Harriot, Thomas, Mss. 6785

List of thumbnails

< >
10
10 (5v) 		11
11 (6)
12
12 (6v) 		13
13 (7)
14
14 (7v) 		15
15 (8)
16
16 (8v) 		17
17 (9)
18
18 (9v) 		19
19 (10)
< >
page |< < (10) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f010" o="10" n="19"/>
          <head xml:space="preserve"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Iisdem positis: In linea
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            sumatur quovis punctum
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
              <lb/>
            et erigatur perpendicularis
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            quæ erit parallela lineaæ
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            et secabit lineam
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            in puncto
              <math>
                <mstyle>
                  <mi>n</mi>
                </mstyle>
              </math>
            . agatur etiam recta
              <lb/>
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            , quæ secabit
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            in puncto
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <emph style="st">Manifestum est</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The same things being supposed, in the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            there is taken any point
              <math>
                <mstyle>
                  <mi>o</mi>
                </mstyle>
              </math>
            and there is constructed the perpendicular
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            which will be parallel to the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            and will cut the line
              <math>
                <mstyle>
                  <mi>h</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            in the point
              <math>
                <mstyle>
                  <mi>n</mi>
                </mstyle>
              </math>
            . There is also constructed the line
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            , which will cut
              <math>
                <mstyle>
                  <mi>g</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            in the point
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Dico primo quod
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            est maior quam
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            .
              <lb/>
            connectantur puncta
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            et fiat
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            æqualis lineæ
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
              <lb/>
            sitque acta recta
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            quæ
              <lb/>
              <emph style="super">necessario</emph>
            secabit lineam
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            in puncto
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <emph style="st">Quoniam</emph>
              <emph style="super">et
                <math>
                  <mstyle>
                    <mi>t</mi>
                    <mi>z</mi>
                  </mstyle>
                </math>
              in puncto
                <math>
                  <mstyle>
                    <mi>q</mi>
                  </mstyle>
                </math>
              .</emph>
            Quoniam
              <lb/>
            In triangulo
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            , latera
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            sunt æqualia,
              <lb/>
            anguli etiam ad
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
              <lb/>
            sunt etiam
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            I say first that
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Connect the points
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            , and make
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            equal to the line
              <math>
                <mstyle>
                  <mi>n</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            ; let there also be constructed the line
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            which will necessarily cut the line
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            in the point
              <math>
                <mstyle>
                  <mi>r</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>z</mi>
                </mstyle>
              </math>
            in the point
              <math>
                <mstyle>
                  <mi>q</mi>
                </mstyle>
              </math>
            . Because in the triangle
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            , the sides
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            are equal, and also the angles at
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            are also equal. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sed angulus ad
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            nempe
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            hoc est
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            est
              <lb/>
            æqualis duobus angulis interioris
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>s</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            . Duobus videlicet
              <lb/>
            interioris et oppositis triangulis
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            . Ergo maior est
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            anguli,
              <lb/>
            maior etiam angulo
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            qui
              <emph style="super">est</emph>
            ad verticem
              <lb/>
            anguli
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            . Ergo, angulos
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            hoc est
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            est
              <lb/>
            maior quam angulus
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Ergo
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            lineam est maior quam
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            multo igitur maior
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>q</mi>
                </mstyle>
              </math>
            quam
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Sed linea
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>q</mi>
                </mstyle>
              </math>
            , æqualis est
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            ergo
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            est maior quam
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Sed etiam
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            est æqualis
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            , cum
              <lb/>
            sunt latera subtendentia æqualis angulos æqualium triangulum
              <lb/>
            nempe,
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>s</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            . Ergo
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            est maior quam
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            , quod primo
              <lb/>
            demonstrandum
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            But the angle at
              <math>
                <mstyle>
                  <mi>t</mi>
                </mstyle>
              </math>
            , namely
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , that is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            is equal to two interior angles
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>s</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            , clearly the two interior and opposite angles in triangle
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            . Therefore
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            is the greater angle.
              <lb/>
            The angle
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is also greater, which is at the vertex of angle
              <math>
                <mstyle>
                  <mi>t</mi>
                  <mi>r</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            . Therefore, the angle
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            , that is
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            , is greater than the angle
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . Therefore the line
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>r</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , and therefore
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>q</mi>
                </mstyle>
              </math>
            is much greater than
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . But the line
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>q</mi>
                </mstyle>
              </math>
            is equal to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            , therefore
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . But also
              <math>
                <mstyle>
                  <mi>p</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            is equal to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            , since they are sides subtending equal angles of equal triangles, namely,
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>s</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>o</mi>
                  <mi>n</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            . Therefore
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            is greater than
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            , which was to be demonstrated first. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Dico secundo, ut
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            , seu ut
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , ita
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Hoc enim manifestum ex similitudine triangulorum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>s</mi>
                  <mi>u</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            seu
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            et
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>n</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            I say, second, that as
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>s</mi>
                </mstyle>
              </math>
            , or as
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , so is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>n</mi>
                </mstyle>
              </math>
            .
              <lb/>
            For this is clear from the similarity of triangles
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>t</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>s</mi>
                  <mi>u</mi>
                </mstyle>
              </math>
            , or
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>e</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>n</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            . </s>
          </p>
        </div>
      </text>
    </echo>
Impressum