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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            nempe rectangulum fit à diſtantia centri gravitatis
              <lb/>
              <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS.</emph>
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            figuræ ab eadem recta, & </s>
            <s xml:id="echoid-s3030" xml:space="preserve">à ſubcentrica cunei, qui
              <lb/>
            per illam ſuper figura abſcinditur.</s>
            <s xml:id="echoid-s3031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3032" xml:space="preserve">Poſitis enim cæteris omnibus quæ in conſtructione præce-
              <lb/>
              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">TAB. XIX.
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              Fig. 4.</note>
            denti, ſit L A cunei A B D ſubcentrica in rectam E E. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">O-
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            portet igitur oſtendere, ſummam quadratorum omnium à di-
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            ſtantiis particularum figuræ A C B æquari rectangulo ab
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            F A, L A, multiplici ſecundum particularum numerum.</s>
            <s xml:id="echoid-s3034" xml:space="preserve"/>
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            <s xml:id="echoid-s3035" xml:space="preserve">Et conſtat quidem ex demonſtratione præcedenti, altitu-
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            dines parallelepipedorum ſingulorum, ut G K, æquales eſ-
              <lb/>
            ſe diſtantiis particularum, quæ ipſorum baſes ſunt, ut G,
              <lb/>
            ab recta A E. </s>
            <s xml:id="echoid-s3036" xml:space="preserve">Quare, ſi jam parallelepipedum G K ducamus
              <lb/>
            in diſtantiam G H, perinde eſt ac ſi particula G ducatur in
              <lb/>
            quadratum diſtantiæ G H. </s>
            <s xml:id="echoid-s3037" xml:space="preserve">Eodemque modo ſe res habet in
              <lb/>
            reliquis omnibus. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">Atqui producta omnia parallelepipedorum
              <lb/>
            in diſtantias ſuas ab recta A E, æquantur ſimul producto ex
              <lb/>
            cuneo A B D in diſtantiam L A , quia cuneus gravitat
              <note symbol="*" position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">Prop. 1.
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              huj.</note>
            per puncto L. </s>
            <s xml:id="echoid-s3039" xml:space="preserve">Ergo etiam ſumma productorum à particulis
              <lb/>
            ſingulis G, in quadrata ſuarum diſtantiarum ab recta A E,
              <lb/>
            æquabitur producto ex cuneo A B D in rectam L A, hoc
              <lb/>
            eſt, producto ex figura A C B in rectangulum ab F A, L A.
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            </s>
            <s xml:id="echoid-s3040" xml:space="preserve">Nam cuneus A B D, æqualis eſt producto ex figura A C B
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            in rectam F A . </s>
            <s xml:id="echoid-s3041" xml:space="preserve">Rurſus quia figura A C B æqualis eſt
              <note symbol="*" position="left" xlink:label="note-0194-04" xlink:href="note-0194-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            ducto ex particula una G, in numerum ipſarum particula-
              <lb/>
            rum; </s>
            <s xml:id="echoid-s3042" xml:space="preserve">ſequitur, dictum productum ex figura A C B in re-
              <lb/>
            ctangulum ab F A, L A, æquari producto ex particula G
              <lb/>
            in rectangulum ab F A, L A, multiplici ſecundum nume-
              <lb/>
            rum particularum G. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">Cui proinde etiam æqualis erit dicta
              <lb/>
            ſumma productorum, à particulis ſingulis G in quadrata
              <lb/>
            ſuarum diſtantiarum ab recta A E, ſive à particula una G in
              <lb/>
            ſummam omnium horum quadratorum. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">Quare, omiſſa utrin-
              <lb/>
            que multiplicatione in particulam G, neceſſe eſt ſummam
              <lb/>
            @andem quadratorum æquari rectangulo ab F A, L A, mul-
              <lb/>
            tiplici ſecundum numerum particularum in quas figura A C B
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            diviſa intelligitur. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">quod erat demonſtrandum.</s>
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