Harriot, Thomas, Mss. 6785

List of thumbnails

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151
151 (76) 		152
152 (76v)
153
153 (77) 		154
154 (77v)
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155 (78) 		156
156 (78v)
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157 (79) 		158
158 (79v)
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159 (80) 		160
160 (80v)
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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
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            <p>
              <s xml:space="preserve"> This page contains symbolic versions of Propositions II.1 to II.8 from Eculid's
                <emph style="it">Elements</emph>
              : </s>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.1. If there are two straight lines, and one of them is cut into any number of segments whatever, then the rectangle contained by the two straight lines equals the sum of the rectangles contained by the uncut straight line and each of the </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.2. If a straight line is cut at random, then the sum of the rectangles contained by the whole and each of the segments equals the square on the whole.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.3. If a straight line is cut a random, then the rectangle contained by the whole and one of the segments equals the sum of the rectangle contained by the segments and the square on the aforesaid segment.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.4. If a straight line is cut at random, the square on the whole equals the square on the segments plus twice the rectangle contained by the segments.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.5. If a straight line is cut into equal and unequal segments, then the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section equals the square on the </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.6. If a straight line is bisected and a straight line is added to it in a straight line, then the rectangle contained by the whole width with the added straight line and the added straight line together with the square on the half equals the square on the straight line made up of the half and the added straight line.</s>
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              <quote>
                <s xml:space="preserve"> II.7. If a straight line is cut at random, then the sum of the square on the whole and that on one of the segments equals twice the rectangle contained by the hole and the said segment plus the square on the remaining </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> II.8. If a straight line is cut at random, then four times the rectangle contained by the whole and one of the segments plus the square on the remaining segment equals the square described on the whole and the aforesaid segment as on one straight </s>
              </quote>
              <s xml:space="preserve">]</s>
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          <head xml:space="preserve" xml:lang="lat"> a) propositiones 2
            <emph style="super">i</emph>
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          [
            <emph style="bf">Translation: </emph>
          Propositions from the second book of ]</head>
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            [
              <emph style="bf">Commentary: </emph>
            For the full version of Harriot's verse beginning 'If more by more' see Add MS
              <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/XT0KZ8QC/&start=640&viewMode=image&pn=642"> f. </ref>
            . ] If more
              <lb/>
            by more
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            &</s>
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Impressum