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

Page concordance

< >
Scan Original
81 69
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
91 79
92 80
93 81
94 82
95 83
96 84
97 85
98 86
99 87
100 88
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109
110
< >
page |< < (58) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div216" type="section" level="1" n="104">
          <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>
          </p>
        </div>
      </text>
    </echo>
Impressum