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-s4347" xml:space="preserve">
              <pb o="88" file="124" n="125" rhead="Comment. in I. Cap. Sphæræ"/>
            tres lin eę AC, DF, FE, ita ſeſe
              <lb/>
              <figure xlink:label="fig-124-01" xlink:href="fig-124-01a" number="25">
                <image file="124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/124-01"/>
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            habe bũt, vt quælibet duæ ſint
              <lb/>
            reliq ua maiores. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">Si igitur ex
              <lb/>
            ipſis conficiatur triangulum
              <lb/>
            A G C, effectum erit, quod
              <lb/>
            proponitur. </s>
            <s xml:id="echoid-s4349" xml:space="preserve">Erunt enim late-
              <lb/>
              <note position="left" xlink:label="note-124-01" xlink:href="note-124-01a" xml:space="preserve">22. primi.</note>
            ra AG, GC, & </s>
            <s xml:id="echoid-s4350" xml:space="preserve">inter ſe ęqualia,
              <lb/>
            & </s>
            <s xml:id="echoid-s4351" xml:space="preserve">ſimul ſumpta æqualia late-
              <lb/>
            ribus AB, BC, ſimul ſumptis:
              <lb/>
            </s>
            <s xml:id="echoid-s4352" xml:space="preserve">addito igitur communi A C,
              <lb/>
            erunt triangula ABC, AGC,
              <lb/>
            iſoperimetra. </s>
            <s xml:id="echoid-s4353" xml:space="preserve">Propoſito igi-
              <lb/>
            tur triangulo, cuius duo latera ſint inæqualia, ſupra reliquum latus triangulũ,
              <lb/>
            &</s>
            <s xml:id="echoid-s4354" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4355" xml:space="preserve">d eſcripſimus. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s4357" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div234" type="section" level="1" n="80">
          <head xml:id="echoid-head84" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4358" xml:space="preserve">
              <emph style="sc">Cadet</emph>
            autem neceſſario punctum G, extra triangulum A B C: </s>
            <s xml:id="echoid-s4359" xml:space="preserve">Sinamque ca-
              <lb/>
              <note position="left" xlink:label="note-124-02" xlink:href="note-124-02a" xml:space="preserve">20. primi.</note>
            deret in latus A B, ut ad punctum H, eßet ducta recta H C, minor quàm H B, B C, ſi-
              <lb/>
            mul, & </s>
            <s xml:id="echoid-s4360" xml:space="preserve">ob id triangulum A H C, non eſſet iſoperimetrum triangulo A B C, c{ui}us con
              <lb/>
            trarium ex conſtructione eſt demonſtratum. </s>
            <s xml:id="echoid-s4361" xml:space="preserve">Mu
              <unsure/>
            lto minus cadet punctum G, intra trian.</s>
            <s xml:id="echoid-s4362" xml:space="preserve">
              <unsure/>
              <lb/>
            gu lum A B C. </s>
            <s xml:id="echoid-s4363" xml:space="preserve">Quare extra cadet, quod eſt propoſitum.</s>
            <s xml:id="echoid-s4364" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div236" type="section" level="1" n="81">
          <head xml:id="echoid-head85" style="it" xml:space="preserve">THEOR. 7. PROPOS. 8.</head>
          <p style="it">
            <s xml:id="echoid-s4365" xml:space="preserve">
              <emph style="sc">Dvorvm</emph>
            triangulorum iſoperimetrorum eandem habentium ba-
              <lb/>
              <note position="left" xlink:label="note-124-03" xlink:href="note-124-03a" xml:space="preserve">Iſoſeeles
                <lb/>
              triangulũ
                <lb/>
              maius eſt
                <lb/>
              triãgulo ſi
                <lb/>
              bi Iſoperi-
                <lb/>
              metro non
                <lb/>
              @ſoſcele.</note>
            ſim, quorum unius duo latera ſint æqualia, alterius uero inæqualia; </s>
            <s xml:id="echoid-s4366" xml:space="preserve">maius
              <lb/>
            erit i
              <unsure/>
            llud, cuius duo latera æqualia ſunt.</s>
            <s xml:id="echoid-s4367" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4368" xml:space="preserve">
              <emph style="sc">Estg</emph>
            triangulum A B C, cuius latus A B, maius ſit latere B C, conſti-
              <lb/>
            tuaturq́ue ſuper baſim A C, (per præcedentẽ
              <lb/>
              <figure xlink:label="fig-124-02" xlink:href="fig-124-02a" number="26">
                <image file="124-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/124-02"/>
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            propoſi.) </s>
            <s xml:id="echoid-s4369" xml:space="preserve">triangulo A B C, triangulum Iſo-
              <lb/>
            perimetrum A D C, habens latera A D, D C,
              <lb/>
            æqualia & </s>
            <s xml:id="echoid-s4370" xml:space="preserve">inter ſe, & </s>
            <s xml:id="echoid-s4371" xml:space="preserve">lateribus A B, B C, ſi-
              <lb/>
            mul ſumptis. </s>
            <s xml:id="echoid-s4372" xml:space="preserve">Dico triangulum A D C, maius
              <lb/>
            eſſe triangulo A B C. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">Producatur enim A D,
              <lb/>
            ad partes D, ſitq́ue D E, æqualis ipſi A D, ſiue
              <lb/>
              <note position="left" xlink:label="note-124-04" xlink:href="note-124-04a" xml:space="preserve">20. primi.</note>
            ipſi D C. </s>
            <s xml:id="echoid-s4374" xml:space="preserve">Ducantur quoque rectæ D B, B E.
              <lb/>
            </s>
            <s xml:id="echoid-s4375" xml:space="preserve">Quoniam igitur A B, B E, maiores ſunt, quã
              <lb/>
            A E, hoc eſt, quàm A D, D C, ſimul hoc eſt,
              <lb/>
            quàm A B, B C, ſimul; </s>
            <s xml:id="echoid-s4376" xml:space="preserve">ablata communi A B,
              <lb/>
            erit B E, maior quam BC. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Et quia latera E D,
              <lb/>
            D B, trianguli E D B, æqualia ſunt lateribus
              <lb/>
            C D, D B, trianguli C D B. </s>
            <s xml:id="echoid-s4378" xml:space="preserve">Cum ergo baſis
              <lb/>
            B E, baſe B C, maior ſit, erit angulus E D B,
              <lb/>
            maior angulo C D B. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">Quare angulus E D B,
              <lb/>
              <note position="left" xlink:label="note-124-05" xlink:href="note-124-05a" xml:space="preserve">25. primi.</note>
            maior eſt, quàm dimidium anguli E D C: </s>
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