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

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          <p>
            <s xml:id="echoid-s2241" xml:space="preserve">
              <pb o="58" file="070" n="70" rhead=""/>
            minor eſt. </s>
            <s xml:id="echoid-s2242" xml:space="preserve">Duæ vero rectæ lineæ æquales ab eodem puncto in circun
              <lb/>
            ferentiam circuli cadunt, à maxima æqualiter diſtantes.</s>
            <s xml:id="echoid-s2243" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2244" xml:space="preserve">_SVPER_ diametro _A D,_ circuli _A B C D E,_ conſtituatur rectum circuli ſegmen-
              <lb/>
            tum _A F D,_ quod ſecetur non bifariam in _F,_ ſitque minor pars _A F,_ & </s>
            <s xml:id="echoid-s2245" xml:space="preserve">maior _D F:_
              <lb/>
            </s>
            <s xml:id="echoid-s2246" xml:space="preserve">Cadant autem ex _F,_ plurimæ rectæ lineæ _F A, F I, F H, F B, F C, F D, F E._ </s>
            <s xml:id="echoid-s2247" xml:space="preserve">_D_ico
              <lb/>
            omnium minimam eſſe _FA;_ </s>
            <s xml:id="echoid-s2248" xml:space="preserve">maximam vero _F D:_ </s>
            <s xml:id="echoid-s2249" xml:space="preserve">At _F C,_ maiorem, quàm _F B,_ &</s>
            <s xml:id="echoid-s2250" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2251" xml:space="preserve">Et
              <lb/>
            _F I,_ minorem, quàm _F H._ </s>
            <s xml:id="echoid-s2252" xml:space="preserve">&</s>
            <s xml:id="echoid-s2253" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">Denique duas _F E, F C,_ æquales eſſe, ſi æqualiter diſtent
              <lb/>
            à maxima _F D,_ hoc eſt, ſiarcus _D E, D C,_ æquales ſint. </s>
            <s xml:id="echoid-s2255" xml:space="preserve">Demittatur enim ex _F,_ in pla
              <lb/>
              <note position="left" xlink:label="note-070-01" xlink:href="note-070-01a" xml:space="preserve">11. vndec.</note>
            num circuli _A B C D E,_ perpendicularis _F G,_ quæ in _A D,_ communem ſectionem ca-
              <lb/>
              <note position="left" xlink:label="note-070-02" xlink:href="note-070-02a" xml:space="preserve">38. vndec.</note>
            det: </s>
            <s xml:id="echoid-s2256" xml:space="preserve">eritque punctum _G,_ vel inter puncta _A D,_ vt in prima figura; </s>
            <s xml:id="echoid-s2257" xml:space="preserve">(Id quod ſemper
              <lb/>
            continget, quando ſegmentum _A F D,_ ſemicirculo maius non eſt, quamuis idem accide-
              <lb/>
            re poſsit in ſegmento maiore.) </s>
            <s xml:id="echoid-s2258" xml:space="preserve">vel idem quod A; </s>
            <s xml:id="echoid-s2259" xml:space="preserve">vel extra circulum in diametro _D
              <emph style="sc">A</emph>
            ,_
              <lb/>
            protracta, vt poſteriores duæ figuræ indicant. </s>
            <s xml:id="echoid-s2260" xml:space="preserve">Id quod ſolumin ſegmento, quod ſemi-
              <lb/>
            circulo maius ſit, contingere poteſt. </s>
            <s xml:id="echoid-s2261" xml:space="preserve">In prima autem figura non erit _G,_ centrum cir-
              <lb/>
            culi _A B C D E,_ quod _G F,_ non diuidat bifariam ſegmentum _A F D:_ </s>
            <s xml:id="echoid-s2262" xml:space="preserve">Multò minus
              <lb/>
            in poſterioribus duabus figuris erit _G,_ centrum circuli _
              <emph style="sc">Ab</emph>
            CDE._ </s>
            <s xml:id="echoid-s2263" xml:space="preserve">Iungantur rectæ
              <lb/>
            _G I, G H,
              <emph style="sc">Gb</emph>
            , G C, G E;_ </s>
            <s xml:id="echoid-s2264" xml:space="preserve">eruntque omnes anguli ad _G,_ recti, ex defin. </s>
            <s xml:id="echoid-s2265" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2266" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2267" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2268" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s2269" xml:space="preserve">
              <figure xlink:label="fig-070-01" xlink:href="fig-070-01a" number="80">
                <image file="070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/070-01"/>
              </figure>
            Quoniam vero rectarum ex _G,_ in circulum _
              <emph style="sc">Ab</emph>
            CDE,_ cadentium in prima figura,
              <lb/>
              <note position="left" xlink:label="note-070-03" xlink:href="note-070-03a" xml:space="preserve">7. vel 8. ten
                <lb/>
              tij.</note>
            & </s>
