Musschenbroek, Petrus van, Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

Page concordance

< >
Scan Original
341 327
342 328
343 329
344 330
345 331
346 332
347 333
348 334
349 335
350 336
351 337
352 338
353 339
354 340
355 341
356 342
357 343
358 344
359 345
360 346
361 347
362 348
363 349
364 350
365 351
366 352
367 353
368
369
370
< >
page |< < (336) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div235" type="section" level="1" n="235">
          <p>
            <s xml:id="echoid-s8220" xml:space="preserve">
              <pb o="336" file="0350" n="350" rhead="DISSERTATIO"/>
            eſſe eo minores, quo plus diſtant a puncto M.</s>
            <s xml:id="echoid-s8221" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8222" xml:space="preserve">Sed ipſa vis attrahens cujuslibet puncti decreſcit, quo corpus,
              <lb/>
            quod attrahitur, plus diſtat a puncto attrahente, igitur corpus X
              <lb/>
            attrahetur a punctis M, S, V, Q, P, L, eo minus, quo diſtan-
              <lb/>
            tiæ X M, X S, X V, X Q &</s>
            <s xml:id="echoid-s8223" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8224" xml:space="preserve">ſuntmajores. </s>
            <s xml:id="echoid-s8225" xml:space="preserve">Sivero fuerint vires
              <lb/>
            attrahentes cujuslibet puncti, uti reciproce diſtantia attrahentis & </s>
            <s xml:id="echoid-s8226" xml:space="preserve">
              <lb/>
            attracti, tum erit vis puncti M in corpus X, ad vim puncti S in idem
              <lb/>
            X, uti S X ad M X. </s>
            <s xml:id="echoid-s8227" xml:space="preserve">& </s>
            <s xml:id="echoid-s8228" xml:space="preserve">eodem modo vis puncti L in X erit ad vim
              <lb/>
            puncti M in X, uti recta M X ad L X.</s>
            <s xml:id="echoid-s8229" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8230" xml:space="preserve">Concipiatur X eſſe centrum circuli, X M radium, erit M L
              <lb/>
            Tangens circuli in puncto M, ducantur ex punctis S, V, Q, P,
              <lb/>
            L, Tangentis ad centrum X rectæ, erunt hæ ſecantes angulorum
              <lb/>
            S X M, V X M, Q X M, P X M, L X M, erit igitur vis
              <lb/>
            puncti L, qua trahit X, ad vim puncti S, quâ trahit idem X uti
              <lb/>
            S X ad L X, hoc eſt uti ſecans anguli S X M ad ſecantem anguli
              <lb/>
            L X M, ſive in ratione inverſa ſecantium angulorum, quos for-
              <lb/>
            mant diſtantiæ cum recta M X.</s>
            <s xml:id="echoid-s8231" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8232" xml:space="preserve">Supra autem innuimus vim attrahentem puncti M adjuvari ab at-
              <lb/>
            tractionibus omnium punctorum inter M & </s>
            <s xml:id="echoid-s8233" xml:space="preserve">K ab unâ parte: </s>
            <s xml:id="echoid-s8234" xml:space="preserve">ſit vis
              <lb/>
            attrahens hoc modo conſiderata, uti eſt diſtantia a puncto L, erit
              <lb/>
            tum vis in S ad eam in M, uti L S ad L M; </s>
            <s xml:id="echoid-s8235" xml:space="preserve">aſſumatur quæcunque
              <lb/>
            M Y in M X, atque ducantur ex punctis S, V, Q, P, L paral-
              <lb/>
            lelæ ad M X, erit vis in S ad eam in M, uti S a ad M Y: </s>
            <s xml:id="echoid-s8236" xml:space="preserve">Quam-
              <lb/>
            obrem ſi M Y foret maſſa fiuida, hac ratione elevaretur uſque ad
              <lb/>
            L formaretque Triangulum rectangulum M L Y. </s>
            <s xml:id="echoid-s8237" xml:space="preserve">Sed hæc vis at-
              <lb/>
            trahens accedit alteri virtuti, quæ eſt in ratione inverſâ Secantium
              <lb/>
            explicata, adeoque lineæ M Y adjungatur quædam Y X, quæ ſit
              <lb/>
            uti Secans anguli L X M, & </s>
            <s xml:id="echoid-s8238" xml:space="preserve">ad L jungatur linea æqualis radio cir-
              <lb/>
            culi, cujus Secans eſt Y X ſub angulo L X Y, tum ad S a jungatur
              <lb/>
            Secans anguli P X M quæ ſit a c, & </s>
            <s xml:id="echoid-s8239" xml:space="preserve">reciproce ad P a jungatur Se-
              <lb/>
            cans anguli S X M. </s>
            <s xml:id="echoid-s8240" xml:space="preserve">quæ ſit a f: </s>
            <s xml:id="echoid-s8241" xml:space="preserve">ita ut ad V a jungatur Secans an-
              <lb/>
            guli Q X M, quæ ſit a d, & </s>
            <s xml:id="echoid-s8242" xml:space="preserve">ad Z a jungatur Secans anguli V X M
              <lb/>
            quæ ſit e a: </s>
            <s xml:id="echoid-s8243" xml:space="preserve">puncta c, d, e, f, l jungantur, deſcripta erit cur-
              <lb/>
            va, ei ſimilis, quam Aquain Experimento exhibet: </s>
            <s xml:id="echoid-s8244" xml:space="preserve">l, f, e, d, c, x.
              <lb/>
            </s>
            <s xml:id="echoid-s8245" xml:space="preserve">Eſſe curvam ideo patet, quia cum æquales capiuntur M S, S V,
              <lb/>
            V Q, Q P, P L. </s>
            <s xml:id="echoid-s8246" xml:space="preserve">evadent Tangentes a puncto M, duplo, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum