſcillationis .
Page: 340 (235)
[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.
Page: 342 (237)
[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: 347 (242)
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            <s xml:id="echoid-s5151" xml:space="preserve">
              <pb o="235" file="0313" n="340" rhead="CONTROVERSIA."/>
            ſecundum ejus principium, ſumma illorum temporum, quæ
              <lb/>
            eſt tria, diviſa per duo, numerum partium, erit tempus
              <lb/>
            Penduli compoſiti, ſcilicet {3/2}. </s>
            <s xml:id="echoid-s5152" xml:space="preserve">Hiſce poſitis, nil præterea po-
              <lb/>
            nendo præter id quod concedit D
              <emph style="super">us</emph>
            . </s>
            <s xml:id="echoid-s5153" xml:space="preserve">Abbas, deteguntur alti-
              <lb/>
            tudines, ad quas revertuntur pondera, poſtquam a Pendulo
              <lb/>
            compoſito ſunt ſejuncta; </s>
            <s xml:id="echoid-s5154" xml:space="preserve">nempe {4/9} & </s>
            <s xml:id="echoid-s5155" xml:space="preserve">{64/9}; </s>
            <s xml:id="echoid-s5156" xml:space="preserve">quarum ſumma {68/9},
              <lb/>
            diviſa per duo, numerum ponderum, dat {34/9}, vel 3{7/9}, alti-
              <lb/>
            tudinem, ad quam adſcendit commune gravitatis centrum,
              <lb/>
            quæ etiam ſuperat {5/2} vel 2{1/2} unde demonſtravimus centrum
              <lb/>
            deſcendiſſe. </s>
            <s xml:id="echoid-s5157" xml:space="preserve">Non addo methodum computationis quæ facilis
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s5158" xml:space="preserve">D
              <emph style="super">nus</emph>
            . </s>
            <s xml:id="echoid-s5159" xml:space="preserve">Abbas ergo dum quærit principium bis male divi-
              <lb/>
            navit; </s>
            <s xml:id="echoid-s5160" xml:space="preserve">proprie enim divinare eſt, ratiocinia deducere ex
              <lb/>
            principiis, quæ levem tantum veri ſpeciem præ ſe ferunt;
              <lb/>
            </s>
            <s xml:id="echoid-s5161" xml:space="preserve">& </s>
            <s xml:id="echoid-s5162" xml:space="preserve">verum eſſet, quæſtionem de centro Oſcillationis non dif-
              <lb/>
            ficulter reſolvi, ſi, ut ipſe fecit, tantum ponendum foret id,
              <lb/>
            quod ſtatim rem quæſitam determinat.</s>
            <s xml:id="echoid-s5163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5164" xml:space="preserve">De cætero, contraria eſſe inter ſe ambo principia clarum
              <lb/>
            eſt; </s>
            <s xml:id="echoid-s5165" xml:space="preserve">quoniam ut patet, ex his diverſæ ſequuntur concluſio-
              <lb/>
            nes, altitudines enim, ad quas centrum commune gravitatis
              <lb/>
            aſcendit, diverſæ ex utroque deteguntur, nempe 3 {3/50}, 3 {7/9}.</s>
            <s xml:id="echoid-s5166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5167" xml:space="preserve">Unum hoc addam, ut reſpondeam difficultati, quam D
              <emph style="super">nus</emph>
            . </s>
            <s xml:id="echoid-s5168" xml:space="preserve">Ab-
              <lb/>
            bas propoſuit, contra motum in Cycloide , hanc
              <note symbol="*" position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">Vide ſu-
                <lb/>
              pra pag. 227.</note>
            tem ſolutam dari in ipſo meo tractatu de centro Oſcillationis
              <lb/>
            in cujus propoſitione 24 explicavi, quomodo efficiqueat, ut
              <lb/>
            omnia ponderum Penduli puncta moveantur in Cycloidibus
              <lb/>
            æqualibus; </s>
            <s xml:id="echoid-s5169" xml:space="preserve">licet in praxi minime neceſſaria ſit correctio hæc.</s>
            <s xml:id="echoid-s5170" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div436" type="section" level="1" n="178">
          <head xml:id="echoid-head221" xml:space="preserve">IX.</head>
          <head xml:id="echoid-head222" style="it" xml:space="preserve">Reſponſio D
            <emph style="super">ni</emph>
          . Abbatis Catelani ad literas D
            <emph style="super">ni</emph>
          .
            <lb/>
          Bernoulli de Controverſia ſua cum D
            <emph style="super">no</emph>
          . Hu-
            <lb/>
          genio de centro Oſcillationis .</head>
          <note symbol="*" position="right" xml:space="preserve">Vide ſu-
            <lb/>
          pra pag. 23@.</note>
          <p>
            <s xml:id="echoid-s5171" xml:space="preserve">UT reſpondeam ad has literas, idem repetam, quo utitur
              <lb/>
            D
              <emph style="super">nus</emph>
            . </s>
            <s xml:id="echoid-s5172" xml:space="preserve">Bernoulli, exemplum Penduli compoſiti ex pon-
              <lb/>
            deribus æqualibus eidem virgæ applicatis, & </s>
            <s xml:id="echoid-s5173" xml:space="preserve">ex eodem </s>
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