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 |< < (95) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div296" type="section" level="1" n="136">
          <p>
            <s xml:id="echoid-s3630" xml:space="preserve">
              <pb o="95" file="107" n="107" rhead=""/>
            H,I. </s>
            <s xml:id="echoid-s3631" xml:space="preserve">Dico arcus GH, GI, æquales eſſe. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Quoniam enim arcus GC, GF, æqua-
              <lb/>
            les ponuntur, erunt paralleli CD, EF, æquales. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">arcus GK, GL,
              <lb/>
              <note position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">17. 2. huius</note>
            æquales erunt. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">Quare rectæ ductæ CK, FL, æquales erunt; </s>
            <s xml:id="echoid-s3636" xml:space="preserve">ac proinde in cir-
              <lb/>
              <note position="right" xlink:label="note-107-02" xlink:href="note-107-02a" xml:space="preserve">18. 2. huius</note>
            culis æqualibus CD, EF, arcus æquales auferent CK, FL; </s>
            <s xml:id="echoid-s3637" xml:space="preserve">& </s>
            <s xml:id="echoid-s3638" xml:space="preserve">idcirco inter
              <lb/>
              <note position="right" xlink:label="note-107-03" xlink:href="note-107-03a" xml:space="preserve">3. huius.</note>
            ſe ſimiles erunt arcus Ck, FL: </s>
            <s xml:id="echoid-s3639" xml:space="preserve">Eſt autem arcus GH, arcui CK, & </s>
            <s xml:id="echoid-s3640" xml:space="preserve">arcus
              <lb/>
              <note position="right" xlink:label="note-107-04" xlink:href="note-107-04a" xml:space="preserve">28 tertij.</note>
            GI, arcui FL, ſimilis. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3642" xml:space="preserve">arcus GH, GI, ſimiles inter ſe erunt, ac
              <lb/>
              <note position="right" xlink:label="note-107-05" xlink:href="note-107-05a" xml:space="preserve">10. vel. 13.</note>
            proinde, cum ſint eiuſdem circuli, æquales interſe. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">Siigitur in ſphæra ma-
              <lb/>
              <note position="right" xlink:label="note-107-06" xlink:href="note-107-06a" xml:space="preserve">2. huius.</note>
            ximus circulus, &</s>
            <s xml:id="echoid-s3644" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s3646" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div298" type="section" level="1" n="137">
          <head xml:id="echoid-head151" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3647" xml:space="preserve">_HINC_ etiam conſtat, ijsdem poſitis, omnes arcus maximorum circuloruminter
              <lb/>
            parallelos interceptos inter ſe æquales eſſe, quales ſunt _CH, HE, KG, GL, DI,_
              <lb/>
            _IF._ </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Cum enim arcus _
              <emph style="sc">G</emph>
            C, GH,_ arcubus _
              <emph style="sc">G</emph>
            F,
              <emph style="sc">GI</emph>
            ,_ æquales ſint, erunt & </s>
            <s xml:id="echoid-s3649" xml:space="preserve">rectæ _CH_,
              <lb/>
              <note position="right" xlink:label="note-107-07" xlink:href="note-107-07a" xml:space="preserve">3. huius.</note>
            _FI,_ æquales; </s>
            <s xml:id="echoid-s3650" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s3651" xml:space="preserve">arcus _CH, FI,_ æquales erunt: </s>
            <s xml:id="echoid-s3652" xml:space="preserve">Sunt autem arcui _CH_,
              <lb/>
              <note position="right" xlink:label="note-107-08" xlink:href="note-107-08a" xml:space="preserve">28. tertij.</note>
            arcus _
              <emph style="sc">Kg</emph>
            , DI,_ & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">arcui _FI_, arcus _LG, EH,_ æquales. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Igitur omnes illi ſex ars
              <lb/>
              <note position="right" xlink:label="note-107-09" xlink:href="note-107-09a" xml:space="preserve">10. vel 13.</note>
            cus æquales erunt.</s>
            <s xml:id="echoid-s3655" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">2. huius.</note>
        </div>
        <div xml:id="echoid-div300" type="section" level="1" n="138">
          <head xml:id="echoid-head152" xml:space="preserve">THEOREMA 14. PROPOS. 14.</head>
          <note position="right" xml:space="preserve">16.</note>
          <p>
            <s xml:id="echoid-s3656" xml:space="preserve">SI in ſphæra maximus circulus aliquem circu-
              <lb/>
            lumtangat, alius autem maximus circulus obli-
              <lb/>
            quus ad parallelos tangat circulos maiores illis,
              <lb/>
            quos tangebat maximus circulus primo poſitus:
              <lb/>
            </s>
            <s xml:id="echoid-s3657" xml:space="preserve">inæquales intercipient circunferẽtias parallelorũ
              <lb/>
            circulorum, quarum propiores vtriuis polorum
              <lb/>
            maiores erunt, quàm vt ſimiles ſint remotioribus.</s>
            <s xml:id="echoid-s3658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3659" xml:space="preserve">IN ſphæra maximus circulus AB, tangat circulum AC; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">& </s>
            <s xml:id="echoid-s3661" xml:space="preserve">alius maximus
              <lb/>
            DE, tãgat alium maiorẽ DF, ſecet-
              <lb/>
              <figure xlink:label="fig-107-01" xlink:href="fig-107-01a" number="111">
                <image file="107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/107-01"/>
              </figure>
            q́ue duos parallelos quoſcũq; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">GH,
              <lb/>
            BI, in k, E. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">Dico arcus k H, EI, in-
              <lb/>
            æquales eſſe, maioremque eſſe k H,
              <lb/>
            polo conſpicuo propiorem, quàm
              <lb/>
            vt ſimilis ſit arcui EI, remotiori:
              <lb/>
            </s>
            <s xml:id="echoid-s3664" xml:space="preserve">vel ipſum EB, polo occulto pro-
              <lb/>
            piorẽ eſſe maiorem, quam vt arcui
              <lb/>
            KG, remotiori ſimilis ſit. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">Per pun-
              <lb/>
            cta enim E, K, deſcribantur maximi
              <lb/>
              <note position="right" xlink:label="note-107-12" xlink:href="note-107-12a" xml:space="preserve">15. 2. huius.</note>
            circuli LE, CN, tangentes circu-
              <lb/>
            lum AC, ita vt ſemicirculià C, per
              <lb/>
            N, & </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ab A, per B, procedentes non
              <lb/>
            conueniant: </s>
            <s xml:id="echoid-s3667" xml:space="preserve">item ſemicirculi ab L,
              <lb/>
            per E, & </s>
            <s xml:id="echoid-s3668" xml:space="preserve">ab A, per I, tendentes non
              <lb/>
            coeant. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">Erunt igitur arcus MH,
              <lb/>
              <note position="right" xlink:label="note-107-13" xlink:href="note-107-13a" xml:space="preserve">13. 2. huius.</note>
            EI, ſimiles. </s>
            <s xml:id="echoid-s3670" xml:space="preserve">Quare k H, maior eſt, quàm vt arcui EI, ſimilis ſit. </s>
            <s xml:id="echoid-s3671" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum