Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Page concordance

< >
Scan Original
81 69
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
91 79
92 80
93 81
94 82
95 83
96 84
97 85
98 86
99 87
100 88
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109
110
< >
page |< < (14) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div53" type="section" level="1" n="34">
          <p>
            <s xml:id="echoid-s433" xml:space="preserve">
              <pb o="14" file="026" n="26" rhead=""/>
            culi B F D G, ad ipſius planum educta eſt perpendicularis E A, tranſibit hęc
              <lb/>
              <note position="left" xlink:label="note-026-01" xlink:href="note-026-01a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            per H, centrum ſphæræ, atq; </s>
            <s xml:id="echoid-s434" xml:space="preserve">adeo ex H, centro ſphæræ eadem H E, ducta
              <lb/>
            erit perpendicularis ad planum circuli B F D G. </s>
            <s xml:id="echoid-s435" xml:space="preserve">Quocirca H E, vtrinq; </s>
            <s xml:id="echoid-s436" xml:space="preserve">edu-
              <lb/>
              <note position="left" xlink:label="note-026-02" xlink:href="note-026-02a" xml:space="preserve">8. huius.</note>
            cta cadetin polos eiuſdem circuli; </s>
            <s xml:id="echoid-s437" xml:space="preserve">ac proinde C, reliquus polus erit circuli
              <lb/>
            BFDG. </s>
            <s xml:id="echoid-s438" xml:space="preserve">Si igitur ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s439" xml:space="preserve">ab altero polorum eius, &</s>
            <s xml:id="echoid-s440" xml:space="preserve">c. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Quod
              <lb/>
            oſtendendum erat.</s>
            <s xml:id="echoid-s442" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div55" type="section" level="1" n="35">
          <head xml:id="echoid-head46" xml:space="preserve">THEOR. 9. PROPOS. 10.</head>
          <note position="left" xml:space="preserve">13.</note>
          <p>
            <s xml:id="echoid-s443" xml:space="preserve">SI ſit in ſphæra circulus, linea recta per eius po
              <lb/>
            los ducta, ad circulum recta eſt, tranſitq́ per cen-
              <lb/>
            trum circuli, & </s>
            <s xml:id="echoid-s444" xml:space="preserve">ſphæræ.</s>
            <s xml:id="echoid-s445" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s446" xml:space="preserve">IN ſphæra A B C D, ſit circulus B F D G, per cuius polos A, C, recta du
              <lb/>
            catur A C, occurrens plano circuli in E. </s>
            <s xml:id="echoid-s447" xml:space="preserve">Dico rectam A C, ad planum circu
              <lb/>
            li rectam eſſe, tranſireq́; </s>
            <s xml:id="echoid-s448" xml:space="preserve">per eius centrum, (hoc eſt, E, eſſe ipſius centrum)
              <lb/>
            nec non per centrũ ſphæræ. </s>
            <s xml:id="echoid-s449" xml:space="preserve">Ductis namq; </s>
            <s xml:id="echoid-s450" xml:space="preserve">per E, duabus rectis vtcunq; </s>
            <s xml:id="echoid-s451" xml:space="preserve">B D,
              <lb/>
            F G, quarum extrema cum polis A, C, iungantur rectis, vt in figura; </s>
            <s xml:id="echoid-s452" xml:space="preserve">erunt
              <lb/>
              <figure xlink:label="fig-026-01" xlink:href="fig-026-01a" number="19">
                <image file="026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/026-01"/>
              </figure>
            tam A B, A G, A F, A D, inter ſe, quàm C B,
              <lb/>
            C G, C F, C D, inter ſe æquales, ex defin. </s>
            <s xml:id="echoid-s453" xml:space="preserve">poli.
              <lb/>
            </s>
            <s xml:id="echoid-s454" xml:space="preserve">Igitur duo triangula A B C, A D C, duo late-
              <lb/>
            ra A B, A C, duobus lateribus A D, A C, & </s>
            <s xml:id="echoid-s455" xml:space="preserve">ba
              <lb/>
            ſim B C, baſi D C, æqualem habent. </s>
            <s xml:id="echoid-s456" xml:space="preserve">Quapro-
              <lb/>
            pter & </s>
            <s xml:id="echoid-s457" xml:space="preserve">angulos B A C, D A C, æquales habe-
              <lb/>
              <note position="left" xlink:label="note-026-04" xlink:href="note-026-04a" xml:space="preserve">8. primi.</note>
            bunt. </s>
            <s xml:id="echoid-s458" xml:space="preserve">Quoniam igitur duo triangula A B E,
              <lb/>
            A D E, duo latera A B, A E, duobus lateribus
              <lb/>
            A D, A E; </s>
            <s xml:id="echoid-s459" xml:space="preserve">æqualia habent, anguloſq́; </s>
            <s xml:id="echoid-s460" xml:space="preserve">ſub ip-
              <lb/>
            ſis contentos B A E, D A E, æquales, vt pro-
              <lb/>
            xime demonſtratum eſt, erunt & </s>
            <s xml:id="echoid-s461" xml:space="preserve">anguli A E B,
              <lb/>
              <note position="left" xlink:label="note-026-05" xlink:href="note-026-05a" xml:space="preserve">4. primi.</note>
            A E D, æquales, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">ob id recti. </s>
            <s xml:id="echoid-s463" xml:space="preserve">Non aliter de-
              <lb/>
            monſtrabimus, rectos eſſe angu los A E G, A E F. </s>
            <s xml:id="echoid-s464" xml:space="preserve">Recta igitur A E, duabus re-
              <lb/>
            ctis B D, F G, ad rectos inſiſtit angulos. </s>
            <s xml:id="echoid-s465" xml:space="preserve">Quare perpendicularis erit ad planũ
              <lb/>
            circuli B F D G, per rectas B D, F G, ductum. </s>
            <s xml:id="echoid-s466" xml:space="preserve">Quod eſt primo loco propoſi-
              <lb/>
              <note position="left" xlink:label="note-026-06" xlink:href="note-026-06a" xml:space="preserve">4. vndec.</note>
            tum. </s>
            <s xml:id="echoid-s467" xml:space="preserve">Quoniam igitur ex A, polo circuli B F D G, ad eius planum perpendi-
              <lb/>
            cularis eſt ducta A E, cadet A E, in centrum ipſius. </s>
            <s xml:id="echoid-s468" xml:space="preserve">Eſt ergo E, centrum cir-
              <lb/>
              <note position="left" xlink:label="note-026-07" xlink:href="note-026-07a" xml:space="preserve">9. huius.</note>
            culi B F D G. </s>
            <s xml:id="echoid-s469" xml:space="preserve">Rurſus quia ex E, centro circuli B F D G, educta eſt ad eius pla
              <lb/>
            num perpendicularis E A, tranſibit hæc per centrum quoq; </s>
            <s xml:id="echoid-s470" xml:space="preserve">ſphæræ. </s>
            <s xml:id="echoid-s471" xml:space="preserve">Quare
              <lb/>
              <note position="left" xlink:label="note-026-08" xlink:href="note-026-08a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            recta A C, perpendicularis eſt ad planum circuli B F D G, tranſitq́ per eius
              <lb/>
            centrum, & </s>
            <s xml:id="echoid-s472" xml:space="preserve">ſphæræ. </s>
            <s xml:id="echoid-s473" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s474" xml:space="preserve">Si ſit igitur in ſphæra circulus,
              <lb/>
            linea recta per eius polos ducta, &</s>
            <s xml:id="echoid-s475" xml:space="preserve">c. </s>
            <s xml:id="echoid-s476" xml:space="preserve">Quod erat demonftrandum.</s>
            <s xml:id="echoid-s477" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div57" type="section" level="1" n="36">
          <head xml:id="echoid-head47" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s478" xml:space="preserve">_ADDVNTVR_ hoc loco alia duo theoremata huiuſmodi.</s>
            <s xml:id="echoid-s479" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum