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-head213" xml:space="preserve">V.</head>
          <head xml:id="echoid-head214" style="it" xml:space="preserve">Objectio Abbatis Catelani contra motum
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          Pendulorum in Cycloidibus.</head>
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            <s xml:id="echoid-s4988" xml:space="preserve">Si vis gravitatis ageret in corpora tanquam in puncta Ma-
              <lb/>
            thematica, vel ſi ſpatium contentum ſub Cycloide eſſet
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            diviſibile in infinitas alias Cycloides, ſimiles & </s>
            <s xml:id="echoid-s4989" xml:space="preserve">parallelas,
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            quidam Geometræ revera demonſtraſſent, uti contendunt,
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            pendula illam debere deſcribere curvam ut Vibrationes, æ-
              <lb/>
            qualibus temporibus, peragant; </s>
            <s xml:id="echoid-s4990" xml:space="preserve">ſed nulla datur pars in cor-
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            pore gravi, quale eſt Pendulum ex cupro vel plumbo, quæ
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            non æque ac centrum Tellurem verſus propellatur magis mi-
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            nusve pro inclinatione, juxta quam movetur; </s>
            <s xml:id="echoid-s4991" xml:space="preserve">Præterea
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            ſpatium, quod continet Cyclois, non poteſt repleri infini-
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            tis aliis Cycloidibus ſimilibus, quoniam tripla circuli ſuperfi-
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            cies æqualis eſſet duplo quadrato diametri. </s>
            <s xml:id="echoid-s4992" xml:space="preserve">Latet igitur@adhuc
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            Geometras, quamnam lineam curvam deſcribat Pendulum,
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            cujus Vibrationes ſunt iſochronæ. </s>
            <s xml:id="echoid-s4993" xml:space="preserve">Conſequentia hæc patet,
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            ſi conſideremus, in corpore Pendulo, quando centrum vel
              <lb/>
            alia quælibet pars Cycloidem percurrit, partes viciniores
              <lb/>
            Axi, vel inde remotiores, eodem tempore, deſcribere lineas
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            curvas inter ſe ſimiles, ſed quæ non ſunt Cycloides; </s>
            <s xml:id="echoid-s4994" xml:space="preserve">ut
              <lb/>
            patet ex dictis, & </s>
            <s xml:id="echoid-s4995" xml:space="preserve">quia in quovis arcu perpendiculares
              <lb/>
            ductæ e tangentibus ſuis ad tangentes Cycloidis ſunt æqua-
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            les. </s>
            <s xml:id="echoid-s4996" xml:space="preserve">Omnes itaque partes non habent æqualem inclinationem
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            in deſcenſu, neque Tellurem verſus cum eâdem velocitatis
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            proportione propelluntur; </s>
            <s xml:id="echoid-s4997" xml:space="preserve">unde ſequitur, Vibrationem to-
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            tius Penduli, quæ neceſſario pendet a Vibrationibus, quas
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            peragunt partes ejus ſeparatim ſumtæ, differre a Penduli
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            Vibratione, ſi reductum foret ad illam partem, quæ move-
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            tur in Cycloide.</s>
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            <s xml:id="echoid-s4999" xml:space="preserve">Videtur huic potius cauſæ, quam craſſitudini fili, cui
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            pondus alligatur, adſcribendam eſſe artificum praxin, quos
              <lb/>
            experientia cogit curvaturam a Cycloide diverſam laminis
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            tribuere, inter quas ſuſpendunt Pendulum.</s>
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