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

Page concordance

< >
Scan Original
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
41 29
42
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
< >
page |< < (20) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div79" type="section" level="1" n="49">
          <pb o="20" file="032" n="32" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s707" xml:space="preserve">_IN_ ſphæra tranſeat maximus circulus
              <lb/>
              <figure xlink:label="fig-032-01" xlink:href="fig-032-01a" number="27">
                <image file="032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-01"/>
              </figure>
            _A B C D,_ per _A, C,_ polos circuli maximi _B D._
              <lb/>
            </s>
            <s xml:id="echoid-s708" xml:space="preserve">_Dico_ & </s>
            <s xml:id="echoid-s709" xml:space="preserve">maximum circulum _B D,_ per polos ma-
              <lb/>
            ximi circuli _A B C D,_ tranſire. </s>
            <s xml:id="echoid-s710" xml:space="preserve">Quoniam enim
              <lb/>
            circulus maximus _A B C D,_ circulum _B D,_ ſe-
              <lb/>
              <note position="left" xlink:label="note-032-01" xlink:href="note-032-01a" xml:space="preserve">15. huius.</note>
            cat per polos, ſecabit ipſum ad angulos rectos.
              <lb/>
            </s>
            <s xml:id="echoid-s711" xml:space="preserve">Quare vicißim maximus circulus _B D,_ circu-
              <lb/>
            lum _A B C D,_ ad angulos rectos ſccabit; </s>
            <s xml:id="echoid-s712" xml:space="preserve">at-
              <lb/>
            que adeo per ipſius polos eum ſecabit. </s>
            <s xml:id="echoid-s713" xml:space="preserve">Quod eſt
              <lb/>
              <note position="left" xlink:label="note-032-02" xlink:href="note-032-02a" xml:space="preserve">13. huius.</note>
            pr opoſitum.</s>
            <s xml:id="echoid-s714" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div82" type="section" level="1" n="50">
          <head xml:id="echoid-head61" xml:space="preserve">II.</head>
          <note position="left" xml:space="preserve">22.</note>
          <p>
            <s xml:id="echoid-s715" xml:space="preserve">SI in ſphæra circulus circulum per polos ſecet, circulus maxi-
              <lb/>
            mus eſt, & </s>
            <s xml:id="echoid-s716" xml:space="preserve">bifariam eum ſecat, & </s>
            <s xml:id="echoid-s717" xml:space="preserve">ad angulos rectos.</s>
            <s xml:id="echoid-s718" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s719" xml:space="preserve">_IN_ ſphæra circulus _A B C D,_ ſecet circu-
              <lb/>
              <figure xlink:label="fig-032-02" xlink:href="fig-032-02a" number="28">
                <image file="032-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-02"/>
              </figure>
            lum _B D,_ per polos _A, C._ </s>
            <s xml:id="echoid-s720" xml:space="preserve">Dico ipſum eſſe circu-
              <lb/>
            culum maximum, ſecareq́; </s>
            <s xml:id="echoid-s721" xml:space="preserve">circulum _B D,_ bifa-
              <lb/>
            riam, & </s>
            <s xml:id="echoid-s722" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s723" xml:space="preserve">Coniungat enim re-
              <lb/>
            cta _A C,_ polos _A, C,_ quæ neceſſario in plano
              <lb/>
            circuli _A B C D,_ erit, quod circunferentia eius
              <lb/>
            per eoſdem polos _A, C,_ ponatur tranſire. </s>
            <s xml:id="echoid-s724" xml:space="preserve">Quo-
              <lb/>
            niam vero recta _A C,_ per _A, C,_ polos circuli
              <lb/>
              <note position="left" xlink:label="note-032-04" xlink:href="note-032-04a" xml:space="preserve">10. huius.</note>
            _B D,_ ducta tranſit per centrum ſphæræ, tranſi-
              <lb/>
            bit quoque cir culus _A B C D,_ (cum per rectã
              <lb/>
            _A C,_ ducatur) per centrũ ſphæræ; </s>
            <s xml:id="echoid-s725" xml:space="preserve">atque adeo
              <lb/>
              <note position="left" xlink:label="note-032-05" xlink:href="note-032-05a" xml:space="preserve">6. huius.</note>
            maximus erit. </s>
            <s xml:id="echoid-s726" xml:space="preserve">Quare cum per _A, C,_ polos cir
              <lb/>
              <note position="left" xlink:label="note-032-06" xlink:href="note-032-06a" xml:space="preserve">15. huius.</note>
            culi _B D,_ ponatur tranſire, ſecabit eum bifariam, & </s>
            <s xml:id="echoid-s727" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s729" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div84" type="section" level="1" n="51">
          <head xml:id="echoid-head62" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s730" xml:space="preserve">SI in ſphæra circulus circulum bifariam, & </s>
            <s xml:id="echoid-s731" xml:space="preserve">ad angulos rectos
              <lb/>
              <note position="left" xlink:label="note-032-07" xlink:href="note-032-07a" xml:space="preserve">23.</note>
            ſecet, circulus maximus eſt, & </s>
            <s xml:id="echoid-s732" xml:space="preserve">per polos eum ſecat.</s>
            <s xml:id="echoid-s733" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s734" xml:space="preserve">_IN_ſphæra circulus _A B C D,_ ſecet circulum
              <lb/>
              <figure xlink:label="fig-032-03" xlink:href="fig-032-03a" number="29">
                <image file="032-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-03"/>
              </figure>
            _B D,_ bifariam, & </s>
            <s xml:id="echoid-s735" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s736" xml:space="preserve">_Dico_ ipſum
              <lb/>
            eſſe circulum maximum, tranſireq́; </s>
            <s xml:id="echoid-s737" xml:space="preserve">per polos cir-
              <lb/>
            culi _B D._ </s>
            <s xml:id="echoid-s738" xml:space="preserve">Sit recta _BD;_ </s>
            <s xml:id="echoid-s739" xml:space="preserve">communis circu lorum ſe-
              <lb/>
            etio. </s>
            <s xml:id="echoid-s740" xml:space="preserve">Quo niam igitur circulus _A B C D,_ circu-
              <lb/>
            lum _B D,_ ſecat bifariam, erit recta _B D,_ nempe
              <lb/>
            communis ſectio circulorũ, diameter circuli B D,
              <lb/>
            atque adeo diuiſa recta _B D,_ bifari am in E: </s>
            <s xml:id="echoid-s741" xml:space="preserve">erit
              <lb/>
            E, eiuſdem circuli centrum. </s>
            <s xml:id="echoid-s742" xml:space="preserve">Ducatur in plano cir
              <lb/>
            culi _A B C D,_ recta E A, perpendicularis ad re
              <lb/>
            etam _B D._ </s>
            <s xml:id="echoid-s743" xml:space="preserve">Et quoniam circulus _A B C D,_ </s>
          </p>
        </div>
      </text>
    </echo>
Impressum