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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            æqualitatis; </s>
            <s xml:id="echoid-s2490" xml:space="preserve">liquet rationem B G ad G M fore eandem quæ N H
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                <emph style="sc">De linea-</emph>
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                <emph style="sc">RUM CUR-</emph>
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                <emph style="sc">VARUM</emph>
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                <emph style="sc">EVOLUTIO-</emph>
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                <emph style="sc">NE.</emph>
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            ad H L; </s>
            <s xml:id="echoid-s2491" xml:space="preserve">& </s>
            <s xml:id="echoid-s2492" xml:space="preserve">dividendo, B M ad M G, eandem quæ N L
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            ad L H, ſive M K ad K H; </s>
            <s xml:id="echoid-s2493" xml:space="preserve">nam L H, K H pro eadem
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            habentur, propter propinquitatem punctorum B, F. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">Data
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            autem eſt ratio M K ad K H, dato puncto B; </s>
            <s xml:id="echoid-s2495" xml:space="preserve">quoniam
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            tam M K, quam K H dantur magnitudine; </s>
            <s xml:id="echoid-s2496" xml:space="preserve">nam M K
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            æquatur dimidio lateri recto, K H vero duplæ K A. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">Dataque
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            etiam eſt poſitione & </s>
            <s xml:id="echoid-s2498" xml:space="preserve">magnitudine recta B M. </s>
            <s xml:id="echoid-s2499" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2500" xml:space="preserve">M G
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            data erit, adeoque & </s>
            <s xml:id="echoid-s2501" xml:space="preserve">punctum G, ſive D, in curva R D E;
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            <s xml:id="echoid-s2502" xml:space="preserve">quod nempe invenitur productâ B M uſque in G, ut ſit
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            B M ad M G ſicut {1/2} lateris recti ad duplam K A.</s>
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            <s xml:id="echoid-s2504" xml:space="preserve">Et ſic quidem, adſumptis in parabola A B F aliis quotli-
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            bet punctis præter B, totidem quoque puncta lineæ R D E,
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            ſimili ratione, invenientur; </s>
            <s xml:id="echoid-s2505" xml:space="preserve">atque hoc ipſo lineam R D E
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            geometricam eſſe conſtat, unáque proprietas ejus innoteſcit,
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            ex qua cæteræ deduci poſſunt. </s>
            <s xml:id="echoid-s2506" xml:space="preserve">Ut ſi inquirere deinde veli-
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            mus, quanam æquatione exprimatur relatio punctorum
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            omnium curvæ C D E ad rectam A Q: </s>
            <s xml:id="echoid-s2507" xml:space="preserve">ducta in hanc perpen-
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            <s xml:id="echoid-s2509" xml:space="preserve">A Q, x; </s>
            <s xml:id="echoid-s2510" xml:space="preserve">Q D, y. </s>
            <s xml:id="echoid-s2511" xml:space="preserve">Quoniam ratio B M ad M D,
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            hoc eſt, K M ad M Q, eſt ea quæ {1/2} a ad 2 b, eſtque ipſa
              <lb/>
            K M = {1/2} a, erit & </s>
            <s xml:id="echoid-s2512" xml:space="preserve">M Q æqualis 2 b. </s>
            <s xml:id="echoid-s2513" xml:space="preserve">Eſt autem M A = {1/2}
              <lb/>
            a + b. </s>
            <s xml:id="echoid-s2514" xml:space="preserve">ergo A Q ſive x æqualis 3 b + {1/2} a. </s>
            <s xml:id="echoid-s2515" xml:space="preserve">Unde b = {1/3} x
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            -{1/6} a. </s>
            <s xml:id="echoid-s2516" xml:space="preserve">Porro quoniam, ſicut quadratum M K, hoc eſt, {1/4} a a
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            ad quadratum K B, hoc eſt, a b, ita qu. </s>
            <s xml:id="echoid-s2517" xml:space="preserve">M Q, hoc eſt,
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            4 b b ad qu. </s>
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            <s xml:id="echoid-s2519" xml:space="preserve">erit qu. </s>
            <s xml:id="echoid-s2520" xml:space="preserve">Q D, ſive y y = {16b
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            /4}. </s>
            <s xml:id="echoid-s2521" xml:space="preserve">Ubi, ſi in
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            locum b ſubſtituatur {1/3} x - {1/6}a, quod illi æquale inventum eſt,
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            fiet y y = 16. </s>
            <s xml:id="echoid-s2522" xml:space="preserve">cub. </s>
            <s xml:id="echoid-s2523" xml:space="preserve">{1/3} x - {1/6} a diviſis per a. </s>
            <s xml:id="echoid-s2524" xml:space="preserve">Ac proinde {27/16} a y y
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            = cubo ab x - {1/2} a. </s>
            <s xml:id="echoid-s2525" xml:space="preserve">Accipiatur A R in axe parabolæ = {1/2} a; </s>
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            eritque R Q = x - {1/2} a. </s>
            <s xml:id="echoid-s2527" xml:space="preserve">Curvam igitur C D ejus naturæ eſſe
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            liquet, ut ſemper cubus lineæ R Q æquetur parallelepipedo,
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            cujus baſis qu. </s>
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            <s xml:id="echoid-s2529" xml:space="preserve">ac proinde ipſam para-
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            rectum æquale fit {15/27} lateris recti paraboloidis, quemadmo-
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            dum ibi fuit deſinitum.</s>
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