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

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          <p style="it">
            <s xml:id="echoid-s2200" xml:space="preserve">
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            Cumergo _A B, A C,_ ſe mutuo tangant in _A,_ & </s>
            <s xml:id="echoid-s2201" xml:space="preserve">_G H, G I,_ ſe mutue quoq; </s>
            <s xml:id="echoid-s2202" xml:space="preserve">tangant
              <lb/>
              <note position="right" xlink:label="note-069-01" xlink:href="note-069-01a" xml:space="preserve">3. huius.</note>
            in _G,_ conſtat propoſitum.</s>
            <s xml:id="echoid-s2203" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div212" type="section" level="1" n="103">
          <head xml:id="echoid-head115" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s2204" xml:space="preserve">CIRCVLI maximi ad maximum parallelorum æqualiter in-
              <lb/>
              <note position="right" xlink:label="note-069-02" xlink:href="note-069-02a" xml:space="preserve">27.</note>
            clinati, polos habent in circunferentia eiuſdem paralleli. </s>
            <s xml:id="echoid-s2205" xml:space="preserve">Et circuli
              <lb/>
            maximi, qui polos habent in circunferentia eiuſdem paralleli, ad ma-
              <lb/>
            ximum parallelorum æqualiter inclinantur.</s>
            <s xml:id="echoid-s2206" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2207" xml:space="preserve">_CIRCVLI_ maximi _A B, C D,_ quorum poli _E, F,_ æqualiter ſint inclinati ad
              <lb/>
              <figure xlink:label="fig-069-01" xlink:href="fig-069-01a" number="79">
                <image file="069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/069-01"/>
              </figure>
            _D B,_ maximum parallelorum. </s>
            <s xml:id="echoid-s2208" xml:space="preserve">_D_ico eo-
              <lb/>
            rum polos _E, F,_ eſſe in eodem parallelo.
              <lb/>
            </s>
            <s xml:id="echoid-s2209" xml:space="preserve">
              <note position="right" xlink:label="note-069-03" xlink:href="note-069-03a" xml:space="preserve">20. 1. huius.</note>
            Deſcriptis enim per _G,_ polum paralle-
              <lb/>
            lorum, & </s>
            <s xml:id="echoid-s2210" xml:space="preserve">per _E, F,_ polos circulorum
              <lb/>
            _A B, C D,_ maximis circulis _G E, G F,_
              <lb/>
            qui recti erunt ad circulos _A B, C D;_
              <lb/>
            </s>
            <s xml:id="echoid-s2211" xml:space="preserve">
              <note position="right" xlink:label="note-069-04" xlink:href="note-069-04a" xml:space="preserve">15. 1. huius.</note>
            erunt arcus _E G, F G,_ diſtantiæ polorũ
              <lb/>
            _E, F,_ à polo _G:_ </s>
            <s xml:id="echoid-s2212" xml:space="preserve">ſunt autem æquales,
              <lb/>
              <note position="right" xlink:label="note-069-05" xlink:href="note-069-05a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            quòd circuli _A B, C D,_ ponantur æqua
              <lb/>
            liter inclinati ad circulum _D B._ </s>
            <s xml:id="echoid-s2213" xml:space="preserve">Igitur
              <lb/>
            circulus _E F,_ ex polo _G,_ & </s>
            <s xml:id="echoid-s2214" xml:space="preserve">interuallo
              <lb/>
            _G E,_ vel _G F,_ deſcriptus, parallelus
              <lb/>
            eſt circulo _DB;_ </s>
            <s xml:id="echoid-s2215" xml:space="preserve">in quo quidem paralle-
              <lb/>
              <note position="right" xlink:label="note-069-06" xlink:href="note-069-06a" xml:space="preserve">2. huius.</note>
            lo _E F,_ circuli _A B, C D,_ polos _E, F_
              <lb/>
            habent. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s2217" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2218" xml:space="preserve">_SED_ iam circuli maximi _A B, C D,_
              <lb/>
            habeant polos _E, F,_ in parallelo, _E F._
              <lb/>
            </s>
            <s xml:id="echoid-s2219" xml:space="preserve">Dico eos æqualiter inclinari ad _D B,_ ma
              <lb/>
            ximum parallelorum. </s>
            <s xml:id="echoid-s2220" xml:space="preserve">Erunt enim ex defin. </s>
            <s xml:id="echoid-s2221" xml:space="preserve">poli, rectæ _G E, G F,_ æquales, atque obid
              <lb/>
            arcus _E G, F G,_ æquales quoque erunt. </s>
            <s xml:id="echoid-s2222" xml:space="preserve">Cum ergo ijdem arcus ſint diſtantiæpolorum
              <lb/>
              <note position="right" xlink:label="note-069-07" xlink:href="note-069-07a" xml:space="preserve">28. tertij.
                <lb/>
              Schol. 21.
                <lb/>
              huius.</note>
            _E, F,_ à _G,_ polo parallelorum; </s>
            <s xml:id="echoid-s2223" xml:space="preserve">æqualiter inclinati erunt circuli _A B, C D,_ ad _D B,_
              <lb/>
            parallelorum maximum.</s>
            <s xml:id="echoid-s2224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2225" xml:space="preserve">_SEQVITVR_ iam in codice græco prepoſitio 22. </s>
            <s xml:id="echoid-s2226" xml:space="preserve">cuius demon ſtratio longiſsi-
              <lb/>
            ma eſt. </s>
            <s xml:id="echoid-s2227" xml:space="preserve">Vnde quoniam in alia verſione multo breuius, dilucidiusque eadem demon-
              <lb/>
            ſtratur, viſum eſt hoc loco inſerere alia tria theoremata a lterius verſionis, vt faci-
              <lb/>
            lius deinde propoſitionem 22. </s>
            <s xml:id="echoid-s2228" xml:space="preserve">huius libri demonſtremus. </s>
            <s xml:id="echoid-s2229" xml:space="preserve">Eſt autem primum Theorema
              <lb/>
            ſecunda pars propoſ. </s>
            <s xml:id="echoid-s2230" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2231" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2232" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2233" xml:space="preserve">Theodoſii, quamuis magis vniuerſale ſit, vt hic proponi-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2234" xml:space="preserve">Primum ergo Theorema, quod ordine tertium eſt in hoc ſcholio, ita ſe habet.</s>
            <s xml:id="echoid-s2235" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div216" type="section" level="1" n="104">
          <head xml:id="echoid-head116" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s2236" xml:space="preserve">SI ſuper diametro circuli conſtituatur rectum circuli ſegmen-
              <lb/>
              <note position="right" xlink:label="note-069-08" xlink:href="note-069-08a" xml:space="preserve">28.</note>
            tum, diuidatur autem ſegmenti inſiſtẽtis circunferentia in duas inæ-
              <lb/>
            quales partes, & </s>
            <s xml:id="echoid-s2237" xml:space="preserve">à puncto ſectionis ad circunferentiam circuli primi
              <lb/>
            plurimæ rectæ lineæ cadant; </s>
            <s xml:id="echoid-s2238" xml:space="preserve">erit recta ſubtendens minorem partem
              <lb/>
            inſiſtentis ſegmenti omnium minima: </s>
            <s xml:id="echoid-s2239" xml:space="preserve">quæ autem maiorem ſubten-
              <lb/>
            dit, omnium maxima. </s>
            <s xml:id="echoid-s2240" xml:space="preserve">Reliquarum vero propinquior maximæ remo
              <lb/>
            tiore ſem per maior eſt: </s>
            <s xml:id="echoid-s2241" xml:space="preserve">At propinquior minimæ remotiore </s>
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