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

Table of contents

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[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.
Page: 320
[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)
[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)
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          <head xml:id="echoid-head148" style="it" xml:space="preserve">Centrum oſcillationis in Pyramide.</head>
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            <emph style="sc">Decentro</emph>
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            <emph style="sc">OSCILLA-</emph>
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            <emph style="sc">TIONIS</emph>
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            <s xml:id="echoid-s3770" xml:space="preserve">Sit primum A B C pyramis, verticem habens A, axem
              <lb/>
              <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">TAB.XXVI.
                <lb/>
              Fig. 1.</note>
            A D, baſin vero quadratum, cujus latus B C. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">ponaturque
              <lb/>
            agitari circa axem qui, per verticem A, ſit hujus paginæ
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            plano ad angulos rectos.</s>
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          <p>
            <s xml:id="echoid-s3773" xml:space="preserve">Hic figura plana proportionalis O V V, à latere adpo-
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            nenda, ſecundum propoſitionem 14, conſtabit ex reſiduis
              <lb/>
            parabolicis O P V, quæ nempe ſuperſunt, cum, à rectan-
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            gulis Ω P, auferuntur ſemiparabolæ O V Ω, verticem ha-
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            bentes O.</s>
            <s xml:id="echoid-s3774" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3775" xml:space="preserve">Sicut enim inter ſe ſectiones pyramidis B C, N N, ita
              <lb/>
            quoque rectæ V V, R R, ipſis in figura plana reſponden-
              <lb/>
            tes. </s>
            <s xml:id="echoid-s3776" xml:space="preserve">& </s>
            <s xml:id="echoid-s3777" xml:space="preserve">ſicut centrum gravitatis E diſtat, à vertice pyrami-
              <lb/>
            dis, tribus quartis axis A D, ita quoque centrum gravita-
              <lb/>
            tis F, figuræ O V V, diſtabit tribus quartis diametri O P
              <lb/>
            à vertice O.</s>
            <s xml:id="echoid-s3778" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3779" xml:space="preserve">Intellecto porro horizontali plano N E, per centrum gra-
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            vitatis pyramidis A B C, quod idem figuram O V V ſecet
              <lb/>
            ſecundum R F; </s>
            <s xml:id="echoid-s3780" xml:space="preserve">inventâque ſubcentricâ cunei, ſuper figura
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            O V V abſciſſi plano per O Ω, quæ ſubcentrica ſit O G,
              <lb/>
            (eſt autem {4/5} diametri O P) erit rectangulum O F G, mul-
              <lb/>
            tiplex per numerum particularum figuræ O V V, æquale
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            quadratis diſtantiarum ab recta R F , ac proinde
              <note symbol="*" position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">Prop. 10.
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              huj.</note>
            quadratis diſtantiarum à plano N E, particularum ſolidi
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            A B C. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">Fit autem rectangulum O F G æquale {3/80} quadrati
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            O P, vel quadrati A D.</s>
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            <s xml:id="echoid-s3783" xml:space="preserve">Deinde, ad inveniendam ſummam quadratorum à diſtan-
              <lb/>
            tiis à plano A D, noſcenda primo ſubcentrica cunei, ſuper
              <lb/>
            quadratâ baſi pyramidis B C abſciſſi, plano per rectam quæ
              <lb/>
            in B intelligitur axi A parallela; </s>
            <s xml:id="echoid-s3784" xml:space="preserve">quæ ſubcentrica ſit B K;
              <lb/>
            </s>
            <s xml:id="echoid-s3785" xml:space="preserve">eſtque {2/3} B C. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">Noſcenda item diſtantia centr. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">dimidiæ fi-
              <lb/>
            guræ O P V ab O P; </s>
            <s xml:id="echoid-s3789" xml:space="preserve">quæ ſit Φ P; </s>
            <s xml:id="echoid-s3790" xml:space="preserve">eſtque {3/10} P V. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">Inde,
              <lb/>
            diviſà bifariam P V in Δ, ſi fiat ut Δ P ad P Φ, hoc eſt,
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            ut 5 ad 3, ita rectangulum B D K, quod eſt {1/12} quadrati
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            B C, ad aliud ſpatium Z; </s>
            <s xml:id="echoid-s3792" xml:space="preserve">erit hoc, multiplex </s>
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