Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div90" type="section" level="1" n="53">
          <p>
            <s xml:id="echoid-s794" xml:space="preserve">
              <pb o="22" file="034" n="34" rhead=""/>
            quouis alio maximo inſcripti. </s>
            <s xml:id="echoid-s795" xml:space="preserve">Ducatur ex C, ad circulum A B, perpendicu
              <lb/>
              <note position="left" xlink:label="note-034-01" xlink:href="note-034-01a" xml:space="preserve">11. vndee.</note>
            laris C E, quæ in centrum ipſius cadet, quod ſit E, & </s>
            <s xml:id="echoid-s796" xml:space="preserve">producta in reliquum
              <lb/>
              <figure xlink:label="fig-034-01" xlink:href="fig-034-01a" number="31">
                <image file="034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/034-01"/>
              </figure>
              <note position="left" xlink:label="note-034-02" xlink:href="note-034-02a" xml:space="preserve">9. huius.</note>
            polum, qui ſit D, cadet. </s>
            <s xml:id="echoid-s797" xml:space="preserve">Iam per rectas C B,
              <lb/>
              <note position="left" xlink:label="note-034-03" xlink:href="note-034-03a" xml:space="preserve">1. huius.</note>
            C D, planum ducatur faciens in ſphæra cir-
              <lb/>
            culum A D B C, qui cum per E, centrum
              <lb/>
            ſphæræ (Eſt enim E, centrum circuli maxi-
              <lb/>
              <note position="left" xlink:label="note-034-04" xlink:href="note-034-04a" xml:space="preserve">6. huius.</note>
            mi A B, quòd per centrum ſphæræ tranſeat,
              <lb/>
              <note position="left" xlink:label="note-034-05" xlink:href="note-034-05a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            idem, quod ſphæræ) tranſeat, maximus erit,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s798" xml:space="preserve">adeo circulum maximum A B, bifariam
              <lb/>
              <note position="left" xlink:label="note-034-06" xlink:href="note-034-06a" xml:space="preserve">6. huius.</note>
            ſecabit. </s>
            <s xml:id="echoid-s799" xml:space="preserve">Quod etiam inde patet, quòd per
              <lb/>
              <note position="left" xlink:label="note-034-07" xlink:href="note-034-07a" xml:space="preserve">11. huius.</note>
            eius polos incedat. </s>
            <s xml:id="echoid-s800" xml:space="preserve">Hinc enim fit, vt ipſum
              <lb/>
              <note position="left" xlink:label="note-034-08" xlink:href="note-034-08a" xml:space="preserve">15. huius.</note>
            bifariam diuidat. </s>
            <s xml:id="echoid-s801" xml:space="preserve">Sit ergo communis ſectio
              <lb/>
            diameter B E A. </s>
            <s xml:id="echoid-s802" xml:space="preserve">Et quoniam C E, perpendi
              <lb/>
            cularis ducta eſt ad circulum A B, erit eadé
              <lb/>
            perpendicularis ad rectam A B, ex defin. </s>
            <s xml:id="echoid-s803" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s804" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s805" xml:space="preserve">11. </s>
            <s xml:id="echoid-s806" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s807" xml:space="preserve">Duæ ergo diametri A B, C D, in maximo circulo A D B C, ſeſe
              <lb/>
            mutuo ſecãt ad angulos rectos; </s>
            <s xml:id="echoid-s808" xml:space="preserve">ac propterea vt in lib. </s>
            <s xml:id="echoid-s809" xml:space="preserve">4. </s>
            <s xml:id="echoid-s810" xml:space="preserve">Euclidis demonſtra
              <lb/>
              <note position="left" xlink:label="note-034-09" xlink:href="note-034-09a" xml:space="preserve">6. quarti.</note>
            tum eſt, C B, latus eſt quadrati in circulo maximo A D B C, atq; </s>
            <s xml:id="echoid-s811" xml:space="preserve">adeò & </s>
            <s xml:id="echoid-s812" xml:space="preserve">in
              <lb/>
            maximo A B, deſcripti. </s>
            <s xml:id="echoid-s813" xml:space="preserve">Si igitur in ſphæra fit maximus circulus, recta linea
              <lb/>
            ducta, &</s>
            <s xml:id="echoid-s814" xml:space="preserve">c. </s>
            <s xml:id="echoid-s815" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s816" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div92" type="section" level="1" n="54">
          <head xml:id="echoid-head65" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s817" xml:space="preserve">QVONIAM verò quatuor anguli recti ad centrum E, æquales ſunt, atq; </s>
            <s xml:id="echoid-s818" xml:space="preserve">adeò qua-
              <lb/>
            tuor arcus B C, C A, A D, D B, ſuper quos aſcendetunt, æquales, nem pe quadrantes, per-
