Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[61.] DE ORDINE SPÆRARVM CÆLESTIVM.
Page: 100 (63)
[62.] COELVM MOVERI AB ORTV IN OCCASVM.
Page: 109 (72)
[63.] COMMENTARIVS.
Page: 110 (73)
[64.] COMMENTARIVS.
Page: 110 (73)
[65.] COELVM ESSE FIGVRÆ SPHÆRICÆ.
Page: 113 (76)
[66.] COMMENT ARIVS,
Page: 113 (76)
[67.] COMMENTARIVS.
Page: 114 (77)
[68.] DE FIGVRIS ISOPERIMETRIS. DEFINITIONES. I.
Page: 118 (81)
[69.] II.
Page: 118 (81)
[70.] III.
Page: 119 (82)
[71.] IIII.
Page: 119 (82)
[72.] V.
Page: 119 (82)
[73.] THEOR. 1. PROPOS. 1.
Page: 119 (82)
[74.] THEOR. 2. PROPOS. 2.
Page: 120 (83)
[75.] THEOR. 3. PROPOS. 3.
Page: 121 (84)
[76.] THEOR. 4. PROPOS. 4.
Page: 122 (85)
[77.] THEOR. 5. PROPOS. 5.
Page: 122 (85)
[78.] THEOR. 6. PROPOS. 6.
Page: 123 (86)
[79.] THEOR. 1. PROPOS. 7.
Page: 124 (87)
[80.] SCHOLIVM.
Page: 125 (88)
[81.] THEOR. 7. PROPOS. 8.
Page: 125 (88)
[82.] THEOR. 8. PROPOS. 9.
Page: 126 (89)
[83.] PROBL. 2. PROPOS. 10.
Page: 127 (90)
[84.] THEOR. 9. PROPOS. 11.
Page: 128 (91)
[85.] THEOR. 10. PROPOS. 52
Page: 130 (93)
[86.] SCHOLIVM.
Page: 132 (95)
[87.] THEOR. 11. PROPOS. 13.
Page: 134 (97)
[88.] COROLLARIVM.
Page: 135 (98)
[89.] THEOR. 12. PROPOS. 14.
Page: 135 (98)
[90.] THEOR. 13. PROPOS. 15.
Page: 136 (99)
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              <pb o="91" file="127" n="128" rhead="Ioan. de Sacro Boſco."/>
            tuor ſimul, poſterioribus quatuor ſimul æqualia: </s>
            <s xml:id="echoid-s4459" xml:space="preserve">additis ergo communibus
              <lb/>
            A B, C D, fient ſex alte@a A E, E B, B A, C F, F D, D C, ſimul æqualia ſex late-
              <lb/>
            ribus A N, N B B A, C O, O D, D C, ſimul; </s>
            <s xml:id="echoid-s4460" xml:space="preserve">ideoq́uetriangula A N B, C O D,
              <lb/>
            ſimul iſoperimetra erunt triangulis A E B, C F D, ſimul. </s>
            <s xml:id="echoid-s4461" xml:space="preserve">Dico iam, quod & </s>
            <s xml:id="echoid-s4462" xml:space="preserve">ſi-
              <lb/>
            milia inter ſe ſunt triangula A N B, C O D. </s>
            <s xml:id="echoid-s4463" xml:space="preserve">Nam quoniam eſt, ut A B, ad O D,
              <lb/>
            ita G K, ad K H, hoc eſt, ita G L, ad K M, hoc eſt, ita A N, ad C O, & </s>
            <s xml:id="echoid-s4464" xml:space="preserve">N B, ad
              <lb/>
              <note position="right" xlink:label="note-127-01" xlink:href="note-127-01a" xml:space="preserve">15. quinti</note>
            ad O D, erit permutando, vt A B, ad A N, ita C D, ad C O; </s>
            <s xml:id="echoid-s4465" xml:space="preserve">& </s>
            <s xml:id="echoid-s4466" xml:space="preserve">vt A N, ad N B,
              <lb/>
            ita C O; </s>
            <s xml:id="echoid-s4467" xml:space="preserve">ad O D. </s>
            <s xml:id="echoid-s4468" xml:space="preserve">Proportionalia ergo ſunt latera triangulorum A N B, COD;
              <lb/>
            </s>
            <s xml:id="echoid-s4469" xml:space="preserve">ac proinde æquiangula inter ſe erunt, & </s>
            <s xml:id="echoid-s4470" xml:space="preserve">idcireo ſimilia. </s>
            <s xml:id="echoid-s4471" xml:space="preserve">Quare datis duobus
              <lb/>
            triangulis Iſoſcelibus, quorum baſes inæquales exiſtant. </s>
            <s xml:id="echoid-s4472" xml:space="preserve">&</s>
            <s xml:id="echoid-s4473" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4474" xml:space="preserve">conſtituim us. </s>
            <s xml:id="echoid-s4475" xml:space="preserve">quod
              <lb/>
              <note position="right" xlink:label="note-127-02" xlink:href="note-127-02a" xml:space="preserve">5. ſexti.</note>
            faciendum erat.</s>
            <s xml:id="echoid-s4476" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div244" type="section" level="1" n="84">
          <head xml:id="echoid-head88" style="it" xml:space="preserve">THEOR. 9. PROPOS. 11.</head>
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              <emph style="sc">Dvo</emph>
            triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtitu-
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              <note position="right" xlink:label="note-127-03" xlink:href="note-127-03a" xml:space="preserve">Triangulæ
