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

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        <div xml:id="echoid-div522" type="section" level="1" n="253">
          <p>
            <s xml:id="echoid-s7296" xml:space="preserve">
              <pb o="185" file="197" n="197" rhead=""/>
            tia, qua à præcedenti chorda differt, inueniemus per regulam proportionum
              <lb/>
              <note position="right" xlink:label="note-197-01" xlink:href="note-197-01a" xml:space="preserve">arcuum per
                <lb/>
              ſingula Mi
                <lb/>
              nuta exten
                <lb/>
              ſorum.</note>
            chordas aliorum arcuum intermediorum per quina minuta extenſorum: </s>
            <s xml:id="echoid-s7297" xml:space="preserve">& </s>
            <s xml:id="echoid-s7298" xml:space="preserve">ex
              <lb/>
            his chordas omnium arcuum per ſingula minuta progredientium; </s>
            <s xml:id="echoid-s7299" xml:space="preserve">quemadmo-
              <lb/>
            dum ſupra de inuẽtione ſinuum diximus. </s>
            <s xml:id="echoid-s7300" xml:space="preserve">Quod vt facilius intelligatur, propo
              <lb/>
            nemus hoc vnum exemplum. </s>
            <s xml:id="echoid-s7301" xml:space="preserve">Sit inquirenda chorda arcus Min. </s>
            <s xml:id="echoid-s7302" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7303" xml:space="preserve">Quoniam
              <lb/>
            igitur differentia inter 43632. </s>
            <s xml:id="echoid-s7304" xml:space="preserve">chordam Min. </s>
            <s xml:id="echoid-s7305" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7306" xml:space="preserve">& </s>
            <s xml:id="echoid-s7307" xml:space="preserve">87264. </s>
            <s xml:id="echoid-s7308" xml:space="preserve">chordam Min. </s>
            <s xml:id="echoid-s7309" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s7310" xml:space="preserve">eſt 43632. </s>
            <s xml:id="echoid-s7311" xml:space="preserve">Dic. </s>
            <s xml:id="echoid-s7312" xml:space="preserve">Si Min. </s>
            <s xml:id="echoid-s7313" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7314" xml:space="preserve">quibus arcus Min. </s>
            <s xml:id="echoid-s7315" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7316" xml:space="preserve">ab arcu Min. </s>
            <s xml:id="echoid-s7317" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7318" xml:space="preserve">differt, @ re-
              <lb/>
            quirunt differentiam 43632. </s>
            <s xml:id="echoid-s7319" xml:space="preserve">adijciendam ad chordam arcus Min. </s>
            <s xml:id="echoid-s7320" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7321" xml:space="preserve">vt fiat
              <lb/>
            chorda arcus Min. </s>
            <s xml:id="echoid-s7322" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7323" xml:space="preserve">quantã poſtulant differentiam Minuta 5. </s>
            <s xml:id="echoid-s7324" xml:space="preserve">quibus arcus
              <lb/>
            Min. </s>
            <s xml:id="echoid-s7325" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7326" xml:space="preserve">ab arcu Min. </s>
            <s xml:id="echoid-s7327" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7328" xml:space="preserve">differt, addendam ad eandem chordam arcus Min. </s>
            <s xml:id="echoid-s7329" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7330" xml:space="preserve">
              <lb/>
            vt componatur chorda arcus Min. </s>
            <s xml:id="echoid-s7331" xml:space="preserve">20? </s>
            <s xml:id="echoid-s7332" xml:space="preserve">Inuenies enim requiri differentiam
              <lb/>
            14544. </s>
            <s xml:id="echoid-s7333" xml:space="preserve">quæ additaad 43632. </s>
            <s xml:id="echoid-s7334" xml:space="preserve">chordam arcus Min. </s>
            <s xml:id="echoid-s7335" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7336" xml:space="preserve">conſtituet 58176. </s>
            <s xml:id="echoid-s7337" xml:space="preserve">chor-
              <lb/>
            dam arcus Min. </s>
            <s xml:id="echoid-s7338" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7339" xml:space="preserve">Eademq́; </s>
            <s xml:id="echoid-s7340" xml:space="preserve">ratio eſt de cæteris.</s>
            <s xml:id="echoid-s7341" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div529" type="section" level="1" n="254">
          <head xml:id="echoid-head281" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7342" xml:space="preserve">SED magnum compendium nobis in hac re afferet propoſitio ſexta. </s>
            <s xml:id="echoid-s7343" xml:space="preserve">Nam ex ea
              <lb/>
              <note position="right" xlink:label="note-197-02" xlink:href="note-197-02a" xml:space="preserve">Compen-
                <lb/>
              dium miri
                <lb/>
              ficũ pro in
                <lb/>
              uentione
                <lb/>
              plurim arũ
                <lb/>
              chordarũ.</note>
            plurimas chordas ex alijs inuentis per ſolam additionem, ſubtractionemue cõficiemus.
              <lb/>
            </s>
            <s xml:id="echoid-s7344" xml:space="preserve">Si namq; </s>
            <s xml:id="echoid-s7345" xml:space="preserve">chordam cuiuſuis arcus, qui maior non ſit, quàm grad. </s>
            <s xml:id="echoid-s7346" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">addamus chordæ
              <lb/>
            arcus, quem arcus grad. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7349" xml:space="preserve">ſumpto illo arcu ſuperat, componemus chordam arcus,
              <lb/>
            qui eodem illo arcu aſſumpto arcum grad. </s>
            <s xml:id="echoid-s7350" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7351" xml:space="preserve">excedit: </s>
            <s xml:id="echoid-s7352" xml:space="preserve">propterea quòd differentia
              <lb/>
            inter chordas duorum horum arcuum maiorum æqualis eſt chordæ arcus illius aſſum-
              <lb/>
            pti, qui maior non ponitur, quàm grad. </s>
            <s xml:id="echoid-s7353" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7354" xml:space="preserve">vtibi oſtendimus. </s>
            <s xml:id="echoid-s7355" xml:space="preserve">Vt ſi 3472964. </s>
            <s xml:id="echoid-s7356" xml:space="preserve">chor-
              <lb/>
            dam arcus grad. </s>
            <s xml:id="echoid-s7357" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7358" xml:space="preserve">adijciamus ad 15320890. </s>
            <s xml:id="echoid-s7359" xml:space="preserve">chordam arcus grad. </s>
            <s xml:id="echoid-s7360" xml:space="preserve">100. </s>
            <s xml:id="echoid-s7361" xml:space="preserve">quem arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s7362" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7363" xml:space="preserve">ſuperat dicto arcugrad. </s>
            <s xml:id="echoid-s7364" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7365" xml:space="preserve">cõponemus 18793854. </s>
            <s xml:id="echoid-s7366" xml:space="preserve">chordã arcus grad. </s>
            <s xml:id="echoid-s7367" xml:space="preserve">140. </s>
            <s xml:id="echoid-s7368" xml:space="preserve">
              <lb/>
            qui arcum grad. </s>
            <s xml:id="echoid-s7369" xml:space="preserve">120 codem arcu grad. </s>
            <s xml:id="echoid-s7370" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7371" xml:space="preserve">excedit. </s>
            <s xml:id="echoid-s7372" xml:space="preserve">Ita quoque, ſi 10000000. </s>
            <s xml:id="echoid-s7373" xml:space="preserve">chor-
              <lb/>
            dam arcus grad. </s>
            <s xml:id="echoid-s7374" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7375" xml:space="preserve">addamus chordæ 10000000. </s>
            <s xml:id="echoid-s7376" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s7377" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7378" xml:space="preserve">quem arcus grad. </s>
            <s xml:id="echoid-s7379" xml:space="preserve">
              <lb/>
            120. </s>
            <s xml:id="echoid-s7380" xml:space="preserve">dicto illo arcu grad. </s>
            <s xml:id="echoid-s7381" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7382" xml:space="preserve">ſuperat, conficiemus 20000000. </s>
            <s xml:id="echoid-s7383" xml:space="preserve">chordam arcus grad. </s>
            <s xml:id="echoid-s7384" xml:space="preserve">
              <lb/>
            180. </s>
            <s xml:id="echoid-s7385" xml:space="preserve">qui arcum grad. </s>
            <s xml:id="echoid-s7386" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7387" xml:space="preserve">eodem illo arcu grad. </s>
            <s xml:id="echoid-s7388" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7389" xml:space="preserve">ſuperat.</s>
            <s xml:id="echoid-s7390" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7391" xml:space="preserve">ITEM ſichordam cuiuslibet arcus, qui arcu grad. </s>
            <s xml:id="echoid-s7392" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7393" xml:space="preserve">maior non ſit, ſubtraha-
              <lb/>
            mus ex chorda arcus, qui arcum grad. </s>
            <s xml:id="echoid-s7394" xml:space="preserve">120 ſumpto illo arcu ſuperat, relinquetur chor
              <lb/>
            da arcus, quem arcus grad. </s>
            <s xml:id="echoid-s7395" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7396" xml:space="preserve">eodem illo arcu aſſumpto excedit. </s>
            <s xml:id="echoid-s7397" xml:space="preserve">Vt ſi 3472964.
              <lb/>
            </s>
            <s xml:id="echoid-s7398" xml:space="preserve">chordam arcus grad. </s>
            <s xml:id="echoid-s7399" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7400" xml:space="preserve">detrahamus ex 18793854. </s>
            <s xml:id="echoid-s7401" xml:space="preserve">chorda arcus grad. </s>
            <s xml:id="echoid-s7402" xml:space="preserve">140. </s>
            <s xml:id="echoid-s7403" xml:space="preserve">qui ar-
              <lb/>
            cum grad. </s>
            <s xml:id="echoid-s7404" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7405" xml:space="preserve">ſuperat arcu illo ſumpto grad. </s>
            <s xml:id="echoid-s7406" xml:space="preserve">20 remanebit 15320890. </s>
            <s xml:id="echoid-s7407" xml:space="preserve">chorda arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s7408" xml:space="preserve">100. </s>
            <s xml:id="echoid-s7409" xml:space="preserve">qui eodem illo arcu grad. </s>
            <s xml:id="echoid-s7410" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7411" xml:space="preserve">abarcu grad. </s>
            <s xml:id="echoid-s7412" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7413" xml:space="preserve">ſuperatur.</s>
            <s xml:id="echoid-s7414" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7415" xml:space="preserve">RVRSVS ſiex chorda cuiuſuis arcus, qui maior ſit arcu grad. </s>
            <s xml:id="echoid-s7416" xml:space="preserve">120 ſubducatur
              <lb/>
            chorda arcus, qui tanto minor ſit arcu grad. </s>
            <s xml:id="echoid-s7417" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7418" xml:space="preserve">quanto ille maior eſt, reliqua erit
              <lb/>
            chorda arcus, quo vteruis illorum ab arcu grad. </s>
            <s xml:id="echoid-s7419" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7420" xml:space="preserve">differt. </s>
            <s xml:id="echoid-s7421" xml:space="preserve">Vt ſi ex 18793854.
              <lb/>
            </s>
            <s xml:id="echoid-s7422" xml:space="preserve">chorda arcus grad. </s>
            <s xml:id="echoid-s7423" xml:space="preserve">140. </s>
            <s xml:id="echoid-s7424" xml:space="preserve">auferamus 15320890. </s>
            <s xml:id="echoid-s7425" xml:space="preserve">chordam arcus grad. </s>
            <s xml:id="echoid-s7426" xml:space="preserve">100. </s>
            <s xml:id="echoid-s7427" xml:space="preserve">relinque-
              <lb/>
            tur 3472964. </s>
            <s xml:id="echoid-s7428" xml:space="preserve">chorda arcus grad. </s>
            <s xml:id="echoid-s7429" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7430" xml:space="preserve">quo vterq; </s>
            <s xml:id="echoid-s7431" xml:space="preserve">illorum ab arcu grad. </s>
            <s xml:id="echoid-s7432" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7433" xml:space="preserve">differt. </s>
            <s xml:id="echoid-s7434" xml:space="preserve">
              <lb/>
            Quæ omnia ex dicta propoſ. </s>
            <s xml:id="echoid-s7435" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7436" xml:space="preserve">colliguntur.</s>
            <s xml:id="echoid-s7437" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7438" xml:space="preserve">SATIS ergo eſt, vt per regulam proportionum inueſtigentur chordæ omnium ar
              <lb/>
            cuum à principio ſemicirculi vſque ad arcum grad. </s>
            <s xml:id="echoid-s7439" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7440" xml:space="preserve">Si enim ex his reperiantur
              <lb/>
            chordæ arcuum, qui cum illis ſemicirculum conficiant, & </s>
            <s xml:id="echoid-s7441" xml:space="preserve">ex his repertis ſubducantur
              <lb/>
            priores illæ inuentæ, remanebunt chordæ omnium arcuum inter arcum grad. </s>
            <s xml:id="echoid-s7442" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7443" xml:space="preserve">& </s>
            <s xml:id="echoid-s7444" xml:space="preserve">
              <lb/>
            arcum grad. </s>
            <s xml:id="echoid-s7445" xml:space="preserve">120. </s>
            <s xml:id="echoid-s7446" xml:space="preserve">Item ſinotæ eſſent chordæ omnium arcuum ab arcu grad. </s>
            <s xml:id="echoid-s7447" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7448" xml:space="preserve">vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s7449" xml:space="preserve">ad finem ſemicirculi, & </s>
            <s xml:id="echoid-s7450" xml:space="preserve">chordæ omnium arcuũ, qui minores ſint arcu grad 120. </s>
            <s xml:id="echoid-s7451" xml:space="preserve"/>
          </p>
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