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

Page concordance

< >
Scan Original
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
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
< >
page |< < (25) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div103" type="section" level="1" n="59">
          <pb o="25" file="037" n="37" rhead=""/>
          <p>
            <s xml:id="echoid-s923" xml:space="preserve">IN ſphæra data ſumptis vtcunq́ue duobus punctis A, B, deſcribatur ex
              <lb/>
            A, polo, & </s>
            <s xml:id="echoid-s924" xml:space="preserve">interuallo A B, circulus B D, cuius diametro æqualis recta deſcri
              <lb/>
              <note position="right" xlink:label="note-037-01" xlink:href="note-037-01a" xml:space="preserve">18. huius.</note>
            batur F G: </s>
            <s xml:id="echoid-s925" xml:space="preserve">& </s>
            <s xml:id="echoid-s926" xml:space="preserve">fiat ſupra F G, triangulum E F G, habens vtruque reliquorum
              <lb/>
              <figure xlink:label="fig-037-01" xlink:href="fig-037-01a" number="35">
                <image file="037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/037-01"/>
              </figure>
              <note position="right" xlink:label="note-037-02" xlink:href="note-037-02a" xml:space="preserve">Schol 22.
                <lb/>
              primi.</note>
            laterum E F, E G, rectæ ducte
              <lb/>
              <note position="right" xlink:label="note-037-03" xlink:href="note-037-03a" xml:space="preserve">primi.</note>
            A B, æquale. </s>
            <s xml:id="echoid-s927" xml:space="preserve">Deinde ex F, G,
              <lb/>
            ad E F, E G, perpendiculares
              <lb/>
            educantur F H, G H, coeun-
              <lb/>
            tes in H;</s>
            <s xml:id="echoid-s928" xml:space="preserve">iungaturq́; </s>
            <s xml:id="echoid-s929" xml:space="preserve">recta E H.
              <lb/>
            </s>
            <s xml:id="echoid-s930" xml:space="preserve">Dico E H, æqualem eſſe dia-
              <lb/>
            metro datæ ſphæræ. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Ducta em̃
              <lb/>
            ſphæræ diametro A C, traijcia
              <lb/>
            tur per rectas A B, A C, pla-
              <lb/>
            num ſaciens in ſphæra circulũ
              <lb/>
              <note position="right" xlink:label="note-037-04" xlink:href="note-037-04a" xml:space="preserve">1. huius.</note>
            A B C D, qui maximus erit,
              <lb/>
              <note position="right" xlink:label="note-037-05" xlink:href="note-037-05a" xml:space="preserve">6. huius.</note>
            cum per diametrum ſphæræ,
              <lb/>
            atque adeo per centrum eiuſ-
              <lb/>
            dem ducatur. </s>
            <s xml:id="echoid-s932" xml:space="preserve">Quare idẽ per A, polũ circuli B D, ductus circulum B D, bifa-
              <lb/>
              <note position="right" xlink:label="note-037-06" xlink:href="note-037-06a" xml:space="preserve">15. huius.</note>
            riam ſecabit; </s>
            <s xml:id="echoid-s933" xml:space="preserve">ac propterea communis ſectio B D, diameter erit circuli B D.
