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

Page concordance

< >
Scan Original
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 68
< >
page |< < (40) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div164" type="section" level="1" n="87">
          <pb o="40" file="052" n="52" rhead=""/>
          <p>
            <s xml:id="echoid-s1484" xml:space="preserve">IN diametris A C, D F, circulorum æqualium A B C, D E F, inſiſtant
              <lb/>
            ipſis circulis ad angulos rectos ſegmenta circulorũ æqualia A G C, D H F:
              <lb/>
            </s>
            <s xml:id="echoid-s1485" xml:space="preserve">ſumanturq́ æquales arcus A G, D H, ita vt puncta G, H, ſecent ſegmenta
              <lb/>
            A G C, D H F, non bifariam. </s>
            <s xml:id="echoid-s1486" xml:space="preserve">Ex G, H, denique in circunferentias circulo-
              <lb/>
            rum A B C, D E F, cadant rectæ æquales G B, H E. </s>
            <s xml:id="echoid-s1487" xml:space="preserve">Dico circunferentias
              <lb/>
            A B, D E, eſſe æquales. </s>
            <s xml:id="echoid-s1488" xml:space="preserve">Demittantur ex G, H, rectæ G I, H K, ad plana cir-
              <lb/>
            culorum A B C, D E F, perpendiculares, quæ in communes ſectiones A C,
              <lb/>
              <note position="left" xlink:label="note-052-01" xlink:href="note-052-01a" xml:space="preserve">11. vndec.</note>
            D F, cadent in puncta I, K. </s>
            <s xml:id="echoid-s1489" xml:space="preserve">Sumptis quoque L, M, centris circulorũ A B C,
              <lb/>
              <note position="left" xlink:label="note-052-02" xlink:href="note-052-02a" xml:space="preserve">33. vndec.</note>
            D E F, ducantur rectæ L B, B I, A G; </s>
            <s xml:id="echoid-s1490" xml:space="preserve">M E, E K, D H: </s>
            <s xml:id="echoid-s1491" xml:space="preserve">cadantq́; </s>
            <s xml:id="echoid-s1492" xml:space="preserve">primum pun
              <lb/>
            cta I, K, in ſemidiametros A L, D M. </s>
            <s xml:id="echoid-s1493" xml:space="preserve">Quoniam igitur arcus A G C, D H F,
              <lb/>
            æquales ſunt, nec non & </s>
            <s xml:id="echoid-s1494" xml:space="preserve">arcus A G, D H; </s>
            <s xml:id="echoid-s1495" xml:space="preserve">æquales quoque erunt arcus, C G,
              <lb/>
            F H; </s>
            <s xml:id="echoid-s1496" xml:space="preserve">ac propterea anguli G A C, H D F, illis inſiſtentes æquales. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">Sunt autem
              <lb/>
              <note position="left" xlink:label="note-052-03" xlink:href="note-052-03a" xml:space="preserve">27. tertij.</note>
            & </s>
            <s xml:id="echoid-s1498" xml:space="preserve">anguli A I G, D K H, æquales, quòd recti ſint ex defin. </s>
            <s xml:id="echoid-s1499" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Ita-
              <lb/>
            que duo triangula A I G, D K H, habent duos angulos G A I, A I G, duo-
              <lb/>
              <figure xlink:label="fig-052-01" xlink:href="fig-052-01a" number="58">
                <image file="052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/052-01"/>
              </figure>
            bus angulis H D K,
              <lb/>
            D K H, æquales. </s>
            <s xml:id="echoid-s1504" xml:space="preserve">Ha-
              <lb/>
            bent autem & </s>
            <s xml:id="echoid-s1505" xml:space="preserve">latus
              <lb/>
            A G, lateri D H, ęqua
              <lb/>
              <note position="left" xlink:label="note-052-04" xlink:href="note-052-04a" xml:space="preserve">29. tertij.</note>
            le, (ob æqualitatẽ ar
              <lb/>
            cuum A G, D H.)
              <lb/>
            </s>
            <s xml:id="echoid-s1506" xml:space="preserve">quod angulis æquali-
              <lb/>
            bus I, K, ſubtenditur. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">
              <lb/>
            Igitur & </s>
            <s xml:id="echoid-s1508" xml:space="preserve">latus A I, la
              <lb/>
              <note position="left" xlink:label="note-052-05" xlink:href="note-052-05a" xml:space="preserve">26. primi.</note>
            teri D K, & </s>
            <s xml:id="echoid-s1509" xml:space="preserve">latus G I,
              <lb/>
            lateri H K, æquale e-
              <lb/>
            rit. </s>
            <s xml:id="echoid-s1510" xml:space="preserve">Quoniam vero an
              <lb/>
            guli G I B, H K E, re
              <lb/>
            cti ſunt ex defin. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1512" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1513" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1514" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1515" xml:space="preserve">erunt quadrata ex G B, H E, quæ inter ſe æ-
              <lb/>
              <note position="left" xlink:label="note-052-06" xlink:href="note-052-06a" xml:space="preserve">47. primi.</note>
            qualia ſunt, ob æqualitatem rectarum G B, H E, quadratis ex G I, I B, & </s>
            <s xml:id="echoid-s1516" xml:space="preserve">ex
              <lb/>
            H K, K E, æqualia, ac {pro}pterea quadrata ex G I, I B, quadratis ex H K, K E,
              <lb/>
            æqualia erunt. </s>
            <s xml:id="echoid-s1517" xml:space="preserve">Ablatis ergo quadratis æqualibus rectarum æqualiũ G I, H K,
              <lb/>
            remanebunt quadrata rectarũ I B, K E, æqualia; </s>
            <s xml:id="echoid-s1518" xml:space="preserve">& </s>
            <s xml:id="echoid-s1519" xml:space="preserve">idcirco & </s>
            <s xml:id="echoid-s1520" xml:space="preserve">rectæ I B, K E,
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s1521" xml:space="preserve">Et quia A L, D M, ſemidiametri circulorum æqualiũ æquales ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s1522" xml:space="preserve">oſtenſæ autem quoque ſunt æquales A I, D K, erunt & </s>
            <s xml:id="echoid-s1523" xml:space="preserve">reliquæ I L, K M, æ-
              <lb/>
            quales. </s>
            <s xml:id="echoid-s1524" xml:space="preserve">Quare latera I L, L B, lateribus K M, M E, æqualia erunt: </s>
            <s xml:id="echoid-s1525" xml:space="preserve">ſunt au
              <lb/>
            tem & </s>
            <s xml:id="echoid-s1526" xml:space="preserve">baſes I B, K E, oſtenſæ æquales. </s>
            <s xml:id="echoid-s1527" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s1528" xml:space="preserve">anguli L, M, ad centra æqua
              <lb/>
              <note position="left" xlink:label="note-052-07" xlink:href="note-052-07a" xml:space="preserve">8. primi.</note>
            les erunt; </s>
            <s xml:id="echoid-s1529" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s1530" xml:space="preserve">arcus A B, D E, æquales erunt.</s>
            <s xml:id="echoid-s1531" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">26. tertij.</note>
          <p>
            <s xml:id="echoid-s1532" xml:space="preserve">CADANT deinde puncta I, K, in ſemidiametros L A, M D, produ-
              <lb/>
            ctas ad A, & </s>
            <s xml:id="echoid-s1533" xml:space="preserve">D: </s>
            <s xml:id="echoid-s1534" xml:space="preserve">quod quidem contingere poteſt, quando ſegmenta A G C,
              <lb/>
            D H F, ſemicirculo ſunt maiora; </s>
            <s xml:id="echoid-s1535" xml:space="preserve">fiatq́; </s>
            <s xml:id="echoid-s1536" xml:space="preserve">eadem conſtructio, quæ prius. </s>
            <s xml:id="echoid-s1537" xml:space="preserve">Oſten
              <lb/>
            demus, vt prius, angulos G A C, H D F, eſſe æquales; </s>
            <s xml:id="echoid-s1538" xml:space="preserve">ac propterea cum tam
              <lb/>
              <note position="left" xlink:label="note-052-09" xlink:href="note-052-09a" xml:space="preserve">27. tertij.</note>
            G A C, G A I, quàm H D F, H D K, duobus ſint rectis æquales, erũt & </s>
            <s xml:id="echoid-s1539" xml:space="preserve">G A I,
              <lb/>
              <note position="left" xlink:label="note-052-10" xlink:href="note-052-10a" xml:space="preserve">13. primi.</note>
            H D K, æquales. </s>
            <s xml:id="echoid-s1540" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s1541" xml:space="preserve">anguli I, K, æquales ſint, nempe recti, & </s>
            <s xml:id="echoid-s1542" xml:space="preserve">late
              <lb/>
            ra G A, H D, æqualia, ob æquales arcus A G, D H, erunt, vt prius, rectæ
              <lb/>
              <note position="left" xlink:label="note-052-11" xlink:href="note-052-11a" xml:space="preserve">29. tertij.</note>
            G I, I A, rectis H K, K D, æquales; </s>
            <s xml:id="echoid-s1543" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s1544" xml:space="preserve">totæ I L, K M, inter ſe
              <lb/>
              <note position="left" xlink:label="note-052-12" xlink:href="note-052-12a" xml:space="preserve">26. primi.</note>
            æquales erunt. </s>
            <s xml:id="echoid-s1545" xml:space="preserve">Igitur, vt prius, oſtendemus rectam I B, rectæ K E, & </s>
            <s xml:id="echoid-s1546" xml:space="preserve">angu-
              <lb/>
            lum L, angulo M, æqualem eſſe: </s>
            <s xml:id="echoid-s1547" xml:space="preserve">ac denique arcum A B, arcui D E.</s>
            <s xml:id="echoid-s1548" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">47. primi.</note>
          <note position="left" xml:space="preserve">8. primi.</note>
          <p>
            <s xml:id="echoid-s1549" xml:space="preserve">CADANT tertio perpendiculares ex G, H, demiſſæ in plana circulo-
              <lb/>
              <note position="left" xlink:label="note-052-15" xlink:href="note-052-15a" xml:space="preserve">26. tertij.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum