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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        <div xml:id="echoid-div242" type="section" level="1" n="83">
          <head xml:id="echoid-head87" style="it" xml:space="preserve">PROBL. 2. PROPOS. 10.</head>
          <note position="left" xml:space="preserve">Qua arte
            <lb/>
          conſtituan
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          tur duo
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          triangula
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          Iſoſcelia ſi
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          milia qui-
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          dem inter
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          ſe, Iſoperi-
            <lb/>
          metra ue-
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          @o alijs duo
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          bus Iſoſce-
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          libus.</note>
          <p style="it">
            <s xml:id="echoid-s4429" xml:space="preserve">
              <emph style="sc">Datis</emph>
            duobus triangulis Iſoſcelibus, quorum baſes inæquales e-
              <lb/>
            xiſtant, duoque lateraunius æqualia ſint duobus lateribus alterius; </s>
            <s xml:id="echoid-s4430" xml:space="preserve">Super
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            eiſdem baſibus duo alia triangula iſoſcelia iuter ſe quidem ſimilia, priori-
              <lb/>
            bus uero Iſoperimetra, conſtituere.</s>
            <s xml:id="echoid-s4431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4432" xml:space="preserve">
              <emph style="sc">Sint</emph>
            ſuper baſes inæquales AB, CD, duo triangula Iſoſcelia AEB, C F D,
              <lb/>
            ſintq́. </s>
            <s xml:id="echoid-s4433" xml:space="preserve">quatuor lineæ A E, E B, C F, F D, inter ſe æquales; </s>
            <s xml:id="echoid-s4434" xml:space="preserve">maior autem ſit baſis
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            A B, baſe C D. </s>
            <s xml:id="echoid-s4435" xml:space="preserve">quibus poſitis, erit angulus E, maior angulo F, ideoque trian-
              <lb/>
              <note position="left" xlink:label="note-126-02" xlink:href="note-126-02a" xml:space="preserve">25. primi.</note>
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            gula nõ ſi
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            milia, cũ
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            nec æqui
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            angula. </s>
            <s xml:id="echoid-s4436" xml:space="preserve">O
              <lb/>
            porteat iã
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            ſuꝑ baſes
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            eaſdẽ A B,
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            C D, cõſti
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            tuere alia
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            duo trian
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            gula iſo-
              <lb/>
            ſcelia iter
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            fe quidem ſimilia, iſoperimetra uero ſimul ſumpta prioribus triangulis ſimul
              <lb/>
            ſumptis. </s>
            <s xml:id="echoid-s4437" xml:space="preserve">Ponatur recta G H, æqualis quatuor rectis A E, E B, C F, F D, diuidua
              <lb/>
            turq́ue in puncto K, ut eſſet rectacompoſita ex A B, & </s>
            <s xml:id="echoid-s4438" xml:space="preserve">C D, diuiſa in puncto B,
              <lb/>
              <note position="left" xlink:label="note-126-03" xlink:href="note-126-03a" xml:space="preserve">10. ſexti.</note>
            hoc eſt, ſit ea proportio G L, ad K H, quę eſt A B, ad C D. </s>
            <s xml:id="echoid-s4439" xml:space="preserve">Et quia maior eſt re-
              <lb/>
            cta A B, quàm recta C D, maior quoque erit recta G K, quàm recta K H, cum
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            vtrobique ſit proportio maioris inæqualitatis. </s>
            <s xml:id="echoid-s4440" xml:space="preserve">Diuidatur utraque G K, K H,
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            bifariam in punctis L, & </s>
            <s xml:id="echoid-s4441" xml:space="preserve">M. </s>
            <s xml:id="echoid-s4442" xml:space="preserve">Itaque cum ſit vt G K, ad K H, ita A B, ad C D,
              <lb/>
            erit componendo, vt G H, ad K H, ita A B, C D, ſimul ad C D: </s>
            <s xml:id="echoid-s4443" xml:space="preserve">Eſt autem
              <lb/>
            G H, maior, quàm A B, C D, ſimul, quòd & </s>
            <s xml:id="echoid-s4444" xml:space="preserve">quatuor rectæ A E, E B, C F.
              <lb/>
            </s>
            <s xml:id="echoid-s4445" xml:space="preserve">F D, quæ æquales ſunt rectæ G H, maiores ſint, quàm A B, C D. </s>
            <s xml:id="echoid-s4446" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4447" xml:space="preserve">K H,
              <lb/>
              <note position="left" xlink:label="note-126-04" xlink:href="note-126-04a" xml:space="preserve">29. primi.</note>
            maior erit quàm C D: </s>
            <s xml:id="echoid-s4448" xml:space="preserve">Eademque ratione maior erit G K, quàm A B. </s>
            <s xml:id="echoid-s4449" xml:space="preserve">Quo-
              <lb/>
              <note position="left" xlink:label="note-126-05" xlink:href="note-126-05a" xml:space="preserve">14. quinti.</note>
            niam igitur trium rectarum A B, G L, L K, duæ reliqua ſunt maiores omni-
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            fariam ſumptæ; </s>
            <s xml:id="echoid-s4450" xml:space="preserve">(Duæ enim G L, L K, maiores ſunt, quàm A B, quod tota
              <lb/>
            G K, maior ſit, quàm A B, ut modo fuit oſtenſum; </s>
            <s xml:id="echoid-s4451" xml:space="preserve">Manifeſtum autem, eſt,
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            A B, G L, maiores eſſe reliqua L K; </s>
            <s xml:id="echoid-s4452" xml:space="preserve">Itemq́ue A B, L K, reliqua G L, eſſe ma-
              <lb/>
            iores, propterea quòd G K, diuiſa eſt bifariam in puncto L. </s>
            <s xml:id="echoid-s4453" xml:space="preserve">Idem quoque di-
              <lb/>
            ces de tribus rectis C D, K M, M H.) </s>
            <s xml:id="echoid-s4454" xml:space="preserve">conſtituatur ex tribus rectis AB, GL,
              <lb/>
              <note position="left" xlink:label="note-126-06" xlink:href="note-126-06a" xml:space="preserve">22. primi.</note>
            L K, triangulum A N B, quod erit Iſoſceles, cadetq́ue punctum N, extra trian-
              <lb/>
            gulum A E B, cum A E, E B, ſimul dimidium conſtituant rectæ G H; </s>
            <s xml:id="echoid-s4455" xml:space="preserve">at vero,
              <lb/>
            A N, N B, ſimul maius efficiant, quàm dimidium rectæ G H. </s>
            <s xml:id="echoid-s4456" xml:space="preserve">Rurſus ex tri-
              <lb/>
            bus rectis C D, K M, M H, conſtituatur quoque triangulum C O D, quod
              <lb/>
            Iſoſceles erit, cadetq́ue punctum O, intra triangulum C F D, eo quòd CF,
              <lb/>
            FD, ſimul æquales ſint dimidio rectæ G H; </s>
            <s xml:id="echoid-s4457" xml:space="preserve">at C O, O D, ſimul minores ſint
              <lb/>
            dimidio rectæ GH. </s>
            <s xml:id="echoid-s4458" xml:space="preserve">Et quoniam quatuor latera A E, E B, C F, F D, ſimul
              <lb/>
            Item A N, N B, C O, O D, ſimul ęqualia ſunt rectæ G H, erunt priora </s>
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