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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          <p>
            <s xml:id="echoid-s4266" xml:space="preserve">
              <pb o="86" file="122" n="123" rhead="Comment. in I. Cap. Sphæræ"/>
            turq́ue ab acu to angulo A, ad latus oppoſitum B C, recta A D, utcunque. </s>
            <s xml:id="echoid-s4267" xml:space="preserve">Di-
              <lb/>
            co maiore m eſſe proportionem rectæ B C, ad rectam C D, quàm anguli B A C,
              <lb/>
              <figure xlink:label="fig-122-01" xlink:href="fig-122-01a" number="23">
                <image file="122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-01"/>
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            ad angulum C A D. </s>
            <s xml:id="echoid-s4268" xml:space="preserve">Quoniam enim recta A D,
              <lb/>
            maior quidem eſt, quàm A C, minor uero, quã
              <lb/>
            A B, ſi centro A, interuallo autem A D, circu-
              <lb/>
            lus deſcribatur; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">ſecabit is rectam A C, protractã
              <lb/>
              <note position="left" xlink:label="note-122-01" xlink:href="note-122-01a" xml:space="preserve">19. primi.</note>
            infra punctum C, ut in E, at uero rectam A B, ſu
              <lb/>
            pra punctum B, ut in F. </s>
            <s xml:id="echoid-s4270" xml:space="preserve">Et quia maior eſt pro-
              <lb/>
            portio trianguli B A D, ad ſectorem F A D, quã
              <lb/>
            trianguli D A C, ad ſectorem D A E, (propterea
              <lb/>
            quòd ibi eſt proportio maioris inæqualitatis, hic
              <lb/>
            autem minoris inæqualitatis) erit quoque permu
              <unsure/>
              <lb/>
            tando maior proportio trianguli B A D, ad triã-
              <lb/>
              <note position="left" xlink:label="note-122-02" xlink:href="note-122-02a" xml:space="preserve">27. quinti.</note>
            gulum D A C, quàm ſectoris F A D, ad ſectorem
              <lb/>
            D A E. </s>
            <s xml:id="echoid-s4271" xml:space="preserve">Com ponendo igitur maior quoque erit proportio trianguli B A C, ad
              <lb/>
              <note position="left" xlink:label="note-122-03" xlink:href="note-122-03a" xml:space="preserve">28. quinti.</note>
            triangulum D A C, hoc eſt, rectæ B C, ad rectam C D, (habent enim trian-
              <lb/>
            gula B A C, D A C, eandem proportionem, quàm baſes B C, C D.) </s>
            <s xml:id="echoid-s4272" xml:space="preserve">quàm
              <lb/>
              <note position="left" xlink:label="note-122-04" xlink:href="note-122-04a" xml:space="preserve">2. ſexti.</note>
            ſectoris F A E, ad ſectorem D A E, hoc eſt, quàm anguli B A C, ad angulum
              <lb/>
            C A D; </s>
            <s xml:id="echoid-s4273" xml:space="preserve">quòd ex coroll. </s>
            <s xml:id="echoid-s4274" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4275" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4276" xml:space="preserve">33. </s>
            <s xml:id="echoid-s4277" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4278" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4279" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">eandem habeant proportio-
              <lb/>
            n em ſectores, quàm anguli. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">Quocirca in omni triangulo rectangulo, &</s>
            <s xml:id="echoid-s4282" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4283" xml:space="preserve">quod
              <lb/>
            demonſtrandum erat.</s>
            <s xml:id="echoid-s4284" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div230" type="section" level="1" n="78">
          <head xml:id="echoid-head82" style="it" xml:space="preserve">THEOR. 6. PROPOS. 6.</head>
          <note position="left" xml:space="preserve">Inter figu-
            <lb/>
          ras Iſoperi-
            <lb/>
          metras, quę
            <lb/>
          plures an-
            <lb/>
          gulos, ſeu
            <lb/>
          latera con-
            <lb/>
          @inet, illa
            <lb/>
          @aior eſt.</note>
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            <s xml:id="echoid-s4285" xml:space="preserve">
              <emph style="sc">Isoperimetrarvm</emph>
            figurarum regularium maior eſt il-
              <lb/>
            la, quæ plures continet angulos, plur areue latera.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4287" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ figuræ regulares iſoperimetræ A B C, D E F, habeatq́; </s>
            <s xml:id="echoid-s4288" xml:space="preserve">plura
              <lb/>
            latera, ſiue angulos figura A B C, quàm D E F. </s>
            <s xml:id="echoid-s4289" xml:space="preserve">Dico A B C, maiorem eſſe,
              <lb/>
              <figure xlink:label="fig-122-02" xlink:href="fig-122-02a" number="24">
                <image file="122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-02"/>
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            quàm D E F. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">Deſcribantur enim circa figuras circuli, à quorum centris G, H,
              <lb/>
            ducantur ad B C, E F, perpendiculares G I, H K, quæ diuident rectas B C,
              <lb/>
              <note position="left" xlink:label="note-122-06" xlink:href="note-122-06a" xml:space="preserve">@. tertij.</note>
            E F, bifariam. </s>
            <s xml:id="echoid-s4291" xml:space="preserve">Quo niam igitur figura A B C, plura habet latera, quàm D E F.
              <lb/>
            </s>
            <s xml:id="echoid-s4292" xml:space="preserve">f
              <unsure/>
            bi iſoperimetra, efficitur, ut latus B C, ſæpius repetitum metiatur </s>
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