            <s xml:id="echoid-s2270" xml:space="preserve">tertia minima eſt _GA;_ </s>
            <s xml:id="echoid-s2271" xml:space="preserve">In omnibus autem figuris maxima eſt _
              <emph style="sc">G</emph>
            D;_ </s>
            <s xml:id="echoid-s2272" xml:space="preserve">& </s>
            <s xml:id="echoid-s2273" xml:space="preserve">_
              <emph style="sc">G</emph>
            C,_ ma-
              <lb/>
            ior, quàm _
              <emph style="sc">GB</emph>
            _; </s>
            <s xml:id="echoid-s2274" xml:space="preserve">atque _
              <emph style="sc">G</emph>
            I,_ minor, quàm _
              <emph style="sc">G</emph>
            H;_ </s>
            <s xml:id="echoid-s2275" xml:space="preserve">duæ denique _
              <emph style="sc">G</emph>
            C:_ </s>
            <s xml:id="echoid-s2276" xml:space="preserve">_
              <emph style="sc">G</emph>
            E,_ æquales: </s>
            <s xml:id="echoid-s2277" xml:space="preserve">erunt
              <lb/>
              <note position="left" xlink:label="note-070-04" xlink:href="note-070-04a" xml:space="preserve">7. vel 15. vol.</note>
            propterea in prima, & </s>
            <s xml:id="echoid-s2278" xml:space="preserve">tertia figura duo quadrata rectarum _
              <emph style="sc">Ag</emph>
            ,
              <emph style="sc">G</emph>
            F,_ minora duo-
              <lb/>
              <note position="left" xlink:label="note-070-05" xlink:href="note-070-05a" xml:space="preserve">8. tertij.</note>
            bus quadratis recfarum _
              <emph style="sc">Ig</emph>
            ,
              <emph style="sc">G</emph>
            F:_ </s>
            <s xml:id="echoid-s2279" xml:space="preserve">quibus cum æqualia ſint quadrata rectarum _
              <emph style="sc">Fa</emph>
            ,_
              <lb/>
              <note position="left" xlink:label="note-070-06" xlink:href="note-070-06a" xml:space="preserve">47. primi.</note>
            _FI;_ </s>
            <s xml:id="echoid-s2280" xml:space="preserve">minus quoque erit quadratum ex _F A,_ quadrato ex _FI;_ </s>
            <s xml:id="echoid-s2281" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s2282" xml:space="preserve">recta
              <lb/>
            _F A,_ minor erit quàm _F I._ </s>
            <s xml:id="echoid-s2283" xml:space="preserve">Eodem modo oſtendemus _F A,_ in eadem figura prima, & </s>
            <s xml:id="echoid-s2284" xml:space="preserve">
              <lb/>
            tertia minorem eſſe, quàm F H, &</s>
            <s xml:id="echoid-s2285" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2286" xml:space="preserve">In ſecunda verà figura minor quoque eſt _F A,_
              <lb/>
            quam _F I,_ vel _F H,_ &</s>
            <s xml:id="echoid-s2287" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2288" xml:space="preserve">propterea quòd in triangulis _A I F, A H F,_ (in quibus an-
              <lb/>
              <note position="left" xlink:label="note-070-07" xlink:href="note-070-07a" xml:space="preserve">19. paimi.</note>
            gulus _A,_ rectus eſt, ex defin. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2290" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2292" xml:space="preserve">Eucl ac proinde alij acuti.) </s>
            <s xml:id="echoid-s2293" xml:space="preserve">recta _F A,_ ſub-
              <lb/>
            tendit angulum acutum _I,_ vel _H,_ at recta _F I,_ vel _F H,_ &</s>
            <s xml:id="echoid-s2294" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2295" xml:space="preserve">angulum rectum _A._
              <lb/>
            </s>
            <s xml:id="echoid-s2296" xml:space="preserve">Minima ergo omnium èſt recta _F A._ </s>
            <s xml:id="echoid-s2297" xml:space="preserve">Rurſus in omnibus figuris erunt duo quadrata
              <lb/>
            ex _G D, G F,_ maiora duobus quadratis ex _G C, G F:_ </s>
            <s xml:id="echoid-s2298" xml:space="preserve">quibus cum æqualia ſint qua-
              <lb/>
              <note position="left" xlink:label="note-070-08" xlink:href="note-070-08a" xml:space="preserve">47. paimi.</note>
            dxata ex _F D, F C;_ </s>
            <s xml:id="echoid-s2299" xml:space="preserve">maius quoque erit quadratum ex _F D,_ quadrato ex _FC;_ </s>
            <s xml:id="echoid-s2300" xml:space="preserve">ac pro-
              <lb/>
            inde & </s>
            <s xml:id="echoid-s2301" xml:space="preserve">recta _F D,_ maior erit, quam recta _F C._ </s>
            <s xml:id="echoid-s2302" xml:space="preserve">Non aliter oſtendemus, rectam _F </s>
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