Harriot, Thomas, Mss. 6782

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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
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              <s xml:space="preserve"> The irrationals defined by Euclid
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookX/bookX.html"> Book </ref>
              of the
                <emph style="it">Elements</emph>
              are binomes, bimedials, and so on. For their definitions and properties see Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=710&viewMode=image&pn=712"> f. </ref>
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/VWXURW4V&start=680&viewMode=image&pn=686"> f. </ref>
              . Here Harriot defines some further irrational quantities, all of them involving fourth roots, which do not fall into any of Euclid's categories. See also Add MS 6782
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/HSPGZ0AE&start=520&viewMode=image&pn=529"> f. </ref>
              . </s>
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          <head xml:space="preserve" xml:lang="lat"> De speciebus irrationalium ab Euclide
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On types of irrationals missed by ]</head>
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              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
            <lb/>
            <s xml:space="preserve"> Animadvertendum quod quælibet harum
              <emph style="st">specier</emph>
              <emph style="super">irrationalium</emph>
            producit quadratum
              <lb/>
            trinomium compositum ex binomio et </s>
            <s xml:space="preserve"> Et quodlibet bino-
              <lb/>
            mium huius
              <emph style="super">modi</emph>
            speciei
              <emph style="super">logisticæ</emph>
            continet in se implicite duas subspecies.</s>
            <s xml:space="preserve"> Quod
              <lb/>
            si
              <emph style="super">in singulis</emph>
            distincte explica
              <emph style="super">tur</emph>
            , ex istis 5 irrationalibus fient 10.</s>
            <s xml:space="preserve"> Ut
              <lb/>
            alijs chartis sequentibus
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            It is to be noted that any of these irrationals squared produces a trinomial composed of a binome and a medial. And any binome of this form in letters contains in itself two subforms. Which if in each case are set out, from these five irrationals there arise 10. As will appear in the following sheets.</s>
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