Harriot, Thomas, Mss. 6782

List of thumbnails

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501
501 (251) 		502
502 (251v)
503
503 (252) 		504
504 (252v)
505
505 (253) 		506
506 (253v)
507
507 (254) 		508
508 (254v)
509
509 (255) 		510
510 (255v)
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page |< < (366) of 1011 > >|
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      <text xml:lang="eng" type="free">
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          <pb file="add_6782_f366" o="366" n="732"/>
          <head xml:space="preserve" xml:lang="lat"> De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On ]</head>
          <p>
            <s xml:space="preserve">
              <emph style="st">If the</emph>
              <emph style="super">The</emph>
            line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            by his revolution
              <lb/>
            cometh at length to be parallel to
              <lb/>
            the infinite line
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Which
              <lb/>
            motion being from
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            suppose
              <lb/>
            to have been </s>
            <s xml:space="preserve"> The
              <lb/>
            degree of the motion let be
              <lb/>
              <math>
                <mstyle>
                  <mi>m</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            . the time
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> The beginning of the time or first instant
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            .
              <lb/>
            </s>
            <s xml:space="preserve"> The last instant wherein the line is
              <lb/>
            parallel,
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            . Now seing that
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            must cut at
              <lb/>
            an infinite distance &
              <emph style="super">that</emph>
            his last cutting must be
              <lb/>
            before the instant
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Which suppose
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> That
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            as it is argued by the premises
              <lb/>
            must differe from
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            by an indivisible time, so that
              <emph style="st">it </emph>
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            must be the next instant
              <lb/>
            to
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            . & no other </s>
            <s xml:space="preserve"> In which instant
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            must not be parallel but
              <lb/>
            make his last cutting at an infinite </s>
            <s xml:space="preserve"> And therefore it must have
              <lb/>
            a certayne
              <foreign xml:lang="lat">situs</foreign>
            at that instant out of the point
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            towards
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , which let be
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            as it maketh his last </s>
            <s xml:space="preserve"> In which situation the motion ordering it hath
              <lb/>
            the sayd degree
              <math>
                <mstyle>
                  <mi>m</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            , as in all other </s>
            <s xml:space="preserve"> From the which situation to the situation
              <lb/>
            of being parallel it must be moved unto (as it is sayd) in the next </s>
          </p>
          <p>
            <s xml:space="preserve"> Now suppose (as it may be) that the motion from
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            be in half the time
              <lb/>
            of
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Then doth it follow necessarily that the degree of motion or velo-
              <lb/>
            city be double to
              <math>
                <mstyle>
                  <mi>m</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            . And therefore, what space or parte of a space, (be it
              <lb/>
            finite or infinite, so it be positive,) it moved before according to
              <lb/>
            the degree of
              <math>
                <mstyle>
                  <mi>m</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            . it moveth the same now, in half the time.
              <lb/>
            </s>
            <s xml:space="preserve"> Therefore in this second motion when
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            cometh to have his situation
              <lb/>
            at
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            to make the sayd last section; seing that then it hath double
              <lb/>
            degree of velocity; it must afterward be parallel in half an instant
              <lb/>
            that is to say,
              <emph style="st">that</emph>
            in half that time which was sayd to be indivisible.
              <lb/>
            </s>
            <s xml:space="preserve"> Which doth imply </s>
          </p>
          <p>
            <s xml:space="preserve"> Agayne if it be sayd that
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            at that
              <emph style="st">& in the position</emph>
            (when &
              <lb/>
            where it maketh his last section with
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            before it be
              <emph style="st">then</emph>
              <lb/>
            be
              <foreign xml:lang="lat">deinceps</foreign>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            . or that the poynts
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
              <foreign xml:lang="lat">deinceps</foreign>
            at an infinite
              <lb/>
            distance so that no point can be </s>
            <s xml:space="preserve"> Yet from the poynt
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            may
              <lb/>
            be interposed a line
              <math>
                <mstyle>
                  <mi>k</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . and also from
              <math>
                <mstyle>
                  <mi>l</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            . & by the doctrine of Elements
              <lb/>
            the angle
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>k</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , or
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>l</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            must
              <emph style="st">greater</emph>
              <emph style="super">lesser</emph>
            than
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            . & therefore lesse than that
              <lb/>
            which was sayd to be least or indivisible. & therefore the lines
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , or the
              <lb/>
            poynts
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            be not
              <foreign xml:lang="lat">deinceps. quæ implicant</foreign>
            </s>
          </p>
        </div>
      </text>
    </echo>
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