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

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        <div xml:id="echoid-div286" type="section" level="1" n="286">
          <pb o="391" file="0405" n="405" rhead="DE MAGNITUDINE TERRÆ."/>
        </div>
        <div xml:id="echoid-div287" type="section" level="1" n="287">
          <head xml:id="echoid-head341" xml:space="preserve">XXIX.
            <emph style="sc">Problema.</emph>
          </head>
          <head xml:id="echoid-head342" style="it" xml:space="preserve">Datis quadrilateri L R V Q lateribus & diagonio R V, abſque
            <lb/>
          Triangulorum canonibus invenire reliquam diagonium Q L.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          Tab. XVI. fig. 16. Per Problema XIX datur R L di- \\ ſtantia inter Dordracum & Bommeliam # 10755. 3.
            <lb/>
          Per Problema XXII datur RV, diſtantia inter Dor- \\ dracum & Bredam # 7000. 0.
            <lb/>
          Per Problema XXVII datur R Q diſtantia inter Dor- \\ dracum & Bergam ad-Somum # 11735. 6.
            <lb/>
          Per Problema XXVI datur V Q diſtantia inter Bre- \\ dam & Bergam-ad-Somum # 9414. 7.
            <lb/>
          Per Problema XXII datur V L diſtantia inter Bre- \\ dam & Bommeliam # 10887. 2.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9184" xml:space="preserve">Quibus datis diagonius Q L diſtantia inter Bommeliam & </s>
            <s xml:id="echoid-s9185" xml:space="preserve">Ber-
              <lb/>
            gam-ad Somum eruetur hoc modo. </s>
            <s xml:id="echoid-s9186" xml:space="preserve">In triangulo R L V demitta-
              <lb/>
            tur à vertice L perpendicularis L V, in datam diagonium V R.
              <lb/>
            </s>
            <s xml:id="echoid-s9187" xml:space="preserve">Et à Q itidem perpendicularis in eandem ſit Q M. </s>
            <s xml:id="echoid-s9188" xml:space="preserve">Cum itaque
              <lb/>
            in triangulo R L V tria dentur latera, dabuntur quoque ſegmenta
              <lb/>
            R V N V ab angulis ad perpendicularem L N. </s>
            <s xml:id="echoid-s9189" xml:space="preserve">Atque inde de-
              <lb/>
            mum cum in triangulo rectangulo R N L detur baſis recti R L & </s>
            <s xml:id="echoid-s9190" xml:space="preserve">
              <lb/>
            crus alterum R N, dabitur quoque perpendicularis L N. </s>
            <s xml:id="echoid-s9191" xml:space="preserve">Per ea-
              <lb/>
            dem præcepta invenientur ſegmenta M V & </s>
            <s xml:id="echoid-s9192" xml:space="preserve">V R, & </s>
            <s xml:id="echoid-s9193" xml:space="preserve">perpendicu-
              <lb/>
            laris Q M in triangulo R Q V. </s>
            <s xml:id="echoid-s9194" xml:space="preserve">Verum differentia ſegmentorum
              <lb/>
            R M & </s>
            <s xml:id="echoid-s9195" xml:space="preserve">R N eſt ipſa M N inter ſegmentum inter ipſas perpendicu-
              <lb/>
            laris interceptum. </s>
            <s xml:id="echoid-s9196" xml:space="preserve">Continuetur porro perpendicularis Q M uſque
              <lb/>
            in H æqualiter ipſi L M, & </s>
            <s xml:id="echoid-s9197" xml:space="preserve">connectatur L H. </s>
            <s xml:id="echoid-s9198" xml:space="preserve">Erit itaque L H
              <lb/>
            parallela & </s>
            <s xml:id="echoid-s9199" xml:space="preserve">æqualis perpendiculari L M, & </s>
            <s xml:id="echoid-s9200" xml:space="preserve">angulus H rectus: </s>
            <s xml:id="echoid-s9201" xml:space="preserve">
              <lb/>
            dantur autem Q M & </s>
            <s xml:id="echoid-s9202" xml:space="preserve">M H, datur itaque tota Q H. </s>
            <s xml:id="echoid-s9203" xml:space="preserve">Datur ve-
              <lb/>
            ro etiam ipſa M N; </s>
            <s xml:id="echoid-s9204" xml:space="preserve">hoc eſt L H ei parallela & </s>
            <s xml:id="echoid-s9205" xml:space="preserve">æqualis. </s>
            <s xml:id="echoid-s9206" xml:space="preserve">Quam-
              <lb/>
            obrem in triangulo rectangulo L H Q, datis cruribus Q H & </s>
            <s xml:id="echoid-s9207" xml:space="preserve">
              <lb/>
            H L, dabitur quoque baſis Q L diſtantia inter Bommeliam & </s>
            <s xml:id="echoid-s9208" xml:space="preserve">
              <lb/>
            Bredam quæſita. </s>
            <s xml:id="echoid-s9209" xml:space="preserve">Hujus problematis explicatio in numeris ita
              <lb/>
            habet.</s>
            <s xml:id="echoid-s9210" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          Si quadratum ab R L # 11720227600.
            <lb/>
          </note>
        </div>
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    </echo>
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