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

Table of contents

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[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.
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            Pendulo compoſito. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">Nam eandem habent proportionem,
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            quam arcus deſcripti a duobus ponderibus æqualibus, ex
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            quibus Pendulum formatur; </s>
            <s xml:id="echoid-s4970" xml:space="preserve">duo illi arcus ſunt ſpatia, quæ
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            duo pondera percurrunt, eodem tempore, velocitatibus,
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            quæ neceſſario ſunt ipſis ſpatiis proportionales.</s>
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            <s xml:id="echoid-s4972" xml:space="preserve">Celeritas totalis Penduli compoſiti, quæ inter partes dis-
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            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-
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            ratim ex iisdem altitudinibus & </s>
            <s xml:id="echoid-s4974" xml:space="preserve">ad easdem ab axe, diſtantias
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            deſcendiſſent. </s>
            <s xml:id="echoid-s4975" xml:space="preserve">Altitudines ſemper ſunt ut quadrata velocitatum,
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            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
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            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
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            partium illius ſummæ, quæ ſint proportionales dictis magni-
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            tudinibus, quæque adeo communem denominatorem habeant
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            a a † b b, & </s>
            <s xml:id="echoid-s4980" xml:space="preserve">numeratores diverſos a
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            † a a b & </s>
            <s xml:id="echoid-s4981" xml:space="preserve">b
              <emph style="super">3</emph>
            † a b b,
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            demonſtrare, ſummam harum duarum magnitudinum, quæ
              <lb/>
            altitudines, unde duo pondera æqualia Pendulo alligata
              <lb/>
            dimittuntur, repræſentant, non eſſe æqualem ſummæ quadra-
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            torum illarum partium, quæ altitudines exhibent, ad quas
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            duo pondera, poſtquam percuſſione fuerint ſeparata, redeunt,
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            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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            <s xml:id="echoid-s4984" xml:space="preserve">Maxime ſenſibilis hujus veritatis demonſtratio eſt compa-
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            ratio terminorum quæſtionis per regulas Algebraicas, id
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            quod examinandum relinquo iis, qui uſum illarum regula-
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            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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