                <unsure/>
                <lb/>
              duo Iſoſce-
                <lb/>
              lia ſimilia
                <lb/>
              maiora sũt
                <lb/>
              duobus Iſo
                <unsure/>
                <lb/>
              ſcelibus nõ
                <lb/>
              ſimilibus,
                <lb/>
              quæ illis
                <lb/>
              ſint Iſope-
                <lb/>
              rimetta, ba-
                <lb/>
              ſesque ha-
                <lb/>
              beant eaſ-
                <lb/>
              dem.</note>
            ta, utraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, utriuſque ſi-
              <lb/>
            mul, quę habeant eaſdem baſes cum prioribus, ſintq; </s>
            <s xml:id="echoid-s4478" xml:space="preserve">disſimila quidem
              <lb/>
            inter ſe. </s>
            <s xml:id="echoid-s4479" xml:space="preserve">at iſoperimetra prioribus duobus, nec non quatuor latera inter ſe
              <lb/>
            habeant æqualia.</s>
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              <emph style="sc">Svper</emph>
            baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia in-
              <lb/>
            ter ſe non ſimilia A B C, C D E, ita vt quatuor latera A B, B C, C D, D E,
              <lb/>
            inter ſe ſint æqualia. </s>
            <s xml:id="echoid-s4482" xml:space="preserve">At-
              <lb/>
              <figure xlink:label="fig-127-01" xlink:href="fig-127-01a" number="29">
                <image file="127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/127-01"/>
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            que ſuper eiſdem baſibus
              <lb/>
            A C, C E, (per præceden-
              <lb/>
            tem propoſ.) </s>
            <s xml:id="echoid-s4483" xml:space="preserve">conſtituan-
              <lb/>
            tur alia duo triãgula Iſo-
              <lb/>
            ſcelia A F C, C G E; </s>
            <s xml:id="echoid-s4484" xml:space="preserve">ſimi-
              <lb/>
            lia inter ſe, & </s>
            <s xml:id="echoid-s4485" xml:space="preserve">iſoperime-
              <lb/>
            tra ſimul prioribus trian-
              <lb/>
            gulis ſimul. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Dico duo triã
              <lb/>
            gula A F C, C G E, ſimul
              <lb/>
            maiora eſſe duobus trian
              <lb/>
            gulis A B C, C D E, ſi-
              <lb/>
            mul. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">Ponantur enim A C,
              <lb/>
            C E, ſecundum lineam re
              <lb/>
            ctam vnam; </s>
            <s xml:id="echoid-s4488" xml:space="preserve">ſitq́; </s>
            <s xml:id="echoid-s4489" xml:space="preserve">A C, ba-
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            ſis maior baſe C E. </s>
            <s xml:id="echoid-s4490" xml:space="preserve">Dein-
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            de ex F, per B, ducatur
              <lb/>
            recta F B K, ſecans rectam
              <lb/>
            A C, in puncto K; </s>
            <s xml:id="echoid-s4491" xml:space="preserve">Item ex
              <lb/>
            D, per G, punctum duca
              <lb/>
            tur recta D C H, ſecans rectam C E, in H. </s>
            <s xml:id="echoid-s4492" xml:space="preserve">Et quia latera A F, F B, triangu-
              <lb/>
            li A F B, æqualia ſunt lateribus C F, F B, trianguli C F B, & </s>
            <s xml:id="echoid-s4493" xml:space="preserve">baſis A B, baſi
              <lb/>
            B C, æqualis, erit angulus A F B, angulo C F B, æqualis. </s>
            <s xml:id="echoid-s4494" xml:space="preserve">ſurſus quia late-
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            @a A F, F K, trianguli A F K, æqualia ſunt lateribus C F, F K, trianguli,
              <lb/>
              <note position="right" xlink:label="note-127-04" xlink:href="note-127-04a" xml:space="preserve">8. primi.</note>
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