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

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          <p>
            <s xml:id="echoid-s2438" xml:space="preserve">
              <pb o="62" file="074" n="74" rhead=""/>
            quem tangit maximus in principio circulus, & </s>
            <s xml:id="echoid-s2439" xml:space="preserve">ei-
              <lb/>
            dem parallelus erit.</s>
            <s xml:id="echoid-s2440" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2441" xml:space="preserve">IN ſphæra maximus circulus A B C D, cuius polus E, tangat circulum
              <lb/>
            A F, ſecet autem alium huic parallelum G B H D, poſitum inter ſphæræ cen-
              <lb/>
            trum, & </s>
            <s xml:id="echoid-s2442" xml:space="preserve">circulum A F, ita vt circulus G B H D, maior ſit, quam A F; </s>
            <s xml:id="echoid-s2443" xml:space="preserve">ſitque
              <lb/>
            E, polus circuli maximi A B C D, inter vtrumque circulum A F, G B H D.
              <lb/>
            </s>
            <s xml:id="echoid-s2444" xml:space="preserve">Quoniam verò maximus circulus A B C D, ſecat circulum G B H D, non bi-
              <lb/>
            fariam, cum non tranfeat per eius polos, hoc eſt, per polos parallelorum, erit
              <lb/>
              <figure xlink:label="fig-074-01" xlink:href="fig-074-01a" number="83">
                <image file="074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/074-01"/>
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            ſegmentum B H D, ad po
              <lb/>
            lum conſpicuum, qui ſit I,
              <lb/>
            maiꝰ ſemicirculo, & </s>
            <s xml:id="echoid-s2445" xml:space="preserve">B G D,
              <lb/>
              <note position="left" xlink:label="note-074-01" xlink:href="note-074-01a" xml:space="preserve">19. huius.</note>
            minus. </s>
            <s xml:id="echoid-s2446" xml:space="preserve">Ducatur per E, po-
              <lb/>
            lum circuli A B C D, & </s>
            <s xml:id="echoid-s2447" xml:space="preserve">I,
              <lb/>
              <note position="left" xlink:label="note-074-02" xlink:href="note-074-02a" xml:space="preserve">20. 1. huius.</note>
            polũ parallelorũ circulus
              <lb/>
            maximus G A C, qui ſeca-
              <lb/>
            bit ſegmenta B G D, B H D,
              <lb/>
              <note position="left" xlink:label="note-074-03" xlink:href="note-074-03a" xml:space="preserve">9. huius.</note>
            bifariam: </s>
            <s xml:id="echoid-s2448" xml:space="preserve">puncta autem M,
              <lb/>
            N, æqualiter diſtent ab H;
              <lb/>
            </s>
            <s xml:id="echoid-s2449" xml:space="preserve">& </s>
            <s xml:id="echoid-s2450" xml:space="preserve">O, magis diſtet ab H,
              <lb/>
            quàm N. </s>
            <s xml:id="echoid-s2451" xml:space="preserve">Tangant autem
              <lb/>
            parallelum G B H D, in
              <lb/>
              <note position="left" xlink:label="note-074-04" xlink:href="note-074-04a" xml:space="preserve">14. huius.</note>
            punctis G, H, M, N, O, cir-
              <lb/>
            culi maximiGL, H K, M P,
              <lb/>
            N K, O L, qui quidem om-
              <lb/>
            nes inclinati erunt ad ma-
              <lb/>
            ximum circulum A B C D,
              <lb/>
            cum non tranſeant per E,
              <lb/>
            polum ipſius. </s>
            <s xml:id="echoid-s2452" xml:space="preserve">Cum enim E,
              <lb/>
            polus ponatur inter parallelos A F, G B H D, non poterunt circuli tangen-
              <lb/>
            tes circulum G B H D, per E, tranſire, alias ſecarent ipſum, cum alter po-
              <lb/>
            lus, per quem etiam neceſſario tranſeunt, ſit extra dictos parallelos, vt patet.