              <lb/>
              <note position="left" xlink:label="note-034-10" xlink:href="note-034-10a" xml:space="preserve">26. tertij.</note>
            ſpicuum eſt, in ſphæra polum maximi citculi abeſſe à circunferentia maximi circuli, qua-
              <lb/>
            drante maximi circuli. </s>
            <s xml:id="echoid-s819" xml:space="preserve">Abeſt enim C, polus circuli maximi A B, ab eius circunferentia
              <lb/>
            quadrante C B, eademq́; </s>
            <s xml:id="echoid-s820" xml:space="preserve">ratio de ceteris habenda eſt. </s>
            <s xml:id="echoid-s821" xml:space="preserve">Semper enim recta ducta à circunfe-
              <lb/>
            rentia maximi circuli ad eiuſdem polum æqualis eſt lateri quadrati in maximo circulo
              <lb/>
              <note position="left" xlink:label="note-034-11" xlink:href="note-034-11a" xml:space="preserve">16. huius.</note>
            inſcripti, arq; </s>
            <s xml:id="echoid-s822" xml:space="preserve">adeò quadrantem in maximo circulo ſubtendet.</s>
            <s xml:id="echoid-s823" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div94" type="section" level="1" n="55">
          <head xml:id="echoid-head66" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s824" xml:space="preserve">_CONVERSVM_quoq; </s>
            <s xml:id="echoid-s825" xml:space="preserve">huius demonſtratur in alia verſione hoc theoremate.</s>
            <s xml:id="echoid-s826" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s827" xml:space="preserve">SI in ſphæra ſit circulus, & </s>
            <s xml:id="echoid-s828" xml:space="preserve">ab eius polo ad circunferentiam du
              <lb/>
              <note position="left" xlink:label="note-034-12" xlink:href="note-034-12a" xml:space="preserve">26.</note>
            cta recta æqualis ſit lateri quadtati in eo deſcripti, circulus ipſe
              <lb/>
            maximus eſt.</s>
            <s xml:id="echoid-s829" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s830" xml:space="preserve">_IN_ eadem figura ex _C,_ polo ad circunferentiã circuli _A B,_ ductarecta _C B,_ ſit
              <lb/>
            equalis lateri quadrati in circulo _A B,_ deſcripti. </s>
            <s xml:id="echoid-s831" xml:space="preserve">Dico _A B,_ circulum eſſe maxi-
              <lb/>
            mum. </s>
            <s xml:id="echoid-s832" xml:space="preserve">Ducatur enim ex _C,_ ad circulum _A B,_ perpendicularis _C E,_ quæ in eius
              <lb/>
              <note position="left" xlink:label="note-034-13" xlink:href="note-034-13a" xml:space="preserve">11. vndec.</note>
            centrum cadet, quod ſit _E._ </s>
            <s xml:id="echoid-s833" xml:space="preserve">Ducta autem ſemidiametro _E B,_ erit ex deſin. </s>
            <s xml:id="echoid-s834" xml:space="preserve">3. </s>
            <s xml:id="echoid-s835" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s836" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s837" xml:space="preserve">
              <note position="left" xlink:label="note-034-14" xlink:href="note-034-14a" xml:space="preserve">9. huius.</note>
            Eucl. </s>
            <s xml:id="echoid-s838" xml:space="preserve">angulus _E,_ rectus. </s>
            <s xml:id="echoid-s839" xml:space="preserve">Igitur quadratum in circul _A B,_ deſcriptum, æquale eſt
              <lb/>
            quadratis ex _B E, C E:_ </s>
            <s xml:id="echoid-s840" xml:space="preserve">ſed quadratum ſemidiametri _B E,_ dimiaium eſt quadrati
              <lb/>
              <note position="left" xlink:label="note-034-15" xlink:href="note-034-15a" xml:space="preserve">47. primi.</note>
            in circulo _A B,_ deſcripti, vt mox oſtendemus. </s>
            <s xml:id="echoid-s841" xml:space="preserve">I gitur & </s>
            <s xml:id="echoid-s842" xml:space="preserve">quadratum ex _C E,_ eiuſ-
              <lb/>
            dem quadrati in circulo _A B,_ deſcripti dimidium erit; </s>
            <s xml:id="echoid-s843" xml:space="preserve">atque adeo quadrata ex
              <lb/>
            _B E, C E,_ inter ſe æqualia, necnon & </s>
            <s xml:id="echoid-s844" xml:space="preserve">lineæ propterea _B E, C E._ </s>
            <s xml:id="echoid-s845" xml:space="preserve">aquales erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s846" xml:space="preserve">Quare cum _C E,_ ducta ſit ex C, polo circuli _A B,_ ad ipſum circulum perpendicu-
              <lb/>
            laris, oſtenſaq̀; </s>
            <s xml:id="echoid-s847" xml:space="preserve">ſit ſemidiametro _B E,_ aequalis; </s>
            <s xml:id="echoid-s848" xml:space="preserve">erit circulus _A B,_ maximus.</s>
            <s xml:id="echoid-s849" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Schol. 15.
            <lb/>
          huius.</note>
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