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

Table of contents

< >
[131.] PROPOSITIO XXV.
[132.] PROPOSITIO XXVI.
[133.] HOROLOGII OSCILLATORII PARS QUINTA.
[134.] Horologii ſecundi conſtructio.
[135.] DE VI CENTRIFUGA ex motu circulari, Theoremata. I.
[136.] II.
[137.] III.
[138.] IV.
[140.] VI.
[141.] VII.
[142.] VIII.
[143.] IX.
[145.] XI.
[146.] XII.
[147.] XIII.
[148.] FINIS.
[149.] BREVIS INSTITUTIO DE USU HOROLOGIORUM AD INVENIENDAS LONGITUDINES.
[150.] Adr. Metius in Geographicis Inſtitutionibus Cap. 4.
[151.] Fournier in Hydrographia 1. 12. C. 35.
[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
[154.] II.
[155.] III.
[156.] IV.
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
[159.] VII. Mari invenire horam diei.
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
< >
page |< < (173) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div360" type="section" level="1" n="129">
          <p>
            <s xml:id="echoid-s3926" xml:space="preserve">
              <pb o="173" file="0249" n="275" rhead="HOROLOG. OSCILLATOR."/>
            eſt a, multiplici ſecundum ſemiſſem numeri particularum
              <lb/>
              <note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            quas continet. </s>
            <s xml:id="echoid-s3927" xml:space="preserve">Et diſtantiæ omnes particularum ponderis C,
              <lb/>
            ab eodem puncto A, ſunt a c. </s>
            <s xml:id="echoid-s3928" xml:space="preserve">Ita ut ſumma utrarumque di-
              <lb/>
            ſtantiarum ſit {1/2} a b + a c. </s>
            <s xml:id="echoid-s3929" xml:space="preserve">Per quam dividendo ſummam
              <lb/>
            quadratorum prius inventam, {1/3} a a b + a a c, fit
              <lb/>
            {{1/3} a a b + a a c/{1/2} a b + a c} ſive {{1/3} a b + a c/{1/2} b + c}, longitudo penduli iſochroni. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">Quæ
              <lb/>
            itaque habebitur, ſi fiat, ut dimidia gravitas virgæ, una
              <lb/>
            cum gravitate appenſi ponderis, ad trientem gravitatis virgæ,
              <lb/>
            una cum gravitate ejuſdem appenſi ponderis, ita longitudo
              <lb/>
            A C ad aliam. </s>
            <s xml:id="echoid-s3931" xml:space="preserve">Oportet autem ſumere longitudinem A C,
              <lb/>
            à puncto ſuſpenſionis A ad centrum gravitatis ponderis C;
              <lb/>
            </s>
            <s xml:id="echoid-s3932" xml:space="preserve">cum magnitudinis ejus ratio hic non habeatur, ac veluti
              <lb/>
            minimum conſideretur.</s>
            <s xml:id="echoid-s3933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3934" xml:space="preserve">Quod ſi jam, præter pondus C, alterum inſuper D virgæ
              <lb/>
              <note position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">TAB. XXVII@
                <lb/>
              Fig. 4.</note>
            inhærere intelligatur, cujus gravitas, ſeu particularum nume-
              <lb/>
            rus ſit d: </s>
            <s xml:id="echoid-s3935" xml:space="preserve">diſtantia vero A D ſit f. </s>
            <s xml:id="echoid-s3936" xml:space="preserve">Ut pendulum ſimplex
              <lb/>
            huic ita compoſito iſochronum inveniatur, addenda ſunt ad
              <lb/>
            ſummam ſuperiorem quadratorum, quadrata diſtantiarum
              <lb/>
            particularum ponderis D à puncto A, quæ quadrata apparet
              <lb/>
            eſſe d f f. </s>
            <s xml:id="echoid-s3937" xml:space="preserve">Adeo ut ſumma omnium jam ſit futura {1/3} a a b +
              <lb/>
            a a c + f f d. </s>
            <s xml:id="echoid-s3938" xml:space="preserve">Item, ad ſummam diſtantiarum, addendæ
              <lb/>
            diſtantiæ particularum ponderis D, quæ faciunt d f. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">Ac ſum-
              <lb/>
            ma proinde diſtantiarum omnium erit {1/2} b a + c a + d f;
              <lb/>
            </s>
            <s xml:id="echoid-s3940" xml:space="preserve">per quam dividenda eſt iſta quadratorum ſumma, & </s>
            <s xml:id="echoid-s3941" xml:space="preserve">fit
              <lb/>
            {{1/3} a a b + a a c + f f d/{1/2} a b + a c + f d}, longitudo penduli iſochroni.</s>
            <s xml:id="echoid-s3942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3943" xml:space="preserve">Quod ſi vero, hæc longitudo penduli iſochroni, datæ æqualis
              <lb/>
            poſtuletur, quæ ſit p, & </s>
            <s xml:id="echoid-s3944" xml:space="preserve">reliqua omnia quæ prius data ſint,
              <lb/>
            præter diſtantiam A D ſeu f, quæ determinat locum pon-
              <lb/>
            deris D: </s>
            <s xml:id="echoid-s3945" xml:space="preserve">ſitque invenienda hæc diſtantia, id fiet hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s3946" xml:space="preserve">Nempe, cum poſtuletur {{1/3} a a b + a a c + f f d/{1/2} a b + a c + f d} æquale p, orietur ex
              <lb/>
            hac æquatione f f = p f + {{1/2} a b p + c a p - {1/3} a a b - a a c/d}. </s>
            <s xml:id="echoid-s3947" xml:space="preserve">Et f = {1/2} </s>
          </p>
        </div>
      </text>
    </echo>