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

Table of contents

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[171.] MONITUM.
[172.] III. Excerpta ex literis Domini Hugenii, quibus re-ſpondet obſervationi Abbatis Catelani in 4am. pro-poſitionem Tractatus de centris Oſcillationis.
[173.] IV. Exceptio Abbatis Catelani ad reſponſionem Hugenii.
[174.] V. Objectio Abbatis Catelani contra motum Pendulorum in Cycloidibus.
[175.] VI. Reſponſio ad objectiones Hugenii adverſus me-thodum Abbatis Catelani de determinan-do Centro Oſcillationis.
[176.] VII. Excerpta ex litteris D. Bernoullii datis Baſileæ ad Autorem Diarii Pariſienſis, de Controverſia, inter Abbatem Catelanum & Hugenium, de Centro Oſcillationis.
[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.
[178.] IX. Reſponſio Dni. Abbatis Catelani ad literas Dni. Bernoulli de Controverſia ſua cum Dno. Hu-genio de centro Oſcillationis .
[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.
[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.
[181.] XII. Obſervationes Dni Hugenii in liter as præcedentes & in relationem Dni Bernoulli, cujus in iis fit mentio.
[182.] FINIS.
[183.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM.
[184.] MACHINÆ QUÆDAM, ET VARIA CIRCA MECHANICAM. I. Excerpta ex Literis Domini Hugenii, novam quan-dam Inventionem Horologiorum exactiſſino-rum ac portatilium concernentibus.
[185.] II. Nova Libella, Teleſcopio inſtructa, propriam ſecum ferens probationem, & quæ in unica ſtatione verificatur, & rectificatur.
[186.] Rectificationis Libellæ Demonſtratio.
[187.] III. Aſtroſcopia Compendiaria, Tubi Optici molimine liberata.
[188.] AUCTARIUM.
[189.] IV. Excerpta ex literis Dni Hugenii de novâ methodo conſtruendi Barometrum.
[190.] V. Nova vis movens mediante pulvere nitrato & aëre.
[191.] VI. Demonſtratio Æquilibrii bilancis.
[192.] VII. De potentiis fila funesve trahentibus.
[193.] VIII. Solitio problematis a G G. Leibnitio propoſiti in diario (cui titulus Nouvelles de la Republi-que des Lettres) menſis Sept. 1687. PROBLEMA.
[194.] Solutio.
[195.] IX. Chriſtiani Hugenii, Solutio Problematis de linea in quam flexile ſe pondere pro-prio curvat.
[196.] X. Hugenii Annotationes in librum Pariſiis 1689. editum, de Manuaria Nautica.
[197.] XI. Reſponſum Dni Renaldi ad Dominum Hugenium.
[198.] XII. Exceptio Dni Hugenii ad Reſponſum Dni Renaldi.
[199.] FINIS.
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          <head xml:id="echoid-head125" xml:space="preserve">PROPOSITIO IX.</head>
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            <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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            <s xml:id="echoid-s3047" xml:space="preserve">DAtâ figurâ planâ & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">in eodem plano lineâ re-
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            ctâ, quæ vel ſecet figuram vel non, ad quam
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            perpendiculares cadant à particulis ſingulis minimis
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            & </s>
            <s xml:id="echoid-s3049" xml:space="preserve">æqualibus, in quas figura diviſa intelligitur;
              <lb/>
            </s>
            <s xml:id="echoid-s3050" xml:space="preserve">invenire ſummam quadratorum ab omnibus iſtis per-
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            pendicularibus; </s>
            <s xml:id="echoid-s3051" xml:space="preserve">ſive planum, cujus multiplex, ſe-
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            cundum particularum numerum, dictæ quadrato-
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            rum ſummæ æquale ſit.</s>
            <s xml:id="echoid-s3052" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3053" xml:space="preserve">Sit data figura plana A B C, & </s>
            <s xml:id="echoid-s3054" xml:space="preserve">in eodem plano recta
              <lb/>
              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">TAB. XIX.
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              Fig. 5. 6.</note>
            E D; </s>
            <s xml:id="echoid-s3055" xml:space="preserve">divisâque figurâ cogitatu in particulas minimas æqua-
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            les, intelligantur ab unaquaque earum perpendiculares du-
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            ctæ in rectam E D, ſicut à particula F ducta eſt F K. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">O-
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            porteatque invenire ſummam quadratorum ab omnibus iſtis
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            perpendicularibus.</s>
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          <p>
            <s xml:id="echoid-s3058" xml:space="preserve">Sit datæ E D parallela recta A L, quæ figuram tangat,
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            ac tota extra eam poſita ſit. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Poteſt autem figuram vel ab ea-
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            dem parte ex qua eſt E D, vel à parte oppoſita contingere.
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            <s xml:id="echoid-s3060" xml:space="preserve">Diſtantia vero centri gravitatis figuræ ab recta A L ſit recta
              <lb/>
            G A, ſecans E D in E; </s>
            <s xml:id="echoid-s3061" xml:space="preserve">& </s>
            <s xml:id="echoid-s3062" xml:space="preserve">ſubcentrica cunei, ſuper figura
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            abſciſſi plano per rectam A L, ſit H A. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">Dico ſummam qua-
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            dratorum quæſitam æquari rectangulo A G H una cum qua-
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            drato E G, multiplicibus ſecundum particularum numerum,
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            in quas figura diviſa intelligitur.</s>
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          <p>
            <s xml:id="echoid-s3065" xml:space="preserve">Occurrat enim F K, ſi opus eſt producta, tangenti A L
              <lb/>
            in L puncto. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">Itaque primum, eo caſu quo recta E D à ſi-
              <lb/>
            gura diſtat, & </s>
            <s xml:id="echoid-s3067" xml:space="preserve">tangens A L ad eandem figuræ partem ducta
              <lb/>
            eſt, ſic propoſitum oſtendetur. </s>
            <s xml:id="echoid-s3068" xml:space="preserve">Summa omnium quadrato-
              <lb/>
            rum F K æquatur totidem quadratis K L, una cum bis to-
              <lb/>
            tidem rectangulis K L F, & </s>
            <s xml:id="echoid-s3069" xml:space="preserve">totidem inſuper quadratis L F.
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            </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Sed quadrata K L æquantur totidem quadratis E A. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Et re-
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            ctangula K L F æqualia eſſe conſtat totidem </s>
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