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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            <s xml:id="echoid-s4529" xml:space="preserve">
              <pb o="93" file="129" n="130" rhead="Ioan. de Sacro Boſco."/>
            vna linea, deſcripto. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">& </s>
            <s xml:id="echoid-s4531" xml:space="preserve">quadrato ex K M, M H, tanquam ex una linea deſcri-
              <lb/>
            pto, hoc eſt, quadrato K H, vtriuſque ſimul. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">Ablato ergo communi quadrato
              <lb/>
            K H, erit quadratum ex F K, G H, tanquam ex una linea, deſcriptum maius
              <lb/>
            quadrato ex B K, D H, tanquam ex una linea, deſcripto; </s>
            <s xml:id="echoid-s4533" xml:space="preserve">ideòque maiores e-
              <lb/>
            runt rectæ linea F K, G H, ſimul rectis B K, D H, ſimnl: </s>
            <s xml:id="echoid-s4534" xml:space="preserve">Ac propterea, demptis
              <lb/>
            communibus B K, G H, erit F B, reliqua maior quàm reliqua D G. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">Eſt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">K C, maior quàm H C, eò quòd tota A C, cuius dimidium eſt K C, maior
              <lb/>
            ponitur, quam tota C E,
              <lb/>
              <figure xlink:label="fig-129-01" xlink:href="fig-129-01a" number="31">
                <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01"/>
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            cuius dimidium eſt H C.
              <lb/>
            </s>
            <s xml:id="echoid-s4537" xml:space="preserve">Qua propter rectangulũ
              <lb/>
            ſub F B, K C, contentum,
              <lb/>
            maius erit rectangulo
              <lb/>
            ſub D G, H C, contẽto. </s>
            <s xml:id="echoid-s4538" xml:space="preserve">
              <lb/>
            Et quoniam triangulum
              <lb/>
            F B C, dimidium eſt re,
              <lb/>
            ctanguli ſub F B, K C, con
              <lb/>
            tenti; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">(Nam ſi ſuper F B,
              <lb/>
            conſtituatur rectangu--
              <lb/>
            lum altitudinem habens
              <lb/>
            K C, ita ut triangulum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">rectangulum inter eaſ-
              <lb/>
            dem ſint parallelas; </s>
            <s xml:id="echoid-s4541" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">41. primi.</note>
            triangulum parallelo--
              <lb/>
            grammi dimidium. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">quod
              <lb/>
            quidem parallelogram-
              <lb/>
            mum idem eſt, quod re-
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            ctangulum ſub F B, K C,
              <lb/>
            contentum, ut conſtat.
              <lb/>
            </s>
            <s xml:id="echoid-s4543" xml:space="preserve">Triangulum uero D G C, dimidium eſt rectanguli contenti ſub, D G, H C; </s>
            <s xml:id="echoid-s4544" xml:space="preserve">(ſi
              <lb/>
            enim ſuper D G, conſtituatur rectangulum altitudinem habens H C, ita vt
              <lb/>
            triangulum, & </s>
            <s xml:id="echoid-s4545" xml:space="preserve">rectangulum inter eaſdem ſint parallelas; </s>
            <s xml:id="echoid-s4546" xml:space="preserve">erit triangulum pa-
              <lb/>
            rallelogrammi dimidium. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">quod quidem parallelogrammum idem eſt, quod
              <lb/>
              <note position="right" xlink:label="note-129-02" xlink:href="note-129-02a" xml:space="preserve">41. primi.</note>
            rectangulum ſub D H, H C, contentum, ut conſtat. </s>
            <s xml:id="echoid-s4548" xml:space="preserve">(erit quoque triangulum
              <lb/>
            FBC, maius triangulo D G C, ac propterea duplum trianguli F B C, nimirũ
              <lb/>
            rectilineum A F C B A, maius erit duplo trianguli D G C, ut pote rectilineo
              <lb/>
            erunt triangula A F C, C G E, utraque ſimul maiora triangulis A B C, C D E,
              <lb/>
            utriuſque ſimul. </s>
            <s xml:id="echoid-s4549" xml:space="preserve">Duo ergo triangula Iſoſcelia ſimilia ſuper inæqualibus baſi-
              <lb/>
            bus conſtituta, &</s>
            <s xml:id="echoid-s4550" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s4552" xml:space="preserve"/>
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          <head xml:id="echoid-head89" style="it" xml:space="preserve">THEOR. 10. PROPOS. 52</head>
          <note position="right" xml:space="preserve">Inter Iſope-
            <lb/>
          rimetras fi-
            <lb/>
          guras ęqua-
            <lb/>
          lia numero
            <lb/>
          habentes la
            <lb/>
          tera maxi-
            <lb/>
          ma & æqui
            <lb/>
          latera eſt,
            <lb/>
          & æquian-
            <lb/>
          gula.</note>
          <p style="it">
            <s xml:id="echoid-s4553" xml:space="preserve">ISOPERIMETR ARVM figur arum latera numero ęqualia ha-
              <lb/>
            bentium maxima & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">æqualiter eſt, & </s>
            <s xml:id="echoid-s4555" xml:space="preserve">æquiangula.</s>
            <s xml:id="echoid-s4556" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4557" xml:space="preserve">
              <emph style="sc">Esto</emph>
            figura quotcunq; </s>
            <s xml:id="echoid-s4558" xml:space="preserve">laterum ABCDEF, maxima inter omnes totidem
              <lb/>
            laterum ſibi iſoperimetras; </s>
            <s xml:id="echoid-s4559" xml:space="preserve">ita ut maior dari non poſſit. </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Dico eam eſſe æquila-
              <lb/>
            terã, & </s>
            <s xml:id="echoid-s4561" xml:space="preserve">æquiãgulã. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">Sit enim, ſi fieri poteſt, primũ nõ æquilatera, ſed ſint </s>
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