Harriot, Thomas, Mss. 6785

List of thumbnails

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791
791 (396) 		792
792 (396v)
793
793 (397) 		794
794 (397v)
795
795 (398) 		796
796 (398v)
797
797 (399) 		798
798 (399v)
799
799 (400) 		800
800 (400v)
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page |< < (351) of 882 > >|
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          <pb file="add_6785_f351" o="351" n="701"/>
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          <p>
            <s xml:space="preserve"> The 6 sides of a
              <lb/>
            pyramis being geven
              <lb/>
            to find the </s>
          </p>
          <p>
            <s xml:space="preserve"> The sides
              <lb/>
            b, c, d, f, g, </s>
          </p>
          <p>
            <s xml:space="preserve"> I would have the
              <lb/>
            solidity geven without
              <lb/>
            the table of sines.
              <lb/>
            or
              <lb/>
            in specie of
              <lb/>
            the sides only
              <lb/>
            if it may </s>
            <lb/>
            <s xml:space="preserve"> as the superficies
              <lb/>
            of a </s>
          </p>
          <p>
            <s xml:space="preserve"> As the superficies of a triangle is
              <emph style="st">had</emph>
            argued by a circle inscribed, two sides
              <lb/>
            produced, & like triangles: In like manner remember to try to argue
              <lb/>
            the solidity of a pyramis, by a sphære inscribed, three planes produced &
              <lb/>
            like </s>
            <s xml:space="preserve"> Now followeth the way by
              <emph style="super">the</emph>
            perpendicular </s>
          </p>
          <p>
            <s xml:space="preserve"> If the vertex of a
              <emph style="super">triangular</emph>
            pyramis to the base be understood
              <lb/>
            a perpendicular falling, & from the end or poynt in the base
              <lb/>
            be drawne perpendiculars to the sides of the triangles of
              <lb/>
            the </s>
          </p>
          <p>
            <s xml:space="preserve"> pappus
              <lb/>
            lib.6.
              <lb/>
            pr. </s>
          </p>
          <p>
            <s xml:space="preserve"> Then if from the vertex be drawne lines to the sayd poyntes
              <lb/>
            in the triangular base;
              <emph style="st">where</emph>
            those lines shalbe also </s>
          </p>
          <p>
            <s xml:space="preserve"/>
            <lb/>
            <s xml:space="preserve"> Let two perpendiculars be drawne aθ and αx
              <lb/>
            & suppose the perpendicular from the vertex to the playne of
              <lb/>
            the base be </s>
          </p>
          <p>
            <s xml:space="preserve"> Then Drawe the lines θε, εx, </s>
          </p>
          <p>
            <s xml:space="preserve"> θδ & δθ with the anlge θδx are knowne,
              <lb/>
            therefore θx with his angle adjacent are also </s>
            <lb/>
            <s xml:space="preserve"> Therefore in the triangle θxε, besides the side θx the two angles
              <lb/>
            adiacent are also knowne. therefore also the sides θε and </s>
          </p>
          <p>
            <s xml:space="preserve"> Then in the triangle αxε having αεx a right angle; & the
              <lb/>
            two sides εx & xα being knowne, αε cannot be </s>
            <lb/>
            <s xml:space="preserve"> And therefore the solidity of the pyramis wilbe also </s>
          </p>
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    </echo>
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