Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

List of thumbnails

< >
211
211 		212
212
213
213 		214
214
215
215 		216
216
217
217 		218
218
219
219 		220
220
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/218.jpg" pagenum="200"/>
              ball got to the ground, when the little one is ſtill within leſs than
                <lb/>
              a yard of the top of the Tower.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg400"/>
                <emph type="italics"/>
              The error of
                <emph.end type="italics"/>
                <lb/>
              ſtotle
                <emph type="italics"/>
              in affirming,
                <lb/>
              falling grave
                <lb/>
              dies to move
                <lb/>
              ding to the
                <lb/>
              tion of their
                <lb/>
              ties.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>That this propoſition is moſt falſe, I make no doubt in
                <lb/>
              the world; but yet that yours is abſolutely true, I cannot well
                <lb/>
              aſſure my ſelf: nevertheleſs, I believe it, ſeeing that you ſo
                <lb/>
              ſolutely affirm it; which I am ſure you would not do, if you had
                <lb/>
              not certain experience, or ſome clear demonſtration thereof.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I have both: and when we ſhall handle the buſineſs
                <lb/>
              of motions apart, I will communicate them: in the interim, that
                <lb/>
              we may have no more occaſions of interrupting our diſcourſe, we
                <lb/>
              will ſuppoſe, that we are to make our computation upon a ball of
                <lb/>
                <arrow.to.target n="marg401"/>
                <lb/>
              Iron of an hundred
                <emph type="italics"/>
              (a)
                <emph.end type="italics"/>
              pounds, the which by reiterated
                <lb/>
              ments deſcendeth from the altitude of an hundred
                <emph type="italics"/>
              (b)
                <emph.end type="italics"/>
              yards, in
                <lb/>
              five ſecond-minutes of an hour. </s>
              <s>And becauſe, as we have ſaid,
                <lb/>
              the ſpaces that are meaſured by the cadent moveable, increaſe in
                <lb/>
              double proportion; that is, according to the ſquares of the times,
                <lb/>
              being that the time of one firſt-minute is duodecuple to the time
                <lb/>
              of five ſeconds, if we multiply the hundred yards by the ſquare of
                <lb/>
              12, that is by 144, we ſhall have 14400, which ſhall be the
                <lb/>
              ber of yards that the ſame moveable ſhall paſs in one firſt-minute
                <lb/>
              of an hour: and following the ſame rule becauſe one hour is 60
                <lb/>
              minutes, multiplying 14400, the number of yards paſt in one
                <lb/>
              nute, by the ſquare of 60, that is, by 3600, there ſhall come forth
                <lb/>
              51840000, the number of yards to be paſſed in an hour, which
                <lb/>
              make 17280 miles. </s>
              <s>And deſiring to know the ſpace that the ſaid
                <lb/>
              ball would paſs in 4 hours, let us multiply 17280 by 16, (which
                <lb/>
              is the ſquare of 4) and the product will be 276480 miles: which
                <lb/>
              number is much greater than the diſtance from the Lunar concave
                <lb/>
              to the centre of the Earth, which is but 196000 miles, making the
                <lb/>
              diſtance of the concave 56 ſemidiameters of the Earth, as that
                <lb/>
              dern Author doth; and the ſemidiameter of the Earth 3500 miles,
                <lb/>
                <arrow.to.target n="marg402"/>
                <lb/>
              of 3000 ^{*}
                <emph type="italics"/>
              Braces
                <emph.end type="italics"/>
              to a †mile, which are our
                <emph type="italics"/>
              Italian
                <emph.end type="italics"/>
              miles.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg401"/>
                <emph type="italics"/>
              (a) (b)
                <emph.end type="italics"/>
              Note that
                <lb/>
              theſe Calculations
                <lb/>
              are made in
                <emph type="italics"/>
                <lb/>
              an
                <emph.end type="italics"/>
              weights and
                <lb/>
              meaſures. </s>
              <s>And 100
                <lb/>
              pounds
                <emph type="italics"/>
                <lb/>
              poiſe
                <emph.end type="italics"/>
              make 131
                <emph type="italics"/>
              l.
                <lb/>
              </s>
              <s>Florentine.
                <emph.end type="italics"/>
              And
                <lb/>
              100 Engliſh yards
                <lb/>
              makes 150 2/5 Braces
                <lb/>
                <emph type="italics"/>
              Florent.
                <emph.end type="italics"/>
              ſo that the
                <lb/>
              brace or yard of
                <lb/>
              our
                <emph type="italics"/>
              Author
                <emph.end type="italics"/>
              is 3/4
                <lb/>
              of cur yard.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg402"/>
              * The
                <emph type="italics"/>
              Italian
                <emph.end type="italics"/>
                <lb/>
              ſure which I
                <lb/>
              monly tranſl te
                <lb/>
              yards.</s>
            </p>
            <p type="main">
              <s>Therefore,
                <emph type="italics"/>
              Simplicius,
                <emph.end type="italics"/>
              that ſpace from the concave of the Moon
                <lb/>
              to the centre of the Earth, which your Accomptant ſaid could
                <lb/>
                <arrow.to.target n="marg403"/>
                <lb/>
              not be paſſed under more than ſix days, you ſee that (computing
                <lb/>
              by experience, and not upon the fingers ends) that it ſhall be
                <lb/>
              ſed in much leſs than four hours; and making the computation
                <lb/>
              exact, it ſhall be paſſed by the moveable in 3 hours, 22
                <emph type="italics"/>
              min. </s>
              <s>prim.
                <emph.end type="italics"/>
                <lb/>
              and 4 ſeconds.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg403"/>
              † The
                <emph type="italics"/>
              Italian
                <emph.end type="italics"/>
              mile
                <lb/>
              is 1000/1056 of our mile.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I beſeech you, dear Sir, do not defraud me of this
                <lb/>
              act calculation, for it muſt needs be very excellent.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>So indeed it is: therefore having (as I have ſaid) by
                <lb/>
              diligent tryal obſerved, that ſuch a moveable paſſeth in its deſcent,
                <lb/>
              the height of 100 yards in 5 ſeconds of an hour, we will ſay, if
                <lb/>
              100 yards are paſſed in 5 ſeconds; in how many ſeconds ſhall </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum