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

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          <p>
            <s xml:id="echoid-s3243" xml:space="preserve">
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            ralleli; </s>
            <s xml:id="echoid-s3244" xml:space="preserve">per ſingula autem puncta æquales circun ſerentias terminan-
              <lb/>
            tia, deſcribãtur paralleli circuli. </s>
            <s xml:id="echoid-s3245" xml:space="preserve">Circunferentię maximi illins circuli
              <lb/>
            primo poſiti inter parallelos interceptæ, inæquales erunt, ſemperq́;
              <lb/>
            </s>
            <s xml:id="echoid-s3246" xml:space="preserve">ea, quæ propior fuerit maximo parallelorum, remotiore maior erit.</s>
            <s xml:id="echoid-s3247" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3248" xml:space="preserve">IN _circunferentia maximi circuli_ A B, _ſit polus parallelorum, quem alij duo_
              <lb/>
            _maximi_ B C, A C, _ſecent ad angulos rectos, ſitque_ B C, _parall lorum maximus, &_</s>
            <s xml:id="echoid-s3249" xml:space="preserve">
              <lb/>
            A C, _ad parallelos obliquus. </s>
            <s xml:id="echoid-s3250" xml:space="preserve">Sumantur arcus non continui æquales_ D E, F G; </s>
            <s xml:id="echoid-s3251" xml:space="preserve">_ac per_
              <lb/>
            D, E, F, G, _paralleli ducantur_ D H, E I, F K, G L. </s>
            <s xml:id="echoid-s3252" xml:space="preserve">_Dico arcum_ H I, _maiorem eſſe arcu_
              <lb/>
            K L. </s>
            <s xml:id="echoid-s3253" xml:space="preserve">_Aut enim arcus intermedius_ E F, _vtrique æqualium_ D E, F G, _commenſurabilis_
              <lb/>
            _eſt, aut incommenſurabilis. </s>
            <s xml:id="echoid-s3254" xml:space="preserve">Sit primum commenſurabilis. </s>
            <s xml:id="echoid-s3255" xml:space="preserve">Inuenta autem maxima_
              <lb/>
              <note position="left" xlink:label="note-096-01" xlink:href="note-096-01a" xml:space="preserve">4. decim.</note>
            _menſura V, ſecentur tres arcus_ D E, E F, F G, _in partes ipſi_ V, _æquales, & </s>
            <s xml:id="echoid-s3256" xml:space="preserve">per pun=_
              <lb/>
            _cta diuiſionum paralleli deſcribantur, vt in prima figura apparet. </s>
            <s xml:id="echoid-s3257" xml:space="preserve">Quoniam igitur_
              <lb/>
              <figure xlink:label="fig-096-01" xlink:href="fig-096-01a" number="103">
                <image file="096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/096-01"/>
              </figure>
            _arcus continui_ D P, P E, E O, _&</s>
            <s xml:id="echoid-s3258" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3259" xml:space="preserve">æquales ſunt; </s>
            <s xml:id="echoid-s3260" xml:space="preserve">erit arcus_ H T, _maior arcu_ T I,
              <lb/>
              <note position="left" xlink:label="note-096-02" xlink:href="note-096-02a" xml:space="preserve">5. huius.</note>
            _&_</s>
            <s xml:id="echoid-s3261" xml:space="preserve"> T I, _maior, quàm_ I S, _&</s>
            <s xml:id="echoid-s3262" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">Quare cum_ H T, _maior ſit, quàm_ K Q, _&_</s>
            <s xml:id="echoid-s3264" xml:space="preserve"> T I, _ma=_
              <lb/>
            _ior quam_ Q L; </s>
            <s xml:id="echoid-s3265" xml:space="preserve">_erit totus_ H I, _maior toto_ K L. </s>
            <s xml:id="echoid-s3266" xml:space="preserve">_Quod eſt propoſitum._</s>
            <s xml:id="echoid-s3267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3268" xml:space="preserve">SED _iam_ E F, _incommenſurabilis ſit vtrique_ D E, F G. </s>
