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

Table of contents

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[161.] IX.
[163.] XI.
[164.] XII.
[165.] FINIS.
[166.] EXCERPTA EX LITERIS DATIS LONDINI {13/23} JANUARII MDCLXV.
[167.] EXCERPTA EX LITERIS HAGÆ CO-MITUM, DIE XXVI. FEBRUAR MDCLXV. DATIS.
[168.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA.
[169.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA. I. Obſervationes Abbatis Catelani in propoſitio-nem, quæ fundamentum eſt 4æ. partis tra-ctatus de Pendulis, Hugenii.
[170.] II. Domini Abbatis Catelani Examen Ma-thematicum Centri Oſcillationis.
[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.
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          <p>
            <s xml:id="echoid-s3366" xml:space="preserve">Porrò ſummam quadratorum ab rectis, quæ ducuntur à
              <lb/>
              <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            dictis punctis omnibus ad punctum F, eandem eſſe patet cum
              <lb/>
            ſumma quadratorum ab iis rectis, quæ à ſingulis particulis
              <lb/>
            magnitudinis propoſitæ ducuntur perpendiculares in axem
              <lb/>
            oſcillationis per F transeuntem; </s>
            <s xml:id="echoid-s3367" xml:space="preserve">quippe cum lineæ ipſæ,
              <lb/>
            quarum quadrata intelliguntur, utrobique eandem habeant
              <lb/>
            longitudinem. </s>
            <s xml:id="echoid-s3368" xml:space="preserve">Similiter etiam, cum ſuſpenſio eſt ex axe per
              <lb/>
            H, patet ſummam quadratorum ab rectis, quæ ab omnibus
              <lb/>
            punctis, in ſpatio A B C D ſignatis, ducuntur ad punctum
              <lb/>
            H, eandem eſſe cum ſumma quadratorum, ab iis quæ, à
              <lb/>
            particulis omnibus magnitudinis propoſitæ, ducuntur per-
              <lb/>
            pendiculares in axem oſcillationis per H transeuntem. </s>
            <s xml:id="echoid-s3369" xml:space="preserve">Ergo
              <lb/>
            utroque caſu, ſi ſumma quadratorum ab rectis quæ, à pun-
              <lb/>
            ctis omnibus prædictis, ducuntur ad puncta F vel H; </s>
            <s xml:id="echoid-s3370" xml:space="preserve">di-
              <lb/>
            vidatur per rectas E F vel E H, multiplices ſecundum nu-
              <lb/>
            merum particularum in quas magnitudo propoſita diviſa in-
              <lb/>
            telligitur, orietur ex applicatione hac longitudo penduli ſim-
              <lb/>
            plicis, quod magnitudini ſuſpenſæ ex F vel H iſochronum
              <lb/>
            fit. </s>
            <s xml:id="echoid-s3371" xml:space="preserve">Eſt autem ſumma quadratorum utroque caſu æqualis ;</s>
            <s xml:id="echoid-s3372" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">Prop. 13.
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              huj.</note>
            & </s>
            <s xml:id="echoid-s3373" xml:space="preserve">rectæ quoque E F, E H, inter ſe æquales; </s>
            <s xml:id="echoid-s3374" xml:space="preserve">& </s>
            <s xml:id="echoid-s3375" xml:space="preserve">particu-
              <lb/>
            larum idem numerus. </s>
            <s xml:id="echoid-s3376" xml:space="preserve">Ergo, quum & </s>
            <s xml:id="echoid-s3377" xml:space="preserve">applicatæ quantitates,
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            & </s>
            <s xml:id="echoid-s3378" xml:space="preserve">quibus illæ applicantur, utrobique æquales ſint, etiam
              <lb/>
            longitudines ex applicatione ortæ æquales erunt, hoc eſt,
              <lb/>
            longitudines pendulorum iſochronorum magnitudini propoſi-
              <lb/>
            tæ ſuſpenſæ ex F vel ex H. </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Quare conſtat propoſitum.</s>
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          <head xml:id="echoid-head133" xml:space="preserve">PROPOSITIO XVII.</head>
          <p style="it">
            <s xml:id="echoid-s3381" xml:space="preserve">DAto plano, cujus multiplex per numerum par-
              <lb/>
            ticularum, in quas ſuſpenſa figura diviſa in-
              <lb/>
            telligitur, æquetur quadratis omnium diſtantia-
              <lb/>
            rum ab axe oſcillationis; </s>
            <s xml:id="echoid-s3382" xml:space="preserve">ſi illud applicetur ad re-
              <lb/>
            ctam, æqualem diſtantiæ inter axem oſcillationis
              <lb/>
            & </s>
            <s xml:id="echoid-s3383" xml:space="preserve">centrum gravitatis ſuſpenſæ magnitudinis, orie-
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            tur longitudo penduli ſimplicis ipſi iſochroni.</s>
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