Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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        <div xml:id="echoid-div405" type="section" level="1" n="128">
          <pb o="208" file="244" n="245" rhead="Comment. in I. Cap. Sphæræ"/>
        </div>
        <div xml:id="echoid-div409" type="section" level="1" n="129">
          <head xml:id="echoid-head134" style="it" xml:space="preserve">REGVLAE, QVIBVSET SVPERFICIES MA-
            <lb/>
          ximi circuli in orbe terreno, uel etiam in quacunque ſphæra,
            <lb/>
          & ſuperficies conuexa eiuſdem orbis terreni, uel
            <lb/>
          etiam cuiuſque ſpære, immo, & tota
            <lb/>
          ſoliditas inueniatur.</head>
          <p>
            <s xml:id="echoid-s8466" xml:space="preserve">
              <emph style="sc">Hactenvs</emph>
            ex probatis auctoribus uarios modos recenſuimus, quibus
              <lb/>
            terræ ambitus inueſtigetur, præceptaq́ue propoſuimus, quibus ex circumferen-
              <lb/>
            tia nota diameter, & </s>
            <s xml:id="echoid-s8467" xml:space="preserve">contra ex nota diametro circumferentia inueniatur: </s>
            <s xml:id="echoid-s8468" xml:space="preserve">Nũc
              <lb/>
            uero tradam alia præcepta, quibus ex diametro, & </s>
            <s xml:id="echoid-s8469" xml:space="preserve">circumferentia terrę, uel cu
              <lb/>
            iuſuis alterius ſphæræ, ſuperficies maximi circuli in terra, uel alia ſphæra, inue
              <lb/>
            ſtiganda ſit; </s>
            <s xml:id="echoid-s8470" xml:space="preserve">& </s>
            <s xml:id="echoid-s8471" xml:space="preserve">ex hac ſuperficie ſuperficies conuexa eiuſdem terræ, uel ſphęrę,
              <lb/>
            & </s>
            <s xml:id="echoid-s8472" xml:space="preserve">denique ex hac conuexa ſuperficie ſoliditas tota terræ, uel alterius ſphæræ.
              <lb/>
            </s>
            <s xml:id="echoid-s8473" xml:space="preserve">Ita enim fiet, ut terr@ magnitudo omni ex parte cognita reddatur, non autem
              <lb/>
            tantum quo ad ambitum, quod auctor noſter pręſtitit hoc loco.</s>
            <s xml:id="echoid-s8474" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quarte re-
            <lb/>
          periatur a-
            <lb/>
          rea cuiuſuis
            <lb/>
          circuli.</note>
          <p>
            <s xml:id="echoid-s8475" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            igitur ad primum attinet, ſi multiplicetur ſemidiameter cuiuſuis
              <lb/>
            circuli in dimidiatam partem circumferentiæ, ſeu ambirus circuli, producetur
              <lb/>
            area, ſeu ſuperficies circuli intra circumferentiam contenta. </s>
            <s xml:id="echoid-s8476" xml:space="preserve">Vt ſi circumferen-
              <lb/>
            tia alicuius circuli fuerit 132. </s>
            <s xml:id="echoid-s8477" xml:space="preserve">Diameter uero. </s>
            <s xml:id="echoid-s8478" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8479" xml:space="preserve">Si 21. </s>
            <s xml:id="echoid-s8480" xml:space="preserve">diametri dimidiũ, mul-
              <lb/>
            tiplicemus per 66. </s>
            <s xml:id="echoid-s8481" xml:space="preserve">circunferentiæ dimidiatam partem, producetur hic nume-
              <lb/>
            rus 1386. </s>
            <s xml:id="echoid-s8482" xml:space="preserve">pro area circuli. </s>
            <s xml:id="echoid-s8483" xml:space="preserve">Quod quidem ſupra à nobis demonſtratum eſt in tra
              <lb/>
            ctatione de figuris Iſoperimetris, propoſ. </s>
            <s xml:id="echoid-s8484" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8485" xml:space="preserve">in qua habetur, rectangulum com-
              <lb/>
            prehẽſum ſub ſemidiametro cuiuſuis circuli, & </s>
            <s xml:id="echoid-s8486" xml:space="preserve">dimidiata parte circũferentiæ
              <lb/>
            eiuſdem, æquale eſſe circulo. </s>
            <s xml:id="echoid-s8487" xml:space="preserve">Itaque ſi multiplicetur ſemidiameter terræ, nem
              <lb/>
            pe ſtadia 40090 {10/11} ſecundum Era toſthenem per dimidiatam partem ambi-
              <lb/>
            tus, hoc eſt, ſecundum Eratoſthenem, per ſtadia 126000. </s>
            <s xml:id="echoid-s8488" xml:space="preserve">producetur area maxi
              <lb/>
            mi circuli in terra, ſtadiorum 5052454545 {5/11}. </s>
            <s xml:id="echoid-s8489" xml:space="preserve">hoc eſt, ſuperficies plana ma-
              <lb/>
            ximi circuli in terra comprehendet tot quadrata, quorum quodlibet in ſingu-
              <lb/>
            lis lateribus unum ſtadium complectatur, quot unitates ſunt in dicto numero.
