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

Page concordance

< >
Scan Original
101
102
103
104 65
105 66
106 67
107 68
108
109
110
111 69
112 70
113 71
114 72
115
116
117
118 73
119 74
120 75
121 76
122
123
124
125 77
126 78
127 79
128 80
129 81
130 82
< >
page |< < (67) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div83" type="section" level="1" n="34">
          <p style="it">
            <s xml:id="echoid-s1418" xml:space="preserve">
              <pb o="67" file="0101" n="106" rhead="HOROLOG. OSCILLATOR."/>
            dem ſuperficiem vel aliam ſimilem ſimiliter que po-
              <lb/>
              <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            ſitam feratur, æqualibus temporibus per idem ſpa-
              <lb/>
            tium deſcendet atque aſcendet.</s>
            <s xml:id="echoid-s1419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1420" xml:space="preserve">Velut ſi per ſuperficiem A B deſcendat mobile, atque, ubi
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 4.</note>
            ad B pervenerit, converſo motu ſurſum per eandem A B, vel
              <lb/>
            ei ſimilem & </s>
            <s xml:id="echoid-s1421" xml:space="preserve">reſpectu plani horizontalis ſimiliter poſitam
              <lb/>
            B C, aſcendat, conſtat ex ante demonſtratis, perventurum
              <lb/>
            ad eandem ex qua venit altitudinem. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Cum autem perpetuo,
              <lb/>
            in punctis quorum eadem altitudo, eandem velocitatem ha-
              <lb/>
            beat aſcendendo ac deſcendendo ; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">apparet eandem
              <note symbol="*" position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            bis eadem velocitate ſingulis ſui partibus percurri: </s>
            <s xml:id="echoid-s1424" xml:space="preserve">unde & </s>
            <s xml:id="echoid-s1425" xml:space="preserve">
              <lb/>
            tempora utriusque motus æqualia eſſe neceſſe eſt; </s>
            <s xml:id="echoid-s1426" xml:space="preserve">quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s1427" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div86" type="section" level="1" n="35">
          <head xml:id="echoid-head57" xml:space="preserve">PROPOSITIO XII.</head>
          <p style="it">
            <s xml:id="echoid-s1428" xml:space="preserve">ESto circulus A B C, diametro A C, cui ad an-
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">TAB. VI.
                <lb/>
              Fig. 5.</note>
            gulos rectos ſit F G; </s>
            <s xml:id="echoid-s1429" xml:space="preserve">huic vero occurrat à ter-
              <lb/>
            mino diametri A educta A F extra circulum, quæ
              <lb/>
            quidem neceſſario ſecabit circumferentiam, puta
              <lb/>
            in B. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Dico arcum B D, lineis G F, A F inter-
              <lb/>
            ceptum, minorem eſſe recta D F.</s>
            <s xml:id="echoid-s1431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1432" xml:space="preserve">Jungatur enim B C, & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">ducatur ex B puncto tangens cir-
              <lb/>
            cumferentiam recta B E, quæ neceſſario occurret rectæ F G
              <lb/>
            inter F & </s>
            <s xml:id="echoid-s1434" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Eſt igitur angulus B A C in circulo æqualis
              <lb/>
            angulo E B C . </s>
            <s xml:id="echoid-s1436" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">angulus F B E, qui una
              <note symbol="*" position="right" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">Prop. 32.
                <lb/>
              Lib. 3. Eucl.</note>
            E B C conſtituit angulum rectum F B C, erit æqualis B C A.
              <lb/>
            </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Quia autem ſimilia ſunt triangula A B C, A G F, erit & </s>
            <s xml:id="echoid-s1439" xml:space="preserve">
              <lb/>
            angulus F æqualis angulo A C B. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">Ergo idem angulus F æ-
              <lb/>
            qualis angulo F B E. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">Itaque iſoſceles eſt triangulus F E B,
              <lb/>
            habens crura æqualia F E, E B. </s>
            <s xml:id="echoid-s1442" xml:space="preserve">Addita ergo utrique eo-
              <lb/>
            rum recta E D, fiet F D, æqualis duabus B E, E D. </s>
            <s xml:id="echoid-s1443" xml:space="preserve">Has-
              <lb/>
            ce vero duas majores eſſe conſtat arcu B D, iisdem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum