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

Table of contents

< >
[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)
< >
page |< < (139) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div274" type="section" level="1" n="102">
          <p>
            <s xml:id="echoid-s3143" xml:space="preserve">
              <pb o="139" file="0201" n="220" rhead="HOROLOG. OSCILLATOR."/>
            datorum punctorum multitudinem exprimens, dicatur θ; </s>
            <s xml:id="echoid-s3144" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            E R = {ι/θ}; </s>
            <s xml:id="echoid-s3145" xml:space="preserve">& </s>
            <s xml:id="echoid-s3146" xml:space="preserve">R G = {μ/θ}. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">Cumque G S ſit x, erit R S ſive
              <lb/>
            F T = x - {μ/θ}; </s>
            <s xml:id="echoid-s3148" xml:space="preserve">vel {μ/θ} - x, ſi G R major quam G S; </s>
            <s xml:id="echoid-s3149" xml:space="preserve">& </s>
            <s xml:id="echoid-s3150" xml:space="preserve">ſem-
              <lb/>
            per quadratum F T = xx - 2 {xμ/θ} + {μμ/θθ}. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">quo ablato ab qua-
              <lb/>
            drato F E = zz, relinquetur quadratum T E = zz - xx
              <lb/>
            + 2 {xμ/θ} - {μμ/θθ}. </s>
            <s xml:id="echoid-s3152" xml:space="preserve">Et proinde T E =
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s3153" xml:space="preserve">Erat autem E R = {ι/θ}. </s>
            <s xml:id="echoid-s3154" xml:space="preserve">Itaque T R = {ι/θ} + vel -
              <emph style="red">zz - xx
                <lb/>
              + 2 {xμ/θ} - {μμ/θθ}</emph>
            . </s>
            <s xml:id="echoid-s3155" xml:space="preserve">quæ T R, brevitatis gratia, dicatury y. </s>
            <s xml:id="echoid-s3156" xml:space="preserve">Colli-
              <lb/>
            gamus jam porro ſummam quadratorum omnium F A, F B,
              <lb/>
            F C, F D. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">Quadratum A F æquatur quadratis A V, V F. </s>
            <s xml:id="echoid-s3158" xml:space="preserve">
              <lb/>
            Eſt autem A V æqualis differentiæ duarum V K, A K, ſi-
              <lb/>
            ve duarum S G, A K; </s>
            <s xml:id="echoid-s3159" xml:space="preserve">ac proinde A V = x - e vel e - x; </s>
            <s xml:id="echoid-s3160" xml:space="preserve">& </s>
            <s xml:id="echoid-s3161" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">A V = xx - 2 ex + ee. </s>
            <s xml:id="echoid-s3163" xml:space="preserve">V F vero æqualis eſt differen-
              <lb/>
            tiæ duarum F S, V S ſive duarum F S, A L; </s>
            <s xml:id="echoid-s3164" xml:space="preserve">ac proinde
              <lb/>
            V F = y - a vel a - y; </s>
            <s xml:id="echoid-s3165" xml:space="preserve">& </s>
            <s xml:id="echoid-s3166" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">V F = yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">Ad-
              <lb/>
            ditisque quadratis A V, V F, fit quadratum F A = xx - 2 ex
              <lb/>
            + ee + yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3169" xml:space="preserve">Eodemque modo invenientur qua-
              <lb/>
            drata reliquarum F B, F C, F D; </s>
            <s xml:id="echoid-s3170" xml:space="preserve">atque omnia ordine diſ-
              <lb/>
            poſita erunt hæc; </s>
            <s xml:id="echoid-s3171" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3172" xml:space="preserve">F A = xx - 2 ex + ee + yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3174" xml:space="preserve">F B = xx - 2 fx + ff + yy - 2 by + bb. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3176" xml:space="preserve">F C = xx - 2 gx + gg + yy - 2 cy + cc. </s>
            <s xml:id="echoid-s3177" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3178" xml:space="preserve">F D = xx - 2 hx + hh + yy - 2 dy + dd.</s>
            <s xml:id="echoid-s3179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3180" xml:space="preserve">Horum vero ſumma; </s>
            <s xml:id="echoid-s3181" xml:space="preserve">ſi ponamus quadrata ee + ff + gg
              <lb/>
            + hh = nn; </s>
            <s xml:id="echoid-s3182" xml:space="preserve">& </s>
            <s xml:id="echoid-s3183" xml:space="preserve">quadrata aa + bb, + cc + dd = kk;
              <lb/>
            </s>
            <s xml:id="echoid-s3184" xml:space="preserve">erit iſta, θ x x - 2 mx + nn + θ yy - 2 ly + kk. </s>
            <s xml:id="echoid-s3185" xml:space="preserve">Siquidem
              <lb/>
            θ erat numerus datorum punctorum ideoque & </s>
            <s xml:id="echoid-s3186" xml:space="preserve">quadratorum,
              <lb/>
            poſitumque fuerat e + f + g + h = m, & </s>
            <s xml:id="echoid-s3187" xml:space="preserve">a + b + c + d = l.</s>
            <s xml:id="echoid-s3188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3189" xml:space="preserve">In iſta vero ſumma, ſi in terminis θ y y & </s>
            <s xml:id="echoid-s3190" xml:space="preserve">2 l y, pro y,
              <lb/>
            ponatur id cujus loco poſitum erat, nempe {ι/θ} + vel -
              <lb/>
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
              <lb/>
            fiet + θ y y = {ιι/θ} + 2 l
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            + θ zz - θ xx
              <lb/>
            + 2 x m-{μμ/θ}.</s>
            <s xml:id="echoid-s3191" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum