Galilei, Galileo, The systems of the world, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="065/01/011.jpg" pagenum="5"/>
              produced from the term A to any other part of the oppoſite line
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              C D.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Your choice, and the reaſon you bring for it in my
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              ment is moſt excellent; ſo that by this time we have proved that
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              the firſt dimenſion is determined by a right line, the ſecond
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              ly the breadth with another line right alſo, and not onely right,
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              but withall, at right-angles to the other that determineth the
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              length, and thus we have the two dimenſions of length and
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              breadth, definite and certain. </s>
              <s>But were you to bound or
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              nate a height, as for example, how high this Roof is from the
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              ment, that we tread on, being that from any point in the Roof,
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              we may draw infinite lines, both curved, and right, and all of
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              verſe lengths to infinite points of the pavement, which of all theſe
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              lines would you make uſe of?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I would faſten a line to the Seeling, and with a plummet
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              that ſhould hang at it, would let it freely diſtend it ſelf till it
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              ſhould reach well near to the pavement, and the length of ſuch a
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              thread being the ſtreighteſt and ſhorteſt of all the lines, that could
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              poſsibly be drawn from the ſame point to the pavement, I would
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              ſay was the true height of this Room.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Very well, And when from the point noted in the
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              ment by this pendent thread (taking the pavement to be levell
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              and not declining) you ſhould produce two other right lines, one
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              for the length, and the other for the breadth of the ſuperficies of
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              theſaid pavement, what angles ſhould they make with the ſaid
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              thread?</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>They would doubtleſs meet at right angles, the ſaid
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              lines falling perpendicular, and the pavement being very plain and
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              levell.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Therefore if you aſſign any point, for the term from whence
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              to begin your meaſure; and from thence do draw a right line, as
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              the terminator of the firſt meaſure, namely of the length, it will
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              follow of neceſſity, that that which is to deſign out the largeneſs
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              or breadth, toucheth the firſt at right-angles, and that that which is
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              to denote the altitude, which is the third dimenſion, going from the
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              ſame point formeth alſo with the other two, not oblique but right
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              angles, and thus by the three perpendiculars, as by three lines, one,
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              certain, and as ſhort as is poſſible, you have the three dimenſions
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              A B length, A C breadth, and A D height; and becauſe, clear it
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              is, that there cannot concurre any more lines in the ſaid point, ſo
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              as to make therewith right-angles, and the dimenſions ought to
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              be determined by the ſole right lines, which make between
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              ſelves right-angles; therefore the dimenſions are no more but
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              three, and that which hath three hath all, and that which hath all,
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              is diviſible on all ſides, and that which is ſo, is perfect,
                <emph type="italics"/>
              &c.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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