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

Table of contents

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[131.] PROPOSITIO XXV.
[132.] PROPOSITIO XXVI.
[133.] HOROLOGII OSCILLATORII PARS QUINTA.
[134.] Horologii ſecundi conſtructio.
[135.] DE VI CENTRIFUGA ex motu circulari, Theoremata. I.
[136.] II.
[137.] III.
[138.] IV.
[140.] VI.
[141.] VII.
[142.] VIII.
[143.] IX.
[145.] XI.
[146.] XII.
[147.] XIII.
[148.] FINIS.
[149.] BREVIS INSTITUTIO DE USU HOROLOGIORUM AD INVENIENDAS LONGITUDINES.
[150.] Adr. Metius in Geographicis Inſtitutionibus Cap. 4.
[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.
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          <p>
            <s xml:id="echoid-s4968" xml:space="preserve">
              <pb o="226" file="0304" n="331" rhead="DE CENTRO OSCILL"/>
            Pendulo compoſito. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">Nam eandem habent proportionem,
              <lb/>
            quam arcus deſcripti a duobus ponderibus æqualibus, ex
              <lb/>
            quibus Pendulum formatur; </s>
            <s xml:id="echoid-s4970" xml:space="preserve">duo illi arcus ſunt ſpatia, quæ
              <lb/>
            duo pondera percurrunt, eodem tempore, velocitatibus,
              <lb/>
            quæ neceſſario ſunt ipſis ſpatiis proportionales.</s>
            <s xml:id="echoid-s4971" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4972" xml:space="preserve">Celeritas totalis Penduli compoſiti, quæ inter partes dis-
              <lb/>
            tribuitur proportionaliter ad arcus, quos ipſæ deſcribunt,
              <lb/>
            ſemper æqualis eſt ſummæ celeritatum, quas eædem partes
              <lb/>
            acquirerent, ſi a ſe invicem fuiſſent ſejunctæ, & </s>
            <s xml:id="echoid-s4973" xml:space="preserve">omnes ſepa-
              <lb/>
            ratim ex iisdem altitudinibus & </s>
            <s xml:id="echoid-s4974" xml:space="preserve">ad easdem ab axe, diſtantias
              <lb/>
            deſcendiſſent. </s>
            <s xml:id="echoid-s4975" xml:space="preserve">Altitudines ſemper ſunt ut quadrata velocitatum,
              <lb/>
            ſive pondera ſeparatim adſcendant, ſive deſcendant. </s>
            <s xml:id="echoid-s4976" xml:space="preserve">Omni-
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            bus his bene intellectis facile patet, ad hanc propoſitionem
              <lb/>
            redire quæſtionem. </s>
            <s xml:id="echoid-s4977" xml:space="preserve">Si habeamus du@s magnitudines inæquales
              <lb/>
            a a & </s>
            <s xml:id="echoid-s4978" xml:space="preserve">b b, ſummam radicum ipſarum a † b, & </s>
            <s xml:id="echoid-s4979" xml:space="preserve">quadrata
              <lb/>
            partium illius ſummæ, quæ ſint proportionales dictis magni-
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            tudinibus, quæque adeo communem denominatorem habeant
              <lb/>
            a a † b b, & </s>
            <s xml:id="echoid-s4980" xml:space="preserve">numeratores diverſos a
              <emph style="super">3</emph>
            † a a b & </s>
            <s xml:id="echoid-s4981" xml:space="preserve">b
              <emph style="super">3</emph>
            † a b b,
              <lb/>
            demonſtrare, ſummam harum duarum magnitudinum, quæ
              <lb/>
            altitudines, unde duo pondera æqualia Pendulo alligata
              <lb/>
            dimittuntur, repræſentant, non eſſe æqualem ſummæ quadra-
              <lb/>
            torum illarum partium, quæ altitudines exhibent, ad quas
              <lb/>
            duo pondera, poſtquam percuſſione fuerint ſeparata, redeunt,
              <lb/>
            niſi minor ex hiſce magnitudinibus a a & </s>
            <s xml:id="echoid-s4982" xml:space="preserve">b b ſit æqualis majo-
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            ri, id eſt, quia iſtæ magnitudines in quæſtione propoſitâ ſem-
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            per inæquales ſunt, niſi pars æqualis ſit, toti.</s>
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          <p>
            <s xml:id="echoid-s4984" xml:space="preserve">Maxime ſenſibilis hujus veritatis demonſtratio eſt compa-
              <lb/>
            ratio terminorum quæſtionis per regulas Algebraicas, id
              <lb/>
            quod examinandum relinquo iis, qui uſum illarum regula-
              <lb/>
            rum norunt. </s>
            <s xml:id="echoid-s4985" xml:space="preserve">Quod rem ipſam ſpectat, nullius eſt momenti;
              <lb/>
            </s>
            <s xml:id="echoid-s4986" xml:space="preserve">ſive centrum Mathematicum Oſcillationis bene ſive male de-
              <lb/>
            terminatum ſit, inventio Penduli nec minus utilis homini-
              <lb/>
            bus, nec minus auctore ſuo digna eſt.</s>
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