            <s xml:id="echoid-s3269" xml:space="preserve">_Dico adhucarcum_ H I,
              <lb/>
            _maiorem eſſe arcu_ K L. </s>
            <s xml:id="echoid-s3270" xml:space="preserve">_Sienim maior non eſt, erit vel minor, vel æqualis. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">Sit pri=_
              <lb/>
            _mum minor; </s>
            <s xml:id="echoid-s3272" xml:space="preserve">& </s>
            <s xml:id="echoid-s3273" xml:space="preserve">ex_ K L, _(vt in ſecunda ſigura) auferatur ipſi_ H I, _æqualis_ K M; </s>
            <s xml:id="echoid-s3274" xml:space="preserve">_&_</s>
            <s xml:id="echoid-s3275" xml:space="preserve">
              <lb/>
            _per_ M, _parallelus ducatur_ M N. </s>
            <s xml:id="echoid-s3276" xml:space="preserve">_Deinde per Lemma 2. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">Propoſ._ </s>
            <s xml:id="echoid-s3278" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3279" xml:space="preserve">_huius lib. </s>
            <s xml:id="echoid-s3280" xml:space="preserve">reperia=_
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            _tur arcus_ F O, _maior quidem, quàm_ F N, _minor verò quam_ F G, _& </s>
            <s xml:id="echoid-s3281" xml:space="preserve">commenſurabi=_
              <lb/>
            _lis intermedio arcui_ E F: </s>
            <s xml:id="echoid-s3282" xml:space="preserve">_Sitque_ E P, _ipſi_ F O, _(qui minor eſt, quàm_ F G, _atque_
              <lb/>
            _adeo minor etiam, quam_ D E, _ipſi_ F G, _æqualis) æqualis, ac per_ O, P, _paralleli de=_
              <lb/>
            _ſcribantur_ O R, P Q. </s>
            <s xml:id="echoid-s3283" xml:space="preserve">_Quoniam igitur arcus non continui_ P E, F O, _æquales ſunt,_
              <lb/>
            _eſtque vtrique illorum commenſurabilis arcus intermedius_ E F; </s>
            <s xml:id="echoid-s3284" xml:space="preserve">_erit, vt iam eſt de=_
              <lb/>
            _monſtratum in prima figura, arcus_ Q I, _maior arcu_ K R. </s>
            <s xml:id="echoid-s3285" xml:space="preserve">_Ergo & </s>
            <s xml:id="echoid-s3286" xml:space="preserve">multo maior erit,_
              <lb/>
            _quaàm_ K M; </s>
            <s xml:id="echoid-s3287" xml:space="preserve">_ac proinde multo magis arcus_ H I, _maior erit quàm_ K M: </s>
            <s xml:id="echoid-s3288" xml:space="preserve">_Sed &_</s>
            <s xml:id="echoid-s3289" xml:space="preserve"> H I,
              <lb/>
            _equalis ponitur ipſi_ K M. </s>
            <s xml:id="echoid-s3290" xml:space="preserve">_Quod eſt abſurdum. </s>
            <s xml:id="echoid-s3291" xml:space="preserve">Non ergo_ H I, _minor eſt, quàm_ K L.</s>
            <s xml:id="echoid-s3292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3293" xml:space="preserve">SIT _deinde, ſi fieripoteſt, arcus_ H I, _arcui_ K L, _æqualis, vt in tertia figura._
              <lb/>
            </s>
            <s xml:id="echoid-s3294" xml:space="preserve">_Diniſis autem arcubus_ D E, F G, _bifariam in_ M, N, _ducantur per_ M, N, _paralleli_ M O,
              <lb/>
            N P. </s>
            <s xml:id="echoid-s3295" xml:space="preserve">_Erit igitur arcus_ H O, _maior, quàm_ O I; </s>
            <s xml:id="echoid-s3296" xml:space="preserve">_&_</s>
            <s xml:id="echoid-s3297" xml:space="preserve"> K P, _maior, quàm_ P L. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">_Quare_
              <lb/>
              <note position="left" xlink:label="note-096-03" xlink:href="note-096-03a" xml:space="preserve">5. huius.</note>
            O I, _minor erit, quam dimidium ipſius_ H I, _&_</s>
            <s xml:id="echoid-s3299" xml:space="preserve"> K P, _maior dimidio ipſius_ K L. </s>
            <s xml:id="echoid-s3300" xml:space="preserve"/>
          </p>
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