              <lb/>
            </s>
            <s xml:id="echoid-s2453" xml:space="preserve">
              <note position="left" xlink:label="note-074-05" xlink:href="note-074-05a" xml:space="preserve">Coroll. 10.
                <lb/>
              1. huius.</note>
            Dico circulum H K, eſſe rectiſsimum, hoc eſt, minime inclinatum, humilimum
              <lb/>
            autem, id eſt, maximè inclinatum eſſe G L; </s>
            <s xml:id="echoid-s2454" xml:space="preserve">At M P, N K, ſimiliter inclinari,
              <lb/>
            & </s>
            <s xml:id="echoid-s2455" xml:space="preserve">O L, magis quàm N K: </s>
            <s xml:id="echoid-s2456" xml:space="preserve">Polos denique horum circulorum tangentium eſſe
              <lb/>
            in vno eodemq́ue parallelo, qui minor ſit, quàm A F. </s>
            <s xml:id="echoid-s2457" xml:space="preserve">Quoniam enim E, polus
              <lb/>
            eſt circuli A B C D, erit E A, quadrans maximi circuli; </s>
            <s xml:id="echoid-s2458" xml:space="preserve">ſumatur ei æqualis
              <lb/>
              <note position="left" xlink:label="note-074-06" xlink:href="note-074-06a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. huius.</note>
            arcus H Q; </s>
            <s xml:id="echoid-s2459" xml:space="preserve">eritque punctum Q, inter puncta A, & </s>
            <s xml:id="echoid-s2460" xml:space="preserve">I, cum arcus H A, ma-
              <lb/>
            ior ſit quadrante, (quòd E A, quadrans ſit oſtenſus.) </s>
            <s xml:id="echoid-s2461" xml:space="preserve">& </s>
            <s xml:id="echoid-s2462" xml:space="preserve">H I, quadrante mi-
              <lb/>
              <note position="left" xlink:label="note-074-07" xlink:href="note-074-07a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. huius.</note>
            nor, propterea quòd arcus ex I, polo per H, vſque ad maximum parallelorum
              <lb/>
            porrectus ſit quadrans. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">Si igitur ex polo I, ad interuallum I Q, circulus de-
              <lb/>
              <note position="left" xlink:label="note-074-08" xlink:href="note-074-08a" xml:space="preserve">2. huius.</note>
            ſcribatur Q T R, erit is ipſi A F, parallelus, & </s>
            <s xml:id="echoid-s2464" xml:space="preserve">eo minor. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">In hoc ergo paral-
              <lb/>
            lelo Q T R, dico eſſe polos omnium circulorum parallelum G B H D, tan-
              <lb/>
              <note position="left" xlink:label="note-074-09" xlink:href="note-074-09a" xml:space="preserve">20. 1. huius.</note>
            gentium. </s>
            <s xml:id="echoid-s2466" xml:space="preserve">Per polum enim I, & </s>
            <s xml:id="echoid-s2467" xml:space="preserve">puncta contactuum deſcribantur circuli maxi-
              <lb/>
            mi M I S, N I T, O I V; </s>
            <s xml:id="echoid-s2468" xml:space="preserve">qui tranſibunt quoque per polos tangentium. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">Quia
              <lb/>
              <note position="left" xlink:label="note-074-10" xlink:href="note-074-10a" xml:space="preserve">5. huius.
                <lb/>
              28. tertij.</note>
            vero arcus H I, M I, N I, O I, G I, æquales ſunt, quòd ex definitione poli,
              <lb/>
            rectæ illis arcubus ſubtenſæ æquales ſint, eademq́ue ratione & </s>
            <s xml:id="echoid-s2470" xml:space="preserve">arcus I Q, I S,
              <lb/>
            I T, I V, I R, æquales ſunt;</s>
            <s xml:id="echoid-s2471" xml:space="preserve">erunt toti arcus H Q, M S, N T, O V, G </s>
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