Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="80">
          <pb file="0154" n="154" rhead="FED. COMMANDINI"/>
        </div>
        <div type="section" level="1" n="81">
          <head xml:space="preserve">THE OREMA XII. PROPOSITIO XVI.</head>
          <p>
            <s xml:space="preserve">In ſphæra, & </s>
            <s xml:space="preserve">ſphæroide idem eſt grauitatis, & </s>
            <s xml:space="preserve">
              <lb/>
            figuræ centrum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Secetur ſphæra, uel ſphæroid
              <gap/>
            no per axem ducto;
              <lb/>
            </s>
            <s xml:space="preserve">quod ſectionem faciat circulum,
              <gap/>
            ellipſim a b c d, cuius
              <lb/>
            diameter, & </s>
            <s xml:space="preserve">ſphæræ, uelſphæroidis axis d b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrume. </s>
            <s xml:space="preserve">
              <lb/>
            Dico e grauitatis etiam centrum eſſe. </s>
            <s xml:space="preserve">ſecetur enim altero
              <lb/>
            plano per e, ad planum ſecans recto, cuius fectio ſit circu-
              <lb/>
            lus circa diametrum a c. </s>
            <s xml:space="preserve">erunt a d c, a b c dimidiæ portio-
              <lb/>
            nes ſphæræ, uel fphæroidis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portionis a d c gra
              <lb/>
            uitatis centrum eſt in linea d, & </s>
            <s xml:space="preserve">centrum portionis a b c in
              <lb/>
            ipſa b e; </s>
            <s xml:space="preserve">totius ſphæræ, uel ſphæroidis grauitatis centrum
              <lb/>
            in axe d b conſiſtet. </s>
            <s xml:space="preserve">Quòd ſi portionis a d c centrum graui
              <lb/>
            tatis ponatur eſſe f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fiat ipſi f e æqualis e g: </s>
            <s xml:space="preserve">punctũ g por
              <lb/>
              <anchor type="figure" xlink:label="fig-0154-01a" xlink:href="fig-0154-01"/>
            tionis a b c centrum erit. </s>
            <s xml:space="preserve">ſolidis enim figuris ſimilibus & </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0154-01a" xlink:href="note-0154-01"/>
            æqualibus inter ſe aptatis, & </s>
            <s xml:space="preserve">centra grauitatis ipſarum in-
              <lb/>
            ter fe aptentur neceſſe eſt. </s>
            <s xml:space="preserve">ex quo fit, ut magnitudinis, quæ
              <lb/>
              <anchor type="note" xlink:label="note-0154-02a" xlink:href="note-0154-02"/>
            ex utriſque cõſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
              <lb/>
            uitatis centrum ſitin medio lineæ f g, uidelicet in e. </s>
            <s xml:space="preserve">Sphæ-
              <lb/>
            ræ igitur, uel ſphæroidis grauitatis centrum eſtidem, quod
              <lb/>
            centrum figuræ.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a">
              <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0154-01"/>
            </figure>
            <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">per 2. pe-
              <lb/>
            titionem</note>
            <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">4 Arch-
              <lb/>
            medis.</note>
          </div>
        </div>
      </text>
    </echo>