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

Table of contents

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[151.] Fournier in Hydrographia 1. 12. C. 35.
Page: 299
[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
Page: 299
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
Page: 300
[154.] II.
Page: 300
[155.] III.
Page: 300
[156.] IV.
Page: 300
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
Page: 301 (196)
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
Page: 307 (202)
[159.] VII. Mari invenire horam diei.
Page: 309 (204)
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
Page: 310 (205)
[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)
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            <s xml:id="echoid-s2226" xml:space="preserve">
              <pb o="100" file="0148" n="160" rhead="CHRISTIANI HUGENII"/>
            ut quadratum B D ad quadratum D G ita eſt H K ad K G.
              <lb/>
            </s>
            <s xml:id="echoid-s2227" xml:space="preserve">
              <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            Ut autem H K ad K G, ita eſt quadratum F K ad quadra-
              <lb/>
            tum K G. </s>
            <s xml:id="echoid-s2228" xml:space="preserve">Ergo ſicut quadratum B D ad quadratum D G,
              <lb/>
            ita quadratum F K ad quadratum K G. </s>
            <s xml:id="echoid-s2229" xml:space="preserve">Et proinde ſicut
              <lb/>
            B D ad D G longitudine, ita F K ad K G. </s>
            <s xml:id="echoid-s2230" xml:space="preserve">Unde ſequitur
              <lb/>
            B G F eſſe lineam rectam. </s>
            <s xml:id="echoid-s2231" xml:space="preserve">Sed G F occurrit parabolæ E F ad
              <lb/>
            angulos rectos. </s>
            <s xml:id="echoid-s2232" xml:space="preserve">Ergo apparet B G, tangentem paraboloidis,
              <lb/>
            productam occurrere eidem parabolæ ad angulos rectos. </s>
            <s xml:id="echoid-s2233" xml:space="preserve">Idque
              <lb/>
            ſimiliter de quavis illius tangente demonſtrabitur. </s>
            <s xml:id="echoid-s2234" xml:space="preserve">Ergo con-
              <lb/>
            ſtat ex evolutione lineæ E A B, à termino E incepta, de-
              <lb/>
            ſcribi parabolam E F . </s>
            <s xml:id="echoid-s2235" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2236" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">Propoſ. 4.
            <lb/>
          huj.</note>
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        <div xml:id="echoid-div175" type="section" level="1" n="64">
          <head xml:id="echoid-head88" xml:space="preserve">PROPOSITIO IX.</head>
          <p style="it">
            <s xml:id="echoid-s2237" xml:space="preserve">REctam lineam invenire æqualem datæ portioni
              <lb/>
            curvæ paraboloidis, ejus nempe in qua qua-
              <lb/>
            drata ordinatim applicatarum ad axem, ſunt in-
              <lb/>
            ter ſe ſicut cubi abſciſſarum ad verticem.</s>
            <s xml:id="echoid-s2238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2239" xml:space="preserve">Quomodo hoc fiat ex prop. </s>
            <s xml:id="echoid-s2240" xml:space="preserve">præcedenti manifeſtum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2241" xml:space="preserve">
              <note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">TAB. XIII.
                <lb/>
              Fig. 2.</note>
            Parabola vero E F ad conſtructionem non requiritur, quæ
              <lb/>
            ſic peragetur. </s>
            <s xml:id="echoid-s2242" xml:space="preserve">Data quavis parte paraboloidis hujus A B, cui
              <lb/>
            rectam æqualem invenire oporteat, ducatur B G tangens in
              <lb/>
            puncto B, quæ occurrat axi A G in G. </s>
            <s xml:id="echoid-s2243" xml:space="preserve">Tanget autem ſi
              <lb/>
            A G fuerit tertia pars A D, inter verticem & </s>
            <s xml:id="echoid-s2244" xml:space="preserve">ordinatim ap-
              <lb/>
            plicatam B D interceptæ. </s>
            <s xml:id="echoid-s2245" xml:space="preserve">Porro ſumpta A E æquali {8/27} lineæ
              <lb/>
            M, quæ latus rectum eſt paraboloidis A B, ducatur E F
              <lb/>
            parallela B G, occurratque lineæ A F, quæ parallela eſt
              <lb/>
            B D, in F. </s>
            <s xml:id="echoid-s2246" xml:space="preserve">Jam ſi ad rectam B G addatur N F, exceſſus
              <lb/>
            rectæ E F ſupra E A, habebitur recta æqualis curvæ A B.
              <lb/>
            </s>
            <s xml:id="echoid-s2247" xml:space="preserve">Cujus demonſtratio ex ante dictis facile perſpicitur.</s>
            <s xml:id="echoid-s2248" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2249" xml:space="preserve">Semper ergo curva A B tantum ſuperat tangentem B G,
              <lb/>
            quantum recta E F rectam E A.</s>
            <s xml:id="echoid-s2250" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2251" xml:space="preserve">Rurſus autem hic in lineam incidimus, cujus longitudi-
              <lb/>
            nem alii jam ante dimenſi ſunt. </s>
            <s xml:id="echoid-s2252" xml:space="preserve">Illam nempe quam anno 1659
              <lb/>
            Joh. </s>
            <s xml:id="echoid-s2253" xml:space="preserve">Heuratius Harlemenſis rectæ æqualem oſtendit, cujus
              <lb/>
            demonſtratio poſt commentarios Joh. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">Schotenii in </s>
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