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

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          <p>
            <s xml:id="echoid-s2154" xml:space="preserve">
              <pb o="56" file="068" n="68" rhead=""/>
            æqualiter inclinati ad maximum parallelorum, tangunt eundem pa-
              <lb/>
            rallelum: </s>
            <s xml:id="echoid-s2155" xml:space="preserve">Qui vero inclinatior eſt ad maximum parallelorum, ma-
              <lb/>
            iorem parallelum tangit.</s>
            <s xml:id="echoid-s2156" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2157" xml:space="preserve">_MAXIMI_ circuli _A B, C B,_ tan-
              <lb/>
            gant eundem parallelum _A C,_ ſitque
              <lb/>
              <figure xlink:label="fig-068-01" xlink:href="fig-068-01a" number="78">
                <image file="068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/068-01"/>
              </figure>
            parallelorum maximus _D E._ </s>
            <s xml:id="echoid-s2158" xml:space="preserve">Dico cir-
              <lb/>
            culos _A B, C B,_ æqualiter inclinari ad
              <lb/>
            circulum _D E._ </s>
            <s xml:id="echoid-s2159" xml:space="preserve">Sit enim _F,_ polus pa-
              <lb/>
            rallelorum, & </s>
            <s xml:id="echoid-s2160" xml:space="preserve">per _F,_ & </s>
            <s xml:id="echoid-s2161" xml:space="preserve">contactus _A,_
              <lb/>
              <note position="left" xlink:label="note-068-01" xlink:href="note-068-01a" xml:space="preserve">20. 1. huius</note>
            _C,_ circuli maximi deſcribantur _F A D,_
              <lb/>
            _F C E,_ qui per polos circulorum _A B,_
              <lb/>
              <note position="left" xlink:label="note-068-02" xlink:href="note-068-02a" xml:space="preserve">3. huius.</note>
            _C B,_ tranſibunt; </s>
            <s xml:id="echoid-s2162" xml:space="preserve">atque adeo ipſos ad
              <lb/>
              <note position="left" xlink:label="note-068-03" xlink:href="note-068-03a" xml:space="preserve">@5. 1. huius.</note>
            angulos rectos ſecabunt. </s>
            <s xml:id="echoid-s2163" xml:space="preserve">Quare arcus
              <lb/>
            _A F, C F,_ metientur altitudinem po-
              <lb/>
            li _F,_ circuli _D E,_ ſupra circulos _A B,_
              <lb/>
            _CB;_ </s>
            <s xml:id="echoid-s2164" xml:space="preserve">ac proinde cum arcus _A F, C F;_
              <lb/>
            </s>
            <s xml:id="echoid-s2165" xml:space="preserve">
              <note position="left" xlink:label="note-068-04" xlink:href="note-068-04a" xml:space="preserve">28. tertij.</note>
            æquales ſint, propterea quòd rectæ ſub
              <lb/>
            tenſæ _F A, F C,_ æquales ſunt, ex defin.
              <lb/>
            </s>
            <s xml:id="echoid-s2166" xml:space="preserve">
              <note position="left" xlink:label="note-068-05" xlink:href="note-068-05a" xml:space="preserve">21. huius.</note>
            poli, æqualiter inclinabitur circulus
              <lb/>
            _D E,_ ad circulos _A B, C B;_ </s>
            <s xml:id="echoid-s2167" xml:space="preserve">& </s>
            <s xml:id="echoid-s2168" xml:space="preserve">hi vi-
              <lb/>
            ciſsim ad illũ æqualiter inclinabuntur.</s>
            <s xml:id="echoid-s2169" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2170" xml:space="preserve">_TANGAT_ iam maximus cireulus _G H,_ maiorem parallelum _G I._ </s>
            <s xml:id="echoid-s2171" xml:space="preserve">Dico maio-
              <lb/>
            rem eſſe inclinationem circuli _G H,_ ad maximum parallelorum _D E,_ quàm circuli
              <lb/>
            _A B._ </s>
            <s xml:id="echoid-s2172" xml:space="preserve">Deſcripto enim per _F,_ & </s>
            <s xml:id="echoid-s2173" xml:space="preserve">contactum _G,_ circulo maximo _F G E,_ metietur eodem
              <lb/>
              <note position="left" xlink:label="note-068-06" xlink:href="note-068-06a" xml:space="preserve">20. 1. huius.</note>
            modo, vt proxime demonſtratum eſt, arcus _F G,_ altitudinem poli _F,_ circuli _D E,_ ſu-
              <lb/>
            pra circulum _G H._ </s>
            <s xml:id="echoid-s2174" xml:space="preserve">Eſt autem arcus _F G,_ maior arcu _F A,_ quòd circulus _G I,_ maior
              <lb/>
            pònatur circulo _A C,_ ac proinde à polo _F,_ remotior. </s>
            <s xml:id="echoid-s2175" xml:space="preserve">Igitur magis inclinabitur cir-
              <lb/>
            culus _D E,_ ad circulum _G H,_ quàm ad circulum _AB;_ </s>
