Alberti, Leone Battista, Architecture, 1755

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="003/01/277.jpg" pagenum="200"/>
              theſe other two in a juſt Relation or proporti­
                <lb/>
              onate Interval, which Interval is the equal re­
                <lb/>
              lative Diſtance which this Number ſtands from
                <lb/>
              the other two. </s>
              <s>Of the three Methods moſt
                <lb/>
              approved by the Philoſophers for finding this
                <lb/>
              Mean, that which is called the arithmetical is
                <lb/>
              the moſt eaſy, and is as follows. </s>
              <s>Taking the
                <lb/>
              two extreme Numbers, as for Inſtance, eight
                <lb/>
              for the greateſt, and four for the leaſt, you add
                <lb/>
              them together, which produce twelve, which
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              twelve being divided in two equal Parts, gives
                <lb/>
              us ſix.
                <lb/>
                <arrow.to.target n="table16"/>
              </s>
            </p>
            <table>
              <table.target id="table16"/>
              <row>
                <cell>8</cell>
                <cell/>
                <cell>4</cell>
              </row>
              <row>
                <cell/>
                <cell>12</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>6</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>THIS Number ſix the Arithmeticians ſay, is
                <lb/>
              the Mean, which ſtanding between four and
                <lb/>
              eight, is at an equal Diſtance from each of
                <lb/>
              them.
                <lb/>
                <arrow.to.target n="table17"/>
              </s>
            </p>
            <table>
              <table.target id="table17"/>
              <row>
                <cell>8.</cell>
                <cell>6.</cell>
                <cell>4.</cell>
              </row>
            </table>
            <p type="main">
              <s>THE next Mean is that which is called the
                <lb/>
              Geometrical, and is taken thus. </s>
              <s>Let the ſmall­
                <lb/>
              eſt Number, for Example, four, be multiplied
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              by the greateſt, which we ſhall ſuppoſe to be
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              nine; the Multiplication will produce 36:
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              The Root of which Sum as it is called, or the
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              Number of its Side being multiplied by itſelf
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              muſt alſo produce 36. The Root therefore
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              will be ſix, which multiplied by itſelf is 36,
                <lb/>
              and this Number ſix, is the Mean.
                <lb/>
                <arrow.to.target n="table18"/>
              </s>
            </p>
            <table>
              <table.target id="table18"/>
              <row>
                <cell>4 Times 9</cell>
                <cell>36</cell>
              </row>
              <row>
                <cell>6 Times 6</cell>
                <cell>36</cell>
              </row>
            </table>
            <p type="main">
              <s>THIS geometrical Mean is very difficult to
                <lb/>
              find by Numbers, but it is very clear by Lines;
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              but of thoſe it is not my Buſineſs to ſpeak
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              here. </s>
              <s>The third Mean, which is called the
                <lb/>
              Muſical, is ſomewhat more difficult to work
                <lb/>
              than the Arithmetical; but, however, may be
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              very well performed by Numbers. </s>
              <s>In this the
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              Proportion between the leaſt Term and the
                <lb/>
              greateſt, muſt be the ſame as the Diſtance be­
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              tween the leaſt and the Mean, and between the
                <lb/>
              Mean and the greateſt, as in the following Ex­
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              ample. </s>
              <s>Of the two given Numbers, let the
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              leaſt be thirty, and the greateſt ſixty, which is
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              juſt the Double of the other. </s>
              <s>I take ſuch
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              Numbers as cannot be leſs to be double, and
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              theſe are one, for the leaſt, and two, for the
                <lb/>
              greateſt, which added together make three. </s>
              <s>I
                <lb/>
              then divide the whole Interval which was be­
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              tween the greateſt Number, which was ſixty,
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              and the leaſt, which was thirty, into three
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              Parts, each of which Parts therefore will be
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              ten, and one of theſe three Parts I add to the
                <lb/>
              leaſt Number, which will make it forty; and
                <lb/>
              this will be the muſical Mean deſired.
                <lb/>
                <arrow.to.target n="table19"/>
              </s>
            </p>
            <table>
              <table.target id="table19"/>
              <row>
                <cell>30</cell>
                <cell/>
                <cell>60</cell>
              </row>
              <row>
                <cell>1</cell>
                <cell/>
                <cell>2</cell>
              </row>
              <row>
                <cell/>
                <cell>3</cell>
                <cell/>
              </row>
              <row>
                <cell>3</cell>
                <cell/>
                <cell>30</cell>
              </row>
              <row>
                <cell/>
                <cell/>
                <cell>10</cell>
              </row>
              <row>
                <cell/>
                <cell>30</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>10</cell>
                <cell/>
              </row>
              <row>
                <cell>30</cell>
                <cell>40</cell>
                <cell>60</cell>
              </row>
            </table>
            <p type="main">
              <s>AND this mean Number forty will be diſ­
                <lb/>
              tant from the greateſt Number juſt double the
                <lb/>
              Interval which the Number of the Mean is
                <lb/>
              diſtant from the leaſt Number; and the Con­
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              dition was, that the greateſt Number ſhould
                <lb/>
              bear that Portion to the leaſt. </s>
              <s>By the Help of
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              theſe Mediocrites the Architects have diſcover­
                <lb/>
              ed many excellent Things, as well with Rela­
                <lb/>
              tion to the whole Structure, as to its ſeveral
                <lb/>
              Parts; which we have not Time here to par­
                <lb/>
              ticularize. </s>
              <s>But the moſt common Uſe they
                <lb/>
              have made of theſe Mediocrities, has been how­
                <lb/>
              ever for their Elevations.</s>
            </p>
            <p type="head">
              <s>CHAP. VII.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              Of the Invention of Columns, their Dimenſions and Collocation.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>It will not be unpleaſant to conſider ſome
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              further Particulars relating to the three
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              Sorts of Columns which the Ancients invent­
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              ed, in three different Points of Time: And it
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              is not at all improbable, that they borrowed the
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              Proportions of their Columns from that of the
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              Members of the human Body. </s>
              <s>Thus they
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              found that from one Side of a Man to the
                <lb/>
              other was a ſixth Part of his Height, and that
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              from the Navel to the Reins was a tenth. </s>
              <s>From
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              this Obſervation the Interpreters of our ſacred
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              Books, are of Opinion, that
                <emph type="italics"/>
              Noah
                <emph.end type="italics"/>
              's Ark for
                <lb/>
              the Flood was built according to the Propor­
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              tions of the human Body. </s>
              <s>By the ſame Pro­
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              portions we may reaſonably conjecture, that the
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              Ancients erected their Columns, making the
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              Height in ſome ſix Times, and in others ten
                <lb/>
              Times, the Diameter of the Bottom of the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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