Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of figures

< >
[111. Figure]
[112. Figure]
[113. Figure]
[114. Figure]
[115. Figure]
[116. Figure]
[117. Figure]
[118. Figure]
[119. Figure]
[120. Figure]
[121. Figure]
[122. Figure]
[123. Figure]
[124. Figure]
[125. Figure]
[126. Figure]
[127. Figure]
[128. Figure]
[129. Figure]
[130. Figure]
[131. Figure]
[132. Figure]
[133. Figure]
[134. Figure]
[135. Figure]
[136. Figure]
[137. Figure]
[138. Figure]
[139. Figure]
[140. Figure]
< >
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>