Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
181 35
182
183 36
184
185 37
186
187 38
188
189 39
190
< >
page |< < (38) of 213 > >|
DE CENTRO GRA VIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="91">
          <p>
            <s xml:space="preserve">
              <pb o="38" file="0187" n="187" rhead="DE CENTRO GRA VIT. SOLID."/>
            ad portiones ſolidas maiorem habet proportioné, quàm
              <lb/>
            n l ad l m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo fruſtum pyramidis ad dictas por-
              <lb/>
            tiones maiorem proportionem habet, quàm n m ad m l.
              <lb/>
            </s>
            <s xml:space="preserve">fiat igitur ut fruſtum pyramidis ad portiones, ita q m ad
              <lb/>
            m l. </s>
            <s xml:space="preserve">Itaque quoniam à fruſto coni, uel coni portionis a d,
              <lb/>
            cuius grauitatis centrum eſtm, aufertur fruſtum pyrami-
              <lb/>
            dis habens centruml; </s>
            <s xml:space="preserve">erit reliquæ magnitudinis, quæ ex
              <lb/>
            portionibus ſolidis conſtat; </s>
            <s xml:space="preserve">grauitatis cẽtrum in linea l m
              <lb/>
            producta, atque in puncto q, extra figuram poſito. </s>
            <s xml:space="preserve">quod
              <lb/>
            fieri nullo modo poteſt. </s>
            <s xml:space="preserve">relinquitur ergo, ut punctum l ſit
              <lb/>
            fruſti a d grauitatis centrum. </s>
            <s xml:space="preserve">quæ omnia demonſtranda
              <lb/>
            proponebantur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a">
              <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0186-01"/>
            </figure>
            <note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">22. huius</note>
            <note position="left" xlink:label="note-0186-02" xlink:href="note-0186-02a" xml:space="preserve">19. quinti</note>
          </div>
        </div>
        <div type="section" level="1" n="92">
          <head xml:space="preserve">THEOREMA XXII. PROPOSITIO XXVII.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Omnivm</emph>
            ſolidorum in ſphæra deſcripto-
              <lb/>
            rum, quæ æqualibus, & </s>
            <s xml:space="preserve">ſimilibus baſibus conti-
              <lb/>
            nentur, centrum grauitatis eſt idem, quod ſphæ-
              <lb/>
            ræ centrum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Solida eiuſmodi corpora regularia appellare ſolent, de
              <lb/>
            quibus agitur in tribus ultimis libris elementorum: </s>
            <s xml:space="preserve">ſunt
              <lb/>
            autem numero quinque, tetrahedrum, uel pyramis, hexa-
              <lb/>
            hedrum, uel cubus, octahedrum, dodecahedrum, & </s>
            <s xml:space="preserve">icoſa-
              <lb/>
            hedrum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Sit primo a b c d pyramis ĩ ſphæra deſcripta, cuíus ſphæ
              <lb/>
            ræ centrum ſit e. </s>
            <s xml:space="preserve">Dico e pyramidis a b c d grauitatis eſſe
              <lb/>
            centrum. </s>
            <s xml:space="preserve">Si enim iuncta d e producatur ad baſim a b c in
              <lb/>
            f; </s>
            <s xml:space="preserve">ex iis, quæ demonſtrauit Campanus in quartodecimo li
              <lb/>
            bro elementorum, propoſitione decima quinta, & </s>
            <s xml:space="preserve">decima
              <lb/>
            ſeptima, erit f centrum circuli circa triangulum a b c de-
              <lb/>
            ſcripti: </s>
            <s xml:space="preserve">atque erit e f ſexta pars ipſius ſphæræ axis. </s>
            <s xml:space="preserve">quare
              <lb/>
            ex prima huius conſtat trianguli a b c grauitatis centrum
              <lb/>
            eſſe punctum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco lineam d f eſſe pyramidis axem.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>