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

Page concordance

< >
Scan Original
221 140
222 141
223 142
224
225
226
227 143
228 144
229 145
230 146
231 147
232 148
233 149
234 150
235 151
236 152
237 153
238 154
239
240
241
242 155
243 156
244
245
246
247 157
248 158
249 159
250 160
< >
page |< < (149) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div291" type="section" level="1" n="106">
          <pb o="149" file="0213" n="233" rhead="HOROLOG. OSCILLATOR."/>
          <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.
                <lb/>
              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,
              <lb/>
            & </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>
            <s xml:id="echoid-s3380" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="107">
          <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-
              <lb/>
            tur longitudo penduli ſimplicis ipſi iſochroni.</s>
            <s xml:id="echoid-s3384" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum