Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="75">
          <p>
            <s xml:space="preserve">
              <pb file="0146" n="146" rhead="FED. COMMANDINI"/>
            partes d. </s>
            <s xml:space="preserve">in pyramide igitur inſcripta erit quædam figura,
              <lb/>
            ex priſinatibus æqualem altitudinem habentibus cóſtans,
              <lb/>
            ad partes e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altera circumſcripta ad partes d. </s>
            <s xml:space="preserve">Sed unum-
              <lb/>
            quodque eorum priſmatum, quæ in figura inſcripta conti-
              <lb/>
            nentur, æquale eſt priſmati, quod ab eodem fit triangulo in
              <lb/>
            figura circumſcripta: </s>
            <s xml:space="preserve">nam priſma p q priſmati p o eſt æ-
              <lb/>
            quale; </s>
            <s xml:space="preserve">priſma s t æquale priſmati s r; </s>
            <s xml:space="preserve">priſma x y priſmati
              <lb/>
            x u; </s>
            <s xml:space="preserve">priſma η θ priſinati η z; </s>
            <s xml:space="preserve">priſina μ ν priſmati μ λ; </s>
            <s xml:space="preserve">priſ-
              <lb/>
            ma ρ σ priſmati ρ π; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſma φ χ priſinati φ τ æquale. </s>
            <s xml:space="preserve">re-
              <lb/>
            linquitur ergo, ut circumſcripta figura exuperet inſcriptã
              <lb/>
            priſmate, quod baſim habet a b c triangulum, & </s>
            <s xml:space="preserve">axem e f.
              <lb/>
            </s>
            <s xml:space="preserve">Illud uero minus eſt ſolida magnitudine propoſita. </s>
            <s xml:space="preserve">Eadȩ
              <lb/>
            ratione inſcribetur, & </s>
            <s xml:space="preserve">circumſcribetur ſolida figura in py-
              <lb/>
            ramide, quæ quadrilateram, uel plurilaterã baſim habeat.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
        <div type="section" level="1" n="76">
          <head xml:space="preserve">PROBLEMA II. PROPOSITIO XI.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Dato</emph>
            cono, fieri poteſt, ut figura ſolida in-
              <lb/>
            ſcribatur, & </s>
            <s xml:space="preserve">altera circumſcribatur ex cylindris
              <lb/>
            æqualem habentibus altitudinem, ita ut circum-
              <lb/>
            ſcripta ſuperet inſcriptam, magnitudine, quæ ſo-
              <lb/>
            lida magnitudine propoſita ſit minor.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">SIT conus, cuius axis b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano per axem
              <lb/>
            ducto, ut ſectio ſit triangulum a b c: </s>
            <s xml:space="preserve">intelligaturq; </s>
            <s xml:space="preserve">cylin-
              <lb/>
            drus, qui baſim eandem, & </s>
            <s xml:space="preserve">eundem axem habeat. </s>
            <s xml:space="preserve">Hoc igi-
              <lb/>
            tur cylindro continenter bifariam ſecto, relinquetur cylin
              <lb/>
            drus minor ſolida magnitudine propoſita. </s>
            <s xml:space="preserve">Sit autem is cy
              <lb/>
            lindrus, qui baſim habet circulum circa diametrum a c, & </s>
            <s xml:space="preserve">
              <lb/>
            axem d e. </s>
            <s xml:space="preserve">Itaque diuidatur b d in partes æquales ipſi d e
              <lb/>
            in punctis f g h _K_lm: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per ea ducantur plana conum ſe-
              <lb/>
            cantia; </s>
            <s xml:space="preserve">quæ baſi æquidiſtent. </s>
            <s xml:space="preserve">erunt ſectiones circuli, cen-
              <lb/>
            tra in axi habentes, ut in primo libro conicorum, propoſi-</s>
          </p>
        </div>
      </text>
    </echo>