Harriot, Thomas, Mss. 6789

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            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> As in his letter of 6 February 1610, Lower is again concerned with problem 5 from Appendix II of Viète's
                <emph style="it">Apollonius Gallus</emph>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p>
            <s xml:space="preserve"> I so overwhelmed you the last time with a longe
              <lb/>
            letter, as it is iust I should make you amends
              <lb/>
            now with one as shorte. to send you none att all
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            (which perchance had been lost consideringe the use you
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            have of all your time) I could not consent unto,
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            out of the addiction and delighte I have to be still con
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            versinge with you. therfore I will onlie signifie
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            how it is with us and so an end. my course of cal-
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            culation I have stopte untill I heare from you; the two
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            greate causes of my stay I declared in my last let
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            ters. I fell since into Vieta's last probleme of his
              <lb/>
            second apendicle Apol: Gal: and compared his way with
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            yours that you last gave me: but to confesse a
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            truth I can have my will of neither; and the
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            probleme appeares to me not universall but requires
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            determination. for let the,
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                </mstyle>
              </math>
            given, have the same
              <lb/>
            sides,
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . that Vieta's hath and lett,
              <math>
                <mstyle>
                  <mi>v</mi>
                  <mo>"</mo>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>s</mi>
                  <mo/>
                </mstyle>
              </math>
            . be the
              <lb/>
            same that Vieta gives; now I will give a,
              <math>
                <mstyle>
                  <mo>Δ</mo>
                </mstyle>
              </math>
              <lb/>
            that shall have thos sides, so it shalbe impossible
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            to finde anie pointe, from whence lines drawen unto
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            the corners be in the given rate. and that is by
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            givein a,
              <math>
                <mstyle>
                  <mo>Δ</mo>
                </mstyle>
              </math>
            . with the same sides
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . but
              <emph style="super">onlie</emph>
            such
              <emph style="super">a</emph>
              <lb/>
              <emph style="super">position</emph>
            as the [angle]
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <emph style="super">be</emph>
              <math>
                <mstyle>
                  <mo>></mo>
                </mstyle>
              </math>
            or
              <math>
                <mstyle>
                  <mo>&</mo>
                  <mi>l</mi>
                  <mi>t</mi>
                  <mo>;</mo>
                </mstyle>
              </math>
            then Vieta's [angle]
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . in such measure
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            as Vieta's two circles doe neither cut nor touch. this
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            rubbe put me out of this course. whereuppon I betooke
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            me to your problemes for the distinguishinge of the sides
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            of
              <math>
                <mstyle>
                  <mo>Δ</mo>
                </mstyle>
              </math>
              <emph style="super">les</emph>
            whether the summe or difference of the sides
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            and the angle adjacente or contained with the other
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            side were given. in this I proceed still with much
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            pleasure and satisfaction. I have also putt in order
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            all thos propositions which you also gave me, but I
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            had copied in lose papers & with ill diagrammes
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            so that all those thinges stand well and so I thanke god
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            doe we also. Excepte my catle which have all this
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            winter been persecuted wiht the Murraine. since
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            Christmas verie neare I have lost, 100. beasts; Vieta's
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            sacrifice
              <emph style="super">to the witch Melusina</emph>
            for the invention of our probleme. but
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            I scarce keepe my promise with you. farewell.
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            I am all yours. Willm. </s>
          </p>
          <p>
            <s xml:space="preserve"> Tra'venti; 3.
              <lb/>
            April. </s>
          </p>
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