Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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        <div xml:id="echoid-div265" type="section" level="1" n="91">
          <pb o="102" file="138" n="139" rhead="Comment. in I. Cap. Sphæræ"/>
        </div>
        <div xml:id="echoid-div269" type="section" level="1" n="92">
          <head xml:id="echoid-head96" style="it" xml:space="preserve">THEOR. 15. PROPOS. 17.</head>
          <p style="it">
            <s xml:id="echoid-s4906" xml:space="preserve">
              <emph style="sc">Sphaera</emph>
            omnibus corporibus ſibi iſoperimetris, planis ſuperficie-
              <lb/>
              <note position="left" xlink:label="note-138-01" xlink:href="note-138-01a" xml:space="preserve">Sphæra ma
                <lb/>
              ior eſt om-
                <lb/>
              nibus cor
                <lb/>
              poribus ſi-
                <lb/>
              bi Iſoperi-
                <lb/>
              metris, &
                <lb/>
              @irca alias
                <lb/>
              ſphæ as cir
                <lb/>
              cũſeriptibi-
                <lb/>
              libus, quæ
                <lb/>
              planis ſuꝑ
                <lb/>
              ficiebus co
                <lb/>
              tinentur.</note>
            bus contineãtur; </s>
            <s xml:id="echoid-s4907" xml:space="preserve">circa{q́ue} alias ſphæras circumſcriptibilia ſint, hoc eſt, quorũ
              <lb/>
            omnes perpendiculares ad baſes productę ab aliquo puncto medio ſint equa
              <lb/>
            les, maior eſt.</s>
            <s xml:id="echoid-s4908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4909" xml:space="preserve">
              <emph style="sc">Esto</emph>
            ſphęra A, cuius centrum A, & </s>
            <s xml:id="echoid-s4910" xml:space="preserve">ſemidiameter A B: </s>
            <s xml:id="echoid-s4911" xml:space="preserve">Solidum autem
              <lb/>
            circa aliquam ſphęram circum ſcriptibile ſibi iſoperimetrum C, cuius una per
              <lb/>
            pendicularium C D. </s>
            <s xml:id="echoid-s4912" xml:space="preserve">Dico ſphęram A, maiorem eſſe ſolido C. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Intelligatur
              <lb/>
            enim circa ſphæram A, corpus deſcriptum ſimile prorſus ſolido C, ita ut ſin-
              <lb/>
            gula quoque latera contingant ſphæram A, hoc eſt, eius perpendiculares,
              <lb/>
            quarum una ſit A B, ſint quoque æquales, nempe ſemidiametri ſphæræ A exi-
              <lb/>
            ſtentes. </s>
            <s xml:id="echoid-s4914" xml:space="preserve">Itaque quoniam ambitus corporis circa ſphęram A, maior eſt ambi-
              <lb/>
            tu ſphæræ A, (per ea, quę ab Archimede ſunt demonſtrata lib. </s>
            <s xml:id="echoid-s4915" xml:space="preserve">I. </s>
            <s xml:id="echoid-s4916" xml:space="preserve">de ſphæ-
              <lb/>
              <figure xlink:label="fig-138-01" xlink:href="fig-138-01a" number="39">
                <image file="138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/138-01"/>
              </figure>
            ra, & </s>
            <s xml:id="echoid-s4917" xml:space="preserve">cylindro, propoſ. </s>
            <s xml:id="echoid-s4918" xml:space="preserve">27.) </s>
            <s xml:id="echoid-s4919" xml:space="preserve">e-
              <lb/>
            rit quoque eiuſdem corporis
              <lb/>
            ambitus maior ambitu corpo-
              <lb/>
            ris C. </s>
            <s xml:id="echoid-s4920" xml:space="preserve">Quare perpendicularis
              <lb/>
            A B, hoc eſt ſemidiametri ſphę
              <lb/>
            ræ A, maior erit perpendicula
              <lb/>
            ri C D. </s>
            <s xml:id="echoid-s4921" xml:space="preserve">Quamobrem rectangu
              <lb/>
            lum ſolidum contentum ſub
              <lb/>
            ſemidiametro A B, & </s>
            <s xml:id="echoid-s4922" xml:space="preserve">tertia
              <lb/>
            parte ambitus ſphęrę A, quod
              <lb/>
            (per præcedentẽ propoſ.) </s>
            <s xml:id="echoid-s4923" xml:space="preserve">ſphę
              <lb/>
            ræ A, æquale eſt, maius erit,
              <lb/>
            quàm rectangulum ſolidum
              <lb/>
            contentum ſub perpendicula-
              <lb/>
            ri C D, & </s>
            <s xml:id="echoid-s4924" xml:space="preserve">tertia parte ambitus
              <lb/>
            corporis C, hoc eſt, (per 15. </s>
            <s xml:id="echoid-s4925" xml:space="preserve">ꝓ-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s4926" xml:space="preserve">huius) quàm corpus C.
              <lb/>
            </s>
            <s xml:id="echoid-s4927" xml:space="preserve">Sphæra igitur omnibus corpo
              <lb/>
            ribus ſibi Iſoperimetris, quæ
              <lb/>
            planis ſuperficiebus continean
              <lb/>
            tur, &</s>
            <s xml:id="echoid-s4928" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4929" xml:space="preserve">maior eſt, quod erat de
              <lb/>
            @onſtr andum.</s>
            <s xml:id="echoid-s4930" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div272" type="section" level="1" n="93">
          <head xml:id="echoid-head97" style="it" xml:space="preserve">THEOR. 16. PROPOS. 18.</head>
          <note position="left" xml:space="preserve">Sphæra ma
            <lb/>
          ior eſt om-
            <lb/>
          nibus cor-
            <lb/>
          poribus ſi
            <lb/>
          bi iſoperi
            <lb/>
          metris, &
            <lb/>
          circa alias
            <lb/>
          ſphæras cir
            <lb/>
          cunſcripti-
            <lb/>
          @ilibus.</note>
          <p style="it">
            <s xml:id="echoid-s4931" xml:space="preserve">
              <emph style="sc">Sphaera</emph>
            omnibus corporibus ſibiiſoperimetris, & </s>
            <s xml:id="echoid-s4932" xml:space="preserve">circa alias ſphę
              <lb/>
            ras circumſcriptibilibus, quæ ſuperficiebus conicis contineantur, ita ut la-
              <lb/>
            tera omnia conica ſint æqualia, maior eſt.</s>
            <s xml:id="echoid-s4933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4934" xml:space="preserve">
              <emph style="sc">Esto</emph>
            circulus A B C D, cui circumſcribatur figura regularis E F G H-
              <lb/>
            I K L M, ita ut numerus laterum à quaternario menſuretur, cuiuſmodi eſt qua
              <lb/>
            dratum, figura 8. </s>
            <s xml:id="echoid-s4935" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4936" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">20. </s>
            <s xml:id="echoid-s4938" xml:space="preserve">24. </s>
            <s xml:id="echoid-s4939" xml:space="preserve">vel 28. </s>
            <s xml:id="echoid-s4940" xml:space="preserve">laterum, angulorumq́. </s>
            <s xml:id="echoid-s4941" xml:space="preserve">ęqualium, &</s>
            <s xml:id="echoid-s4942" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4943" xml:space="preserve"/>
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