            <s xml:id="echoid-s2176" xml:space="preserve">& </s>
            <s xml:id="echoid-s2177" xml:space="preserve">viciſsim _G H,_ magis ad
              <lb/>
              <note position="left" xlink:label="note-068-07" xlink:href="note-068-07a" xml:space="preserve">21. 1. huius.</note>
            _D E,_ inclinabitur, quàm _A B._</s>
            <s xml:id="echoid-s2178" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2179" xml:space="preserve">_RVRSVS_ circuli maximi _A B, C B,_ æqualiter inclinentur ad circulum _D E,_
              <lb/>
            maximnm parallelorum. </s>
            <s xml:id="echoid-s2180" xml:space="preserve">Dico illos eundem parallelum tangere. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">Per F, enim polum pa-
              <lb/>
              <note position="left" xlink:label="note-068-08" xlink:href="note-068-08a" xml:space="preserve">20. 1. huius.</note>
            rallelorum, & </s>
            <s xml:id="echoid-s2182" xml:space="preserve">polos circulorum _A B, C B,_ circuli maximi deſcribantur _F A D,_
              <lb/>
            _F C E,_ ſecantes circulos _A B, C B,_ in _A, C._ </s>
            <s xml:id="echoid-s2183" xml:space="preserve">Et quoniam cos ſecant ad angulos re-
              <lb/>
              <note position="left" xlink:label="note-068-09" xlink:href="note-068-09a" xml:space="preserve">15. 1. huius.</note>
            ctos; </s>
            <s xml:id="echoid-s2184" xml:space="preserve">metientur arcus _F A, F C,_ altitudinem poli _F,_ circuli _D E,_ ſupra circulos _A B,_
              <lb/>
            _C B:_ </s>
            <s xml:id="echoid-s2185" xml:space="preserve">ſunt autem arcus _F A, F C,_ æquales, quòd circuli _
              <emph style="sc">Ab</emph>
            , C B,_ æqualiter ponantur
              <lb/>
              <note position="left" xlink:label="note-068-10" xlink:href="note-068-10a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            inclinari ad circulum _D E,_ atque adeo & </s>
            <s xml:id="echoid-s2186" xml:space="preserve">hic viciſsim ad illos. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">Si igitur ex polo _F,_
              <lb/>
            interuallo _F A,_ vel _F C,_ circulus deſcribatur _A C,_ tanget hic circulos _
              <emph style="sc">Ab</emph>
            , C B;_
              <lb/>
            </s>
            <s xml:id="echoid-s2188" xml:space="preserve">
              <note position="left" xlink:label="note-068-11" xlink:href="note-068-11a" xml:space="preserve">3. huius.</note>
            propterea quod circulus _
              <emph style="sc">A</emph>
            C,_ & </s>
            <s xml:id="echoid-s2189" xml:space="preserve">circuli _A B, C B,_ in eiſaem punctis _A, C,_ ſecant
              <lb/>
            circulos maximos _F D, F E,_ qui per eorum polos tranſeunt.</s>
            <s xml:id="echoid-s2190" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2191" xml:space="preserve">_IAM_ vero circulus maximus _G H,_ magis inclinatus ſit ad circulum _D E._
              <lb/>
            </s>
            <s xml:id="echoid-s2192" xml:space="preserve">Dico illum tangere maiorem parallelum. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">Deſcripto enim per _F,_ polum parallelo-
              <lb/>
              <note position="left" xlink:label="note-068-12" xlink:href="note-068-12a" xml:space="preserve">20. 1. huius.</note>
            rum, & </s>
            <s xml:id="echoid-s2194" xml:space="preserve">per polum circuli _G H,_ circulo maximo _F G,_ qui circulum _G H,_ ſeca-
              <lb/>
            bit adangulos rectos, nimirum in puncto _G;_ </s>
            <s xml:id="echoid-s2195" xml:space="preserve">metietur rurſus arcus _F G,_ altitu-
              <lb/>
              <note position="left" xlink:label="note-068-13" xlink:href="note-068-13a" xml:space="preserve">15. 1. huius.</note>
            dinem poli _F,_ circuli _D E,_ ſupra circulum _G H:_ </s>
            <s xml:id="echoid-s2196" xml:space="preserve">Eſt autem _F G,_ maior quàm _F A,_ quod
              <lb/>
              <note position="left" xlink:label="note-068-14" xlink:href="note-068-14a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            magis inclinatus ponatur circulus _G H,_ quàm _
              <emph style="sc">A</emph>
            B._ </s>
            <s xml:id="echoid-s2197" xml:space="preserve">Igitur circulus ex polo _F,_ & </s>
            <s xml:id="echoid-s2198" xml:space="preserve">in-
              <lb/>
            teruallo _F G,_ deſcriptus maior erit circulo ex eodẽ polo _F,_ & </s>
            <s xml:id="echoid-s2199" xml:space="preserve">interuallo _F A,_ deſcripto.</s>
            <s xml:id="echoid-s2200" xml:space="preserve"/>
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