              <lb/>
            </s>
            <s xml:id="echoid-s934" xml:space="preserve">Iunctis autem rectis A D, D C, erunt duo latera A B, B D, duobus lateribus
              <lb/>
            E F, F G, æqualia, nec non & </s>
            <s xml:id="echoid-s935" xml:space="preserve">baſes A D, E G, æquales. </s>
            <s xml:id="echoid-s936" xml:space="preserve">Eſt enium F G, diame-
              <lb/>
            tro B D, æqualis, ex conſtructione: </s>
            <s xml:id="echoid-s937" xml:space="preserve">& </s>
            <s xml:id="echoid-s938" xml:space="preserve">vtraque E F, E G, rectæ A B, vel A D. </s>
            <s xml:id="echoid-s939" xml:space="preserve">
              <lb/>
            Igitur & </s>
            <s xml:id="echoid-s940" xml:space="preserve">anguli A B D, E F G, æquales erunt. </s>
            <s xml:id="echoid-s941" xml:space="preserve">Eſt autem angulo A B D, an-
              <lb/>
              <note position="right" xlink:label="note-037-07" xlink:href="note-037-07a" xml:space="preserve">8. primi.</note>
            gulus A C D, æqualis: </s>
            <s xml:id="echoid-s942" xml:space="preserve">& </s>
            <s xml:id="echoid-s943" xml:space="preserve">angulo E F G, angulus E H G, vt in præcedenti
              <lb/>
              <note position="right" xlink:label="note-037-08" xlink:href="note-037-08a" xml:space="preserve">27. tertij.</note>
            propoſ. </s>
            <s xml:id="echoid-s944" xml:space="preserve">demonſtratum eſt. </s>
            <s xml:id="echoid-s945" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s946" xml:space="preserve">anguli A C D, E H G, æquales erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s947" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s948" xml:space="preserve">recti A D C, E G H, æquales, & </s>
            <s xml:id="echoid-s949" xml:space="preserve">latus A D, lateri E G, quod
              <lb/>
            vni æqualium angulorum obijcitur, æquale. </s>
            <s xml:id="echoid-s950" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s951" xml:space="preserve">recta E H, rectæ A C,
              <lb/>
              <note position="right" xlink:label="note-037-09" xlink:href="note-037-09a" xml:space="preserve">26. primi.</note>
            æqualis erit. </s>
            <s xml:id="echoid-s952" xml:space="preserve">Lineam igitur rectam E H, deſcripſimus æqualẽ diametro A C,
              <lb/>
            datæ ſphæræ. </s>
            <s xml:id="echoid-s953" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s954" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div105" type="section" level="1" n="60">
          <head xml:id="echoid-head71" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s955" xml:space="preserve">_ADDITVR_in alia verſione ſequens hoc Theorema.</s>
            <s xml:id="echoid-s956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s957" xml:space="preserve">LINEA recta à polo cuiuſuis circuli in ſphæra ad ſuperficiem
              <lb/>
              <note position="right" xlink:label="note-037-10" xlink:href="note-037-10a" xml:space="preserve">30.</note>
            ſphæræ ducta, quæ ſit æqualis lineæ rectæ ab eodem polo ad circun-
              <lb/>
            ferentiam circuli ductæ, in circuli circunferentiam cadit.</s>
            <s xml:id="echoid-s958" xml:space="preserve"/>
          </p>
          <figure number="36">
            <image file="037-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/037-02"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s959" xml:space="preserve">_IN_ſphæra ex _A,_ polo circuli _B C,_ recta du-
              <lb/>
            cta ſit vtcumque _A D,_ ad eius circunferentiã,
              <lb/>
            quæ minor erit diametro ſphæræ, atque adeo dia
              <lb/>
            metro circuli maximi in ſphæra, cum diameter
              <lb/>
            ſphæræ ſit omnium rectarum in ſphæra ductarũ
              <lb/>
            maxima Ducatur iam ex eodem polo A. </s>
            <s xml:id="echoid-s960" xml:space="preserve">ad ſu-
              <lb/>
            perficiem ſphæræ recta _A E,_ quæ ipſi _A D,_ æqua-
              <lb/>
            lis ſit. </s>
            <s xml:id="echoid-s961" xml:space="preserve">Dico rectam A E, caderein circunferen-
              <lb/>
            tiam circuli _B C._ </s>
            <s xml:id="echoid-s962" xml:space="preserve">Si enim ſi eri poteſt, non cadat
              <lb/>
            in eius circunferentiam. </s>
            <s xml:id="echoid-s963" xml:space="preserve">Et per rectam _A E,_ & </s>
            <s xml:id="echoid-s964" xml:space="preserve">
              <lb/>
            centrum ſphæræ ducatur planũ faciens in ſphæ-
              <lb/>
              <note position="right" xlink:label="note-037-11" xlink:href="note-037-11a" xml:space="preserve">1. huius.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum