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

Table of contents

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[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)
[181.] XII. Obſervationes Dni Hugenii in liter as præcedentes & in relationem Dni Bernoulli, cujus in iis fit mentio.
Page: 351 (246)
[182.] FINIS.
Page: 353 (248)
[183.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM.
Page: 357
[184.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM. I. Excerpta ex Literis Domini Hugenii, novam quan-dam Inventionem Horologiorum exactiſſino-rum ac portatilium concernentibus.
Page: 359
[185.] II. Nova Libella, Teleſcopio inſtructa, propriam ſecum ferens probationem, & quæ in unica ſtatione verificatur, & rectificatur.
Page: 360 (254)
[186.] Rectificationis Libellæ Demonſtratio.
Page: 364 (258)
[187.] III. Aſtroſcopia Compendiaria, Tubi Optici molimine liberata.
Page: 367 (261)
[188.] AUCTARIUM.
Page: 385 (273)
[189.] IV. Excerpta ex literis Dni Hugenii de novâ methodo conſtruendi Barometrum.
Page: 388 (276)
[190.] V. Nova vis movens mediante pulvere nitrato & aëre.
Page: 395 (280)
[191.] VI. Demonſtratio Æquilibrii bilancis.
Page: 397 (282)
[192.] VII. De potentiis fila funesve trahentibus.
Page: 405 (287)
[193.] VIII. Solitio problematis a G G. Leibnitio propoſiti in diario (cui titulus Nouvelles de la Republi-que des Lettres) menſis Sept. 1687. PROBLEMA.
Page: 408 (290)
[194.] Solutio.
Page: 408 (290)
[195.] IX. Chriſtiani Hugenii, Solutio Problematis de linea in quam flexile ſe pondere pro-prio curvat.
Page: 409 (291)
[196.] X. Hugenii Annotationes in librum Pariſiis 1689. editum, de Manuaria Nautica.
Page: 410 (292)
[197.] XI. Reſponſum Dni Renaldi ad Dominum Hugenium.
Page: 414 (296)
[198.] XII. Exceptio Dni Hugenii ad Reſponſum Dni Renaldi.
Page: 423 (305)
[199.] FINIS.
Page: 426 (308)
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            ce, curva V A deſcribitur; </s>
            <s xml:id="echoid-s6407" xml:space="preserve">atque evolutæ ipſius K N lon-
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            gitudo. </s>
            <s xml:id="echoid-s6408" xml:space="preserve">Velut ſi angulus C G A fuerit 60°, erit K N tripla
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            axis B V. </s>
            <s xml:id="echoid-s6409" xml:space="preserve">Si vero latera G B, B A, A G ſint ut 3, 4, 5,
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            erit illa {9/4} axis B V.</s>
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            <s xml:id="echoid-s6411" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6412" xml:space="preserve">Præterea ſpatii N K V A N quadratura datur. </s>
            <s xml:id="echoid-s6413" xml:space="preserve">Poſi-
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            to enim angulo C G A 60°, erit ſpatium illud æquale rectan-
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            gulo ex axe B V, & </s>
            <s xml:id="echoid-s6414" xml:space="preserve">ea quæ poteſt triplum quadratum
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            ejusdem B V. </s>
            <s xml:id="echoid-s6415" xml:space="preserve">Si vero latera G B, B A, A G ſint ut 3, 4, 5,
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            erit idem ſpatium æquale ſeptuplo quadrato B V, cum par-
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            te octava.</s>
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          <p>
            <s xml:id="echoid-s6417" xml:space="preserve">7. </s>
            <s xml:id="echoid-s6418" xml:space="preserve">Porro puncta quotlibet catenæ inveniri poſſunt, poſi-
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            ta quadratura curvæ alterutrius harum: </s>
            <s xml:id="echoid-s6419" xml:space="preserve">x x y y = a
              <emph style="super">4</emph>
            — a a y y,
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            vel x x y y = 4a
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            — x
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            . </s>
            <s xml:id="echoid-s6420" xml:space="preserve">Vel etiam data diſtantia centri gravi-
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            tatis ab axe, in portionibus planis, quas abſcindunt rectæ
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            axi parallelæ in curva harum priore. </s>
            <s xml:id="echoid-s6421" xml:space="preserve">Quadratura autem hu-
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            jus curvæ pendet a ſummis ſecantium arcuum per minima
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            æqualiter creſcentium: </s>
            <s xml:id="echoid-s6422" xml:space="preserve">quæ ſummæ ex Tabulis ſinuum egre-
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            gio quodam adhibito compendio inveniuntur quamlibet pro-
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            xime. </s>
            <s xml:id="echoid-s6423" xml:space="preserve">Hinc ex. </s>
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            <s xml:id="echoid-s6425" xml:space="preserve">inventum, quod ſi angulus C G A ſit
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            rectus, & </s>
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            21279, non una minus. </s>
            <s xml:id="echoid-s6428" xml:space="preserve">Curva autem V A, per ſuperius
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            indicata cognoſcitur hic eſſe partium 24142, non una minus.</s>
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            <s xml:id="echoid-s6430" xml:space="preserve">In his omnibus non niſi ad caſus ſingulares ſolutiones pro-
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            blematum dedi, vitandæ prolixitatis ſtudio & </s>
            <s xml:id="echoid-s6431" xml:space="preserve">quoniam non
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            dubito quin regulas univerſales Viri docti affatim ſint exhi-
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            bituri. </s>
            <s xml:id="echoid-s6432" xml:space="preserve">Quod ſi tamen aliquæ ex noſtris requirentur, eas lu-
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            benter mittam. </s>
            <s xml:id="echoid-s6433" xml:space="preserve">Ac jam pridem omnes apud Clariſſimum Vi-
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            rum G. </s>
            <s xml:id="echoid-s6434" xml:space="preserve">G. </s>
            <s xml:id="echoid-s6435" xml:space="preserve">Leibnitium involucro quodam obtectas depoſui.</s>
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          <head xml:id="echoid-head253" xml:space="preserve">X.</head>
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          editum, de Manuaria Nautica.</head>
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            neral de Marine), ſumma cura & </s>
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