              <lb/>
            </s>
            <s xml:id="echoid-s8490" xml:space="preserve">Areæ enim figurarum planarum menſurantur per quadrata earum linearum,
              <lb/>
            per quas latera, ſeu ambitus earundem figurarum menſurari ſolent.</s>
            <s xml:id="echoid-s8491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8492" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            vero attinet ad ſecundum, ſi area circuli maximi in ſphæra per 4.
              <lb/>
            </s>
            <s xml:id="echoid-s8493" xml:space="preserve">
              <note position="left" xlink:label="note-244-02" xlink:href="note-244-02a" xml:space="preserve">Qua via ſu
                <lb/>
              perficies cõ
                <lb/>
              uexa cuiuſ-
                <lb/>
              libet ſphæ-
                <lb/>
              ræ inuenia-
                <lb/>
              tur.</note>
            multiplicetur, procreabitur ſuperficies tota conuexa ſphæræ. </s>
            <s xml:id="echoid-s8494" xml:space="preserve">Vt ſi fuerit ſphę-
              <lb/>
            ra, cuius maximi circuli ambitus ſit 132. </s>
            <s xml:id="echoid-s8495" xml:space="preserve">Diameter uero 42. </s>
            <s xml:id="echoid-s8496" xml:space="preserve">erit ex prima regu-
              <lb/>
            la area circuli maximi 1386. </s>
            <s xml:id="echoid-s8497" xml:space="preserve">ut dictum eſt, quæ ſi mnltiplicetur per 4. </s>
            <s xml:id="echoid-s8498" xml:space="preserve">exurget
              <lb/>
            mox ſuperficies conuexa dictæ ſphęrę 5544. </s>
            <s xml:id="echoid-s8499" xml:space="preserve">Hoc autem clariſl
              <unsure/>
            ime ab Archime
              <lb/>
            de eſt demonſtratum lib. </s>
            <s xml:id="echoid-s8500" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8501" xml:space="preserve">de ſphæra & </s>
            <s xml:id="echoid-s8502" xml:space="preserve">cylindro, propoſ. </s>
            <s xml:id="echoid-s8503" xml:space="preserve">31. </s>
            <s xml:id="echoid-s8504" xml:space="preserve">in qua concludi-
              <lb/>
            tur, Supei
              <unsure/>
            ficiem conuexam cuiuslibet ſphęrę eſſe quadruplam maximi circuli
              <lb/>
            in ſphæra. </s>
            <s xml:id="echoid-s8505" xml:space="preserve">Itaque ſi area maximi circuli in terra, qui continet, ut diximus, ſta-
              <lb/>
            dia quadrata 5051454545 {5/11}. </s>
            <s xml:id="echoid-s8506" xml:space="preserve">multiplicetur per 4. </s>
            <s xml:id="echoid-s8507" xml:space="preserve">inuenietur ambitus orbis
              <lb/>
            terreni, ſecundum totam conuexam ſuperſiciem, ſtadior@m quadratorum
              <lb/>
            20205818181 {9/11}. </s>
            <s xml:id="echoid-s8508" xml:space="preserve">Poteſt tamen eadem ſuperficies conuexaiuueniri facilius,
              <lb/>
            etiamſi aream maximi circuli non habeamus, hac ratione.</s>
            <s xml:id="echoid-s8509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8510" xml:space="preserve">
              <emph style="sc">Mvltiplicetvr</emph>
            tota diameter in totam circunferentiam maxi-
              <lb/>
            mi circuli. </s>
            <s xml:id="echoid-s8511" xml:space="preserve">Productus enim numerus dabit ſuperficiem conuexam ſphærę. </s>
            <s xml:id="echoid-s8512" xml:space="preserve">Vt
              <lb/>
            ſi multiplicetur diameter terræ continens ſtadia 80181 {9/11}. </s>
            <s xml:id="echoid-s8513" xml:space="preserve">per totũ ambitũ.
              <lb/>
            </s>
            <s xml:id="echoid-s8514" xml:space="preserve">uidelicet per ſtadia 252000. </s>
            <s xml:id="echoid-s8515" xml:space="preserve">producetur conuexa ſuperficies terræ </s>
          </p>
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