Heron Alexandrinus, Mechanica, 1999

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    <archimedes>
      <text>
        <body>
          <chap n="1">
            <pb n="9">
              <s id="A18-1.09.01">[9] How one enlarges or reduces plane or solid figures in a certain ratio, we want to explain now, in order to be able to enlarge, for example, one cubit of a solid or plane figure in the same ratio.</s>
              <s id="A18-1.09.02">Let us first deal with the plane figures.Let us therefore assume a certain kind of line.</s>
              <s id="A18-1.09.03">Now we want to find such a line that the similar figures described above the two lines are in a ratio to one another that equals the known ratio.</s>
              <s id="A18-1.09.04">Let the known line be in a known ratio to another one and let us assume the mean proportional* between the two known lines, then this is the line sought; for if the lines are proportional among each other, then the ratio of the first to the third equals the ratio of the similar figures that are described above the first and the second according to the similarity.</s>
            </pb>
          </chap>
        </body>
      </text>
    </